Chapter 18: Mobile Robots

In April 2011, a few weeks after an earthquake and tsunami wrecked the Fukushima Daiichi power plant in Japan, engineers faced a problem with no human solution. They needed to know what the air inside the damaged reactor buildings was like — how hot, how radioactive, how badly the structure had broken. Sending a person in to look was not an option.

So they sent two machines instead. The robots ran on tracks rather than wheels, because the floors inside were littered with rubble and slick with water. They were about the size of a suitcase, and they carried what a person would have carried: a camera, a thermometer and a radiation meter. Working as a pair, one machine held a heavy door open while the other drove through it, and the readings came back to operators standing safely outside.

Look closely at what that mission needed. A body that could cross a broken floor. A power source that would last the whole trip. Sensors that could report on a place nobody could see. A link back to a human who was still making the decisions. Every robot that moves — in a warehouse aisle, on a pavement, across a field — is built from those same four answers, arranged differently.

Photograph

Fig. 18.0-1 – a tracked mobile robot inside a damaged or industrial interior, seen from slightly above and to the side; the continuous track units, the camera and sensor mast, and a manipulator or gripper arm must all be clearly visible, along with the rubble-strewn floor it is crossing. Sourcing note: a disaster-response or inspection robot in a real working setting, not a studio product shot and not a rendering; images showing only the top surface of the robot, or cropped so the tracks are hidden, are unusable.

Curiosity Corner

Q1. Why did that mission use a robot on tracks, when almost every robot you see in a warehouse or a hospital runs on wheels? Q2. The Fukushima machines were driven by people standing outside, yet a warehouse robot finds its own way down an aisle. What exactly separates an autonomous robot from a semi-autonomous one? Q3. A robot has no eyes. How does it work out that there is a wall half a metre ahead of it — and why does that measurement sometimes come back wrong? Q4. The small board that makes a robot’s decisions cannot drive its motors directly. Why not, and what sits between them? Q5. Once a robot knows where it is and where it has to go, how does it choose a route — and why is the shortest route not always the one it takes?

This chapter will answer all five of these questions.

18.1 What a Mobile Robot Is

A robotic arm bolted to a factory floor is a formidable machine. It can place a component to within a fraction of a millimetre, repeat that placement for months, and lift loads no person could manage. But it can only work on what is brought to it. Somebody, or some conveyor, has to deliver the work into its reach.

For a great many jobs, that arrangement is impossible. Medicines have to travel from a hospital pharmacy to a ward on the third floor. Cartons have to move from a storage rack to a packing station forty metres away. A field of standing wheat cannot be brought to a machine; the machine has to go to the wheat.

For these tasks the robot itself must move. That single change — a robot that carries itself from place to place — alters almost every design decision that follows, and this chapter is about those decisions.

Carrying its own workspace

You met the idea of a workspace with manipulators: the set of points a fixed arm’s end-effector can actually reach, decided by its link lengths and its joint limits. A fixed arm’s workspace is a region pinned to one spot on the floor. It never grows, and everything the arm works on must be inside it.

18.1.1 Moving to the Task Instead of Waiting for It

A mobile robot solves the problem from the other end. Instead of enlarging its reach, it moves its whole body, taking its modest workspace with it wherever the work happens to be.

The compromise is worth stating plainly. A mobile robot usually reaches less far from its own body than a large industrial arm does, but it can be at any point in a building or a field, which the arm can never be.

Definition

A mobile robot is a robotic system that carries its own locomotion mechanism, so that it can move from one place to another through its environment while performing a task, instead of working from a fixed base.

The means of that movement is its locomotion system, and this chapter will look at the three ways it is usually built.

Definition

Locomotion is the means by which a robot moves its entire body from one place to another, achieved in mobile robots by wheels, by tracks or by legs.

Fig. 18.1-1 sets the two arrangements side by side: the fixed arm with its reach envelope drawn around it, and the mobile robot with a path drawn across the floor plan of the same building.

Diagram

Fig. 18.1-1 – two halves of one floor plan of a workshop. Left half: a manipulator on a fixed base with its reach envelope drawn as a shaded region around it, labelled “workspace fixed in space”; a conveyor drawn bringing work into that region. Right half: the same floor plan with a small wheeled robot and a dashed path curving from a storage rack, past a bench, to a packing table, labelled “workspace travels with the robot”; three obstacle blocks placed on the floor that the path steers around

What mobility costs

Mobility is not free, and every price it charges shows up later in this chapter as a design problem.

The robot must carry its own energy. A fixed arm can be fed from a wall supply indefinitely, but a machine that drives away from the wall runs on a battery, and the mission ends when the battery does.

The robot no longer knows where it is. An arm’s base is bolted down, so the position of every joint is known by construction. A mobile robot’s base moves, its wheels slip, and it must work out its own position from sensor readings.

The ground cannot be assumed. Floors are wet, sloped, cluttered, cracked or covered in cable. A machine that moves has to cope with whatever surface it meets, or detect that it cannot and stop.

Finally, the robot shares its space with people. A caged industrial arm is kept away from human beings by a fence; a robot that travels down a corridor is standing next to them all day, which makes sensing and safe stopping central rather than optional.

Compare Table

Both columns of that table are typical figures rather than universal ones, and payload especially depends entirely on the model chosen.

18.1.2 The Subsystems of a Mobile Robot

Almost every mobile robot, from a school-built line follower to a warehouse machine carrying a loaded rack, is assembled from the same five subsystems. Learning to see them separately is what lets you design one, and what lets you diagnose one when it misbehaves.

The block diagram in Fig. 18.1-2 shows how they are joined, and it is worth noticing that two different things travel along those arrows: signals, which are small and carry information, and power, which is large and does work.

Diagram

Fig. 18.1-2 – block diagram of a mobile robot. Blocks: Environment (outside a dashed robot boundary), Sensors, Control Unit, Motor Driver, Motors, Wheels or Tracks or Legs, Power Source. Thin arrows labelled “signal”: Environment to Sensors, Sensors to Control Unit, Control Unit to Motor Driver. Thick arrows labelled “power”: Power Source to Control Unit, to Sensors and to Motor Driver, then Motor Driver to Motors, Motors to Wheels. One thin arrow from Wheels back out to Environment labelled “robot moves”, closing the loop back to Sensors

The structure and locomotion system

The structure carries everything else and holds it in alignment, and the locomotion system converts the motor’s rotation into travel across the ground. Together they decide what terrain the robot can cross, how fast it can go, and how tightly it can turn.

The actuators

The motors are the muscles. In a mobile robot they do two distinct jobs: driving the machine along, and moving whatever the machine carries, such as a lifting platform, a gripper or a sensor mast. Their torque and speed decide whether the robot can climb a ramp with a load on it.

The sensors

Sensors are the robot’s only contact with the world. They report two different kinds of fact: what is outside the robot, such as an obstacle two metres ahead, and what the robot itself is doing, such as how fast a wheel is turning or how far the body has tilted.

The control unit

The control unit is the decision-maker, usually a microcontroller or a single-board computer. It reads the sensors, applies the program, and issues the commands that make the robot move. It holds the robot’s behaviour, and changing that behaviour means changing the program, not the hardware.

The power source

The power source supplies every one of the others. A rechargeable battery pack, commonly lithium-ion, is the usual choice because it stores a large amount of energy for its mass. It must supply not only the steady running current but also the much larger surge a motor draws at the instant it starts turning.

Exam Corner

Q. Why is the power source treated as a subsystem in its own right, and not simply as one more part inside the drive system?

A. Because it sets limits on everything else. Its capacity fixes how long a mission can last, its mass has to be carried by the drive, and its ability to supply a sudden surge decides whether the control unit keeps running when the motors start. A robot that is under-powered does not fail politely in one place; it browns out, resets and behaves unpredictably.

Where a human operator is involved, a sixth block joins them: a communication link carrying commands out to the robot and readings back to the operator. Section 18.3 looks at when that link is essential and when the robot can manage without it.

18.1.3 The Sense–Plan–Act Loop on the Move

Those five subsystems are not simply connected in a row. They form a cycle that repeats many times a second for as long as the robot is switched on, and that cycle is the single most useful idea in this chapter.

The robot senses, decides what to do about what it sensed, acts on that decision, and then senses again — including the results of its own action. Fig. 18.1-3 draws the cycle with the arrow that closes it.

Diagram

Fig. 18.1-3 – flow: sensors read the surroundings → readings converted to values in the control unit → control unit compares them with the goal and decides → command sent to the motor driver → motors turn the wheels → the robot’s position changes, which changes what the sensors will read, with the last arrow returning to the first block to close the loop

Theory Snapshot

The sense–plan–act loop Statement: A mobile robot operates by repeating a three-stage cycle — sense the current state of the environment and of itself, plan the next action from those readings and the goal, and act on the plan through its actuators — with each pass through the cycle changing what the next pass will sense. In words: Look, decide, move, then look again to see what your move did. Why it holds: The robot’s own motion alters its situation, so a single decision taken once is worthless. Only by re-sensing after acting can it correct for slip, drift, and anything that has changed in the meantime. Used for: Structuring the program of almost every mobile robot, and for locating a fault — a robot behaving wrongly is failing at the sense stage, the plan stage or the act stage, and the three are tested differently. Watch out: The loop is not free. Every stage takes time, and while it runs the robot keeps moving on its last decision.

That last point deserves a number rather than a sentence. Between one pass of the loop and the next, the robot is travelling blind, acting on information that is already slightly out of date.

Definition

Latency is the delay between something changing in the world and the robot’s response to that change reaching its actuators.

Example 18.1

How far a robot travels between two decisions

Given: A warehouse robot travels at a steady speed \(v = 1.2 \text{ m/s}\). Its control unit completes the sense–plan–act loop \(20\) times every second.

Find: The distance the robot covers during one pass of the loop.

Method: The time for one pass is the reciprocal of the loop rate, \(T = 1/f\). At a steady speed the distance is \(d = v \times T\), because speed multiplied by time gives distance travelled.

\[T = \frac{1}{f} = \frac{1}{20 \text{ s}^{-1}} = 0.05 \text{ s}\]

\[d = v \times T = 1.2 \text{ m/s} \times 0.05 \text{ s} = 0.06 \text{ m} = 60 \text{ mm}\]

The robot moves \(60 \text{ mm}\) between one decision and the next.

Check: Is the magnitude sensible? A speed of \(1.2 \text{ m/s}\) is about a brisk walking pace, and one-twentieth of a second is a very short time, so a distance of a few centimetres is what you should expect. A result of several metres would have meant an arithmetic error.

Sixty millimetres does not sound alarming, but it is the robot’s blind travel, and it is only the beginning of the story. The robot cannot stop instantly either, so the distance at which it must begin braking is this blind travel plus its braking distance. Run the same loop at \(2 \text{ Hz}\) instead of \(20 \text{ Hz}\) and the blind travel becomes \(600 \text{ mm}\), which is enough to reach a person’s ankles before the machine has even decided to slow down.

This is why loop timing is a safety matter in mobile robotics and not merely a question of programming neatness. A slow loop and a fast robot are a dangerous pair.

The rest of the chapter follows the loop around. Section 18.2 deals with the act stage — the body that carries the robot across the ground. Section 18.3 asks who does the planning, the robot or a person. Section 18.4 takes the sense stage, section 18.5 the machine that has to be built to hold all of it together, and section 18.6 the planning of a whole route rather than a single step.

18.2 Types of Mobile Robots

Everything a mobile robot does begins with the small patch of ground it is touching. Whatever the machine is meant to achieve, it can only push against the surface underneath it, and the way it makes that contact decides where it can go.

Mobile robots are therefore classified first by their locomotion: wheels, tracks or legs. The three are not three fashions of doing the same thing. They are three different bargains between simplicity, efficiency and the roughness of the ground.

18.2.1 Wheeled Mobile Robots

Wheeled mobile robots are by far the most common type, and the reason is worth understanding rather than memorising. A wheel converts the motor’s rotation directly into travel with almost nothing in between — no linkage, no gait, no sequence of steps. Fewer moving parts means simpler construction, lower cost and less to go wrong.

They are also the most energy-efficient of the three. A rolling wheel touches the ground over a very small patch, and it lays that patch down and picks it up again without dragging. Very little of the motor’s energy is lost to friction, so more of the battery’s charge goes into actual travel.

How a wheeled robot steers

The commonest arrangement in a small robot is differential drive: two wheels on a common axis, each with its own motor, and one or two passive castor wheels that carry the rest of the weight without being driven.

Steering then needs no steering mechanism at all. Drive both wheels at the same speed and the robot runs straight. Drive one faster than the other and it curves towards the slower side. Drive them at equal speeds in opposite directions and it spins about the midpoint between them, turning within its own footprint. Fig. 18.2-1 shows the layout and the three cases.

Diagram

Fig. 18.2-1 – top view of a differential-drive robot chassis: two driven wheels on a common axis at the rear, each labelled with its own motor, and one castor wheel at the front labelled “passive, carries load only”. Beside it, three small versions of the same chassis labelled “straight”, “gentle left turn” and “turn on the spot”, each with an arrow on every driven wheel whose length shows its speed and whose direction shows its rotation, plus a dashed path curve for the first two

Larger wheeled robots use four-wheel drive for extra grip, or omni-wheel arrangements where the wheel can also roll sideways, allowing the robot to move sideways without turning first. Those wheel types — standard, castor, Mecanum and Omni — were covered when you studied the mechanical subsystem, and the choice made there directly limits the paths a robot can follow here.

System Profile

Wheeled mobile robots Working principle: A motor turns a wheel, and friction between the wheel and the ground converts that rotation into forward travel. Direction is controlled by varying the speeds of separate driven wheels rather than by turning a steering linkage. Components: Chassis, driven wheels, drive motors and gearboxes, passive castor or support wheels, motor driver, control unit, battery pack. Advantages: Simple to build and maintain because few parts move; energy-efficient because rolling contact wastes little to friction; capable of high speed and precise, repeatable movement on a good surface. Limitations: Needs a reasonably smooth and firm surface; a rigid wheel cannot climb a step approaching its own radius; wheels lose grip on loose sand, mud, gravel or wet tiles, and a spinning wheel makes the robot’s position estimate wrong as well as leaving it stuck. Where it is used: Warehouse and factory floors, hospital corridors, laboratories, offices, and school robotics benches — smooth, structured, indoor environments where speed and precise navigation matter.

That limitation about step height is a useful piece of workshop judgement. A robot on 65 mm wheels has a wheel radius of about 33 mm, so a doorway threshold or a cable duct 30 mm high is already close to the limit, and it may stop the machine dead however much torque the motor has.

Common Error

Blaming the motors when the robot will not run straight What students do: They send the same speed command to both drive motors and expect the robot to travel in a straight line. When it curves, they assume one motor is faulty and replace it. What happens: The new motor behaves the same way. Two motors of the same model differ slightly in their internal friction and gearing, one wheel may carry more weight than the other, and a castor that has swivelled to a new angle drags to one side. Equal commands do not produce equal wheel speeds. The fix: Do not correct the fault in the hardware. Measure what the wheels are actually doing and correct the commands, either by trimming one motor’s value against measurements taken over a fixed distance, or by adding wheel encoders and closing the loop as section 18.5.5 describes.

18.2.2 Tracked Mobile Robots

A tracked mobile robot replaces its wheels with a continuous belt, or track, wrapped around a driven sprocket at one end and an idler wheel at the other, with smaller rollers pressing the lower run of the belt against the ground. The motor turns the sprocket, the belt is laid down in front and picked up behind, and the machine crawls forward along it. Fig. 18.2-2 shows the arrangement from the side.

Diagram

Fig. 18.2-2 – side view of one track unit: a continuous track drawn as a loop around a large drive sprocket at the rear (labelled, with a curved arrow showing rotation) and an idler wheel at the front, with three small support rollers pressing the lower run down. The straight lower run of the belt marked with a dimension line labelled “contact length”, and the ground drawn as an uneven surface beneath it

The whole lower run of the belt touches the ground, so the robot’s weight is spread over a long strip instead of four small patches. This is the property that decides almost everything else about a tracked machine, and it is called ground pressure.

Definition

Ground pressure is the force a machine presses onto the surface divided by the total area over which it makes contact, and it decides how far the machine sinks into a soft surface.

Example 18.2

Ground pressure of a tracked and a wheeled robot

Given: An inspection robot of mass \(m = 20 \text{ kg}\). Built on wheels, it makes four contact patches of \(2 \text{ cm}^2\) each. Built on tracks, it makes two contact strips each \(30 \text{ cm}\) long and \(5 \text{ cm}\) wide. Take \(g = 9.8 \text{ m/s}^2\).

Find: The ground pressure in each case.

Method: Weight is \(W = mg\), and pressure is force divided by area, \(p = W/A\). The areas must be converted to square metres before dividing, because a pressure in pascals is a force in newtons per square metre.

\[W = mg = 20 \text{ kg} \times 9.8 \text{ m/s}^2 = 196 \text{ N}\]

Wheeled version:

\[A = 4 \times 2 \text{ cm}^2 = 8 \text{ cm}^2 = 8 \times 10^{-4} \text{ m}^2\]

\[p = \frac{196 \text{ N}}{8 \times 10^{-4} \text{ m}^2} = 2.45 \times 10^{5} \text{ Pa} = 245 \text{ kPa}\]

Tracked version:

\[A = 2 \times (0.30 \text{ m} \times 0.05 \text{ m}) = 0.030 \text{ m}^2\]

\[p = \frac{196 \text{ N}}{0.030 \text{ m}^2} = 6.53 \times 10^{3} \text{ Pa} \approx 6.5 \text{ kPa}\]

About \(245 \text{ kPa}\) on wheels and about \(6.5 \text{ kPa}\) on tracks — the same robot presses roughly \(38\) times harder on the ground through its wheels.

Check: Are these magnitudes sensible? A bicycle tyre is inflated to a few hundred kilopascals, so a small hard wheel pressing at \(245 \text{ kPa}\) is believable. An adult standing on two feet presses at roughly \(15 \text{ kPa}\), so the tracked robot presses less than a person walking — which is exactly why it stays on top of mud that a person would sink into.

Spreading the load does two things at once. It stops the machine sinking into soft ground, and it puts far more rubber in contact with the surface, which increases traction — the grip available before the belt slips. A tracked robot can therefore climb, drag and push where a wheeled one would spin helplessly.

The long belt also bridges gaps and small obstacles. Where a rigid wheel meets a step and has to climb it, a track lays itself over the edge and pulls the machine up.

What tracks cost

Tracks turn by skid steering: the two belts are driven at different speeds, and the machine slews round by dragging its belts sideways across the ground. That scrubbing wastes energy, wears the belt, and can scar a smooth floor, so a tracked robot is markedly less efficient than a wheeled one and drains its battery faster.

There is more to go wrong as well. Sprockets, idlers, rollers and belt tension all need maintenance, and a belt thrown off its sprocket in the field immobilises the robot completely.

System Profile

Tracked mobile robots Working principle: A driven sprocket circulates a continuous belt around a set of idlers and rollers, so that the machine rolls along a track it lays down in front of itself. Weight is carried over the whole length of the belt in contact with the ground. Components: Chassis, continuous tracks, drive sprockets, idler wheels, support rollers, drive motors and gearboxes, motor driver, control unit, battery pack. Advantages: Low ground pressure, so the machine does not sink into mud, sand or loose debris; high traction on slippery and loose surfaces; able to cross rubble, small steps and gaps; stable on slopes because of the long contact length. Limitations: Poorer energy efficiency, because skid steering drags the belts sideways; heavier and mechanically more complex; slower than a wheeled robot of the same power; damages polished floors; a shed or broken track stops the mission. Where it is used: Search-and-rescue work in collapsed structures, inspection inside damaged plant, disaster zones, agricultural fields, and any outdoor terrain that is soft, loose or uneven.

18.2.3 Legged Mobile Robots

Wheels and tracks both need a continuous path along the ground. A legged mobile robot does not. It moves by articulated legs that imitate biological locomotion, placing each foot on a chosen spot and lifting it clear of everything in between.

That is the whole point of legs, and it is easy to miss. A staircase, a heap of rubble or a stretch of rocky ground offers no continuous surface at all, but it usually offers plenty of separate places to put a foot. Fig. 18.2-3 shows a four-legged robot on such ground.

Photograph

Fig. 18.2-3 – a four-legged (quadruped) robot walking on rough outdoor ground or a staircase, photographed from the side and low down so that all four legs and the joints in each leg are clearly visible, with at least one foot lifted clear of the surface. Sourcing note: an inspection or research quadruped in a real setting; studio shots on flat floors, renderings, and toy or entertainment robots are unusable because the point of the image is the leg geometry against irregular terrain.

Each leg carries two or three powered joints, which is where the cost lies. A differential-drive robot needs two motors in total. A four-legged robot with three joints per leg needs twelve, each with its own driver, its own position sensing and its own share of the control program.

Staying upright

A wheeled robot is stable simply by standing there. A legged robot has to be kept stable, and the idea that governs this is the support polygon: the shape drawn on the ground by joining the feet that are currently touching it, as in Fig. 18.2-4.

Diagram

Fig. 18.2-4 – top view of a four-legged robot. Three feet marked as filled circles on the ground and one foot marked as a hollow circle labelled “lifted”; a shaded triangle joining the three filled circles labelled “support polygon”; a cross marked inside the triangle labelled “centre of mass projected onto the ground”; a second smaller sketch beside it showing the cross falling outside the triangle, labelled “robot topples”

So long as the robot’s centre of mass falls inside that polygon, the machine stands. Lift a foot and the polygon shrinks, so the robot must shift its body before it lifts, and it must do this afresh for every step. Walking, for a robot, is a continuous balancing calculation.

System Profile

Legged mobile robots Working principle: Powered joints swing each leg through the air and place its foot at a chosen point, then push against that point to move the body. The robot sequences its legs so that the feet still on the ground keep its centre of mass inside the support polygon. Components: Body frame, articulated legs with two or three powered joints each, joint actuators and position sensors, an inertial sensor for body tilt, control unit, battery pack. Advantages: Can cross terrain that offers no continuous path, including stairs, rubble and gaps; can step over an obstacle rather than climb it; can change its footprint to squeeze past or stabilise on a slope. Limitations: Mechanically complex, with many actuators to build, power and control; power-hungry, because the legs must hold the body’s weight up actively rather than resting on a wheel; slower and more expensive than the alternatives; a single failed joint can immobilise the whole machine. Where it is used: Inspection of plant and construction sites, exploration of rough ground, and rescue work in collapsed structures where the floor no longer exists as a floor.

18.2.4 Matching the Locomotion Type to the Terrain

None of the three types is better than the others. Each is the correct answer to a different question, and the question is always about the ground.

Compare Table

The reasoning runs in one direction only. Start with the worst surface the robot will actually meet, not the average one, and then choose the simplest locomotion that can cross it.

Simplest matters because every step up in complexity is paid for twice: once when the machine is built, and again every hour it runs, in battery capacity and in maintenance. A tracked robot patrolling a warehouse aisle is not a safer choice than a wheeled one; it is a slower, thirstier and more expensive one solving a problem the warehouse does not have.

Curiosity Corner

Q1. Why did that mission use a robot on tracks, when almost every robot you see in a warehouse or a hospital runs on wheels?

A. Because the two machines meet completely different ground. A warehouse floor is smooth, firm and swept, so wheels are the right answer there — they are simple, fast and use the least battery charge for the distance covered. Inside a damaged building the floor is broken, wet and covered in fallen debris, and a rigid wheel cannot climb an obstacle approaching its own radius. Tracks spread the machine’s weight along a long belt, giving low ground pressure and far more grip, and they lay themselves over steps and gaps instead of having to climb them. The tracked robot pays for this in efficiency and wear, which is exactly why the warehouse does not use one.

Exam Corner

Q. If tracks handle rough ground and wheels are efficient, why not fit both and switch between them?

A. Machines of that kind do exist, and some rescue robots carry small tracked flippers on a wheeled body. But every hybrid carries the mass, cost and failure points of both systems while being the best at neither. It is worth doing only where the mission genuinely contains two very different surfaces, such as a long smooth approach followed by a short climb over rubble.

Try Yourself

Take the school’s wheeled robot chassis and drive it slowly at a strip of wood laid flat on the floor. Repeat with thicker strips until the robot stalls against the edge instead of climbing it. Measure the height at which it fails and compare it with the radius of the wheel — for a 65 mm wheel, the radius is about 33 mm. Record the two figures and state whether your robot met the limit early, late or about where you predicted.

Safety Note

Run the robot on the floor, never on a bench top from which it can drive off the edge. Keep fingers, hair and loose clothing clear of the wheels and the gap between wheel and chassis while the motors are live, and disconnect the battery before you change any wiring on the chassis.

18.3 Autonomous and Semi-Autonomous Mobile Robots

Section 18.2 settled what carries the robot across the ground. This section settles a different question, and often a harder one: who decides where it goes.

Two machines can be mechanically identical — same chassis, same motors, same sensors — and still be completely different robots, because in one of them a person is inside the decision loop and in the other one nobody is.

18.3.1 What Autonomy Means

The word autonomous is used loosely in everyday speech, where it tends to mean nothing more than “works by itself”. In engineering it has a sharper sense, and the sharpness matters.

An automatic machine repeats a fixed sequence. A domestic washing machine fills, agitates, drains and spins in the same order every time, and it will run that sequence whether the drum is full or empty. Nothing in its surroundings changes what it does next.

An autonomous machine chooses. It is given a goal rather than a sequence, it reads its surroundings, and it selects the action that gets it closer to the goal in the situation it actually finds. Two runs of the same task can produce two different sets of actions, because the corridor was blocked on Tuesday and clear on Wednesday.

Definition

Autonomy is a robot’s ability to decide its own actions from sensor readings in order to achieve a given goal, without a human being making those decisions for it.

Where the human sits in the loop

The clearest way to think about autonomy is to go back to the sense–plan–act loop of section 18.1 and ask which stage the human occupies. Fig. 18.3-1 draws the two extremes.

Diagram

Fig. 18.3-1 – two versions of the sense–plan–act loop side by side inside dashed robot boundaries. Left, labelled “teleoperation”: arrow from Sensors leaves the boundary to a block labelled Human Operator outside it, and the operator’s command arrow returns across the boundary to Actuators; the Plan block inside the robot is drawn empty. Right, labelled “autonomous”: Sensors, Plan and Actuators all inside the boundary with the loop closed internally, and a single thin arrow entering from outside labelled “goal only”

In teleoperation, the sensing is done by the robot and the acting is done by the robot, but every decision is taken by a person watching a screen somewhere else. The machine supplies muscles and eyes; the operator supplies judgement.

Definition

Teleoperation is the control of a robot by a human operator at a distance, in which the operator receives the robot’s sensor data and issues the movement commands directly.

At the other extreme the whole loop closes inside the robot. A person may set the goal — collect the rack from bay fourteen — but nobody chooses the route, nobody decides to swerve round the trolley in the aisle, and nobody is watching.

Between these two lie all the practical machines, which is why autonomy is best pictured as a scale rather than a switch, as in Fig. 18.3-2.

Diagram

Fig. 18.3-2 – a horizontal scale drawn as an arrow, labelled “human decides everything” at the left end and “robot decides everything” at the right end. Four labelled markers placed along it in order: “direct teleoperation — operator drives every movement”, “operator-assisted — robot avoids collisions, operator chooses the route”, “supervised autonomy — robot plans and drives, operator approves critical steps”, “full autonomy — operator sets the goal only”

18.3.2 Autonomous Mobile Robots

An autonomous mobile robot carries out its whole task without a person taking its decisions. It works out where it is, chooses a route to its goal, drives that route, and deals with whatever appears in front of it on the way.

Three things have to be true before that is possible.

The robot must be able to perceive enough. Autonomy rests entirely on sensing, and usually on several sensors at once, because no single sensor sees everything. Section 18.4 takes this up in detail.

The robot must know what it is trying to achieve. A goal — a destination, a row to be inspected, an area to be covered — has to be expressed in terms the program can act on.

The environment must be predictable enough to plan in. Warehouse aisles, hospital corridors and laboratory floors are structured: the layout is known, the surface is uniform, and the surprises are of a limited and expected kind, such as a person stepping out or a carton left on the floor.

Because nobody is watching, an autonomous robot leans heavily on its sensors, and it must combine readings from more than one of them to be confident about anything. A single ultrasonic reading that suddenly says “obstacle at 20 cm” may be an echo off a smooth angled surface rather than a real object.

Where autonomy is worth having

Autonomy earns its cost in three situations, and it is worth naming them because they explain every real deployment you will meet.

Where the work is repetitive and continuous, an autonomous machine can run all shift without occupying a person’s attention — the case for warehouse robots and self-navigating delivery machines.

Where the number of machines is large, autonomy is the only option, because fifty robots would otherwise need fifty operators.

Where a human decision could not arrive in time, or at all, the robot must decide for itself. An exploration robot far from its operators, or one working where the radio link is unreliable, has no alternative.

The honest limitation is that an autonomous robot is only as good as the situations its designers anticipated. Faced with something genuinely outside its programming — a flooded aisle, a sensor blinded by sunlight, a shape it has never been taught — it will do something, and what it does may be wrong. Testing an autonomous robot is therefore a far larger job than building one.

18.3.3 Semi-Autonomous Mobile Robots

A semi-autonomous mobile robot divides the work. The robot handles the fast, continuous, low-level control, and a human operator handles the decisions that need judgement.

This division is not a compromise so much as a sensible allocation. The robot is very good at things that must happen twenty times a second: holding a straight course, stopping before it hits a wall, keeping its body level. The person is very good at things a program handles badly: recognising that the shape ahead is a survivor rather than a beam, or deciding that this doorway is the one worth entering.

So the operator says “go through that opening and look left”, and the robot works out the motor commands, corrects its own drift and refuses to drive into the frame on the way. Neither party could do the task alone.

The link is the weak point

Everything semi-autonomous depends on a communication link, and the link is where these systems fail. Two properties of it decide the design.

The first is bandwidth. Video from a camera is a large amount of data, and if the link cannot carry it, the operator is driving on a stale or stuttering picture.

The second is delay. A command takes time to reach the robot and a picture takes time to come back, and the operator’s own reaction time is added on top of both.

Example 18.3

Reaction distance for a teleoperated robot

Given: A tracked inspection robot is driven at \(v = 0.8 \text{ m/s}\). The round trip for a picture to reach the operator and a command to return takes \(t_\text{link} = 0.25 \text{ s}\). The operator’s own reaction time is \(t_\text{human} = 0.50 \text{ s}\).

Find: How far the robot travels between an obstacle appearing in front of it and the stop command taking effect.

Method: The two delays act one after the other, so the total delay is their sum. At a steady speed the distance covered is \(d = v \times t_\text{total}\).

\[t_\text{total} = t_\text{link} + t_\text{human} = 0.25 \text{ s} + 0.50 \text{ s} = 0.75 \text{ s}\]

\[d = v \times t_\text{total} = 0.8 \text{ m/s} \times 0.75 \text{ s} = 0.60 \text{ m}\]

The robot travels \(0.60 \text{ m}\) before the operator’s stop command has any effect.

Check: Is that sensible? Walking at about \(0.8 \text{ m/s}\) is a slow, careful pace, and three-quarters of a second at that pace is roughly one stride — so a little over half a metre is the right order of magnitude. Notice also that the human reaction time, not the radio link, is the larger part of it.

Compare that \(0.60 \text{ m}\) with the \(60 \text{ mm}\) a robot travels between its own decisions, calculated in section 18.1. The robot’s reflexes are an order of magnitude quicker than the human’s, which is precisely why collision avoidance is given to the machine even when the route is left to the operator.

Common Error

Calling a remote-controlled robot semi-autonomous What students do: They build a robot driven entirely by a joystick or a phone over a Bluetooth link, and describe it as semi-autonomous because a computer is involved. What happens: The description does not survive a single question. If the operator stops sending commands, the machine either coasts into the wall or stops dead; it takes no decision of its own at any point. The fix: Ask which stage of the sense–plan–act loop the robot performs. A machine that senses and acts but never plans is teleoperated. It becomes semi-autonomous only when it takes some decisions itself — holding a heading, stopping when its own sensor sees an obstacle, returning to base when the battery falls low.

18.3.4 Choosing the Degree of Autonomy

The two arrangements are compared feature by feature in Table 18.3.

Compare Table

Table 18.3 – Autonomous vs semi-autonomous mobile robots | Feature | Autonomous mobile robot | Semi-autonomous mobile robot | |—|—|—| | Level of control | The robot holds full control, from goal to motor command | Control is shared; the robot handles low-level motion, a person handles chosen decisions | | Decision-making | Route, obstacle avoidance and task steps are all decided on board | Routine decisions are automatic; the important ones are taken or confirmed by the operator | | Dependence on sensors | Total; several sensors are combined, because a wrong reading has nobody to correct it | High, but a human interpreting a camera view can cover what the sensors miss | | Need for a communication link | Only to receive a goal and report progress; the robot survives a lost link | Continuous and essential; losing the link ends the task | | Suitable environment | Structured or semi-structured, and predictable enough to plan in | Unfamiliar, hazardous or changing places where judgement is needed | | Behaviour when something unexpected happens | Acts on its programming, which may not cover the case | The operator sees it and decides, including deciding to withdraw | | Typical use | Warehouse transport robots, self-navigating delivery robots, autonomous exploration robots | Remote-controlled rescue robots, inspection robots inside damaged plant, assisted-navigation systems |

Choosing between them comes down to four questions, asked in this order.

How predictable is the environment? A known building with a known layout can be planned in; a collapsed structure cannot.

What does a wrong decision cost? Where a mistake means a scuffed carton, let the robot decide. Where it means injury or the loss of an expensive machine in a place nobody can reach, keep a person in the loop.

Is a reliable link available? Radio does not pass easily through thick reinforced concrete, through earth, or through water, and a semi-autonomous design that assumes a link it will not get is a design that fails on the day.

Is a person available for the whole task? One operator per robot is affordable for a single rescue machine and impossible for a fleet.

Curiosity Corner

Q2. The Fukushima machines were driven by people standing outside, yet a warehouse robot finds its own way down an aisle. What exactly separates an autonomous robot from a semi-autonomous one?

A. Not the hardware — the location of the planning stage. Both machines sense and both act; the difference is who decides. In the damaged building the environment was unknown, the readings needed human interpretation, and a wrong turn could have lost the machine for good, so the decisions stayed with the operators and the robot supplied mobility and instruments. In the warehouse the layout is known, the surprises are of a familiar kind, and a fleet of machines could never have an operator each, so the whole loop is closed on board and a person supplies only the goal. The environment’s predictability and the cost of a wrong decision choose the degree of autonomy; the chassis has nothing to do with it.

Exam Corner

Q. If a semi-autonomous robot loses its communication link mid-task, what should it be programmed to do?

A. Not to carry on, and not simply to freeze wherever it happens to be. The usual design is to stop the drive at once, hold position, and after a set waiting period attempt a pre-planned recovery — most often retracing the path back towards the point where the link last worked. Stopping is safe but abandons the machine; retracing is the only action the robot can take with confidence, because that ground has already been crossed once.

18.4 Sensing and Perception

18.4.1 Why a Moving Robot Must Sense Continuously

A manipulator bolted to the floor can be told about its world once. The conveyor is here, the fixture is there, the tray arrives at this height, and none of it moves. Its program can carry those facts as constants.

A mobile robot has no such luxury. Its own position changes with every turn of a wheel, the corridor it planned to use may be blocked, and the floor it is about to cross may have been mopped. Everything it needs to know it must find out, over and over, while moving.

That is why sensing occupies a whole section of this chapter. For a mobile robot, perception is not an accessory. It is the only connection between the machine and reality.

Two kinds of question

The sensors on a mobile robot answer two quite different questions, and it helps to keep them apart from the start.

Definition

Exteroceptive sensing is the measurement of things outside the robot, such as the distance to a wall, the presence of an obstacle, or the position of a line on the floor.

Definition

Proprioceptive sensing is the measurement of the robot’s own state, such as how far a wheel has turned, how fast the body is rotating, or how far it is tilted from level.

You have both yourself. Your eyes are exteroceptive; the sense that tells you, with your eyes shut, that your arm is raised is proprioceptive. A robot needs both for the same reason you do: knowing the world is useless if you do not know what you are doing in it.

Fig. 18.4-1 shows where the two kinds sit on a small wheeled robot.

Diagram

Fig. 18.4-1 – side and top view of a small wheeled robot with its sensors labelled and grouped. Marked exteroceptive: an ultrasonic sensor facing forward with its beam drawn as a widening cone, two IR sensors pointing down at the floor near the front edge, a camera on a short mast, and a bump switch on the front bumper. Marked proprioceptive: an encoder disc drawn on one drive wheel, and an inertial sensor drawn as a small block at the centre of the chassis. A key beside the drawing distinguishing the two groups

One warning before the details. Every sensor in this section has conditions under which it reports something confidently wrong. It does not fail by going silent — it fails by lying. That single fact drives the rest of the section, and it is why subsection 18.4.5 exists at all.

18.4.2 Sensing the Surroundings

The ultrasonic sensor

An ultrasonic sensor emits a short burst of sound at a frequency too high to hear, then measures how long the echo takes to come back. Since sound travels at a known speed, the time gives the distance. It is the same trick a bat uses.

The one subtlety is that the sound makes the journey twice — out to the object and back again — so the measured time must be halved before the distance is worked out. Fig. 18.4-2 shows the path and the timing.

Diagram

Fig. 18.4-2 – two panels. Left panel: an ultrasonic sensor facing a flat wall square on, with an arrow labelled “out” going to the wall and a second arrow labelled “back” returning, the gap between sensor and wall marked d, and a small timing sketch below showing the transmitted burst, a gap labelled t, and the received echo. Right panel: the same sensor facing a wall tilted at about 45 degrees, with the outgoing arrow striking the surface and the reflected arrow going off to one side, past the sensor, labelled “echo never returns”

Example 18.4

Distance from an ultrasonic echo time

Given: An ultrasonic sensor receives its echo \(t = 3.2 \text{ ms}\) after the burst is transmitted. The speed of sound in air is \(v = 343 \text{ m/s}\) at \(20\ ^\circ\text{C}\).

Find: The distance to the object.

Method: The pulse travels to the object and back, so the total path is \(2d\). From \(2d = v \times t\), the distance is \(d = (v \times t)/2\). The time must be converted to seconds before it is multiplied by a speed in metres per second.

\[t = 3.2 \text{ ms} = 3.2 \times 10^{-3} \text{ s}\]

\[d = \frac{v \times t}{2} = \frac{343 \text{ m/s} \times 3.2 \times 10^{-3} \text{ s}}{2} = \frac{1.0976 \text{ m}}{2} = 0.5488 \text{ m}\]

The object is about \(0.55 \text{ m}\) away.

Check: Is the magnitude sensible? A common ultrasonic module works from roughly \(2 \text{ cm}\) to about \(4 \text{ m}\), so half a metre sits comfortably inside its range. Forgetting to halve would have given \(1.10 \text{ m}\) — a wrong answer that still looks plausible, which is exactly why this step is worth writing out every time.

That calculation also shows where the sensor’s accuracy comes from. The speed of sound is not a fixed number: it rises by roughly \(0.6 \text{ m/s}\) for every degree the air warms. A robot calibrated in a cool laboratory and driven into a hot yard will read about two per cent short, which is a centimetre in every half metre.

The larger problems are geometric. Sound spreads out in a cone rather than a narrow beam, so the sensor reports the nearest object anywhere in that cone, not the object directly ahead. A chair leg can slip between successive cones and be missed entirely. Cloth, foam and thick dust absorb the pulse and return almost nothing. And a hard surface met at a slant reflects the pulse away like a mirror, so the sensor hears no echo and reports a clear path where there is a wall.

Curiosity Corner

Q3. A robot has no eyes. How does it work out that there is a wall half a metre ahead of it — and why does that measurement sometimes come back wrong?

A. It times something. An ultrasonic sensor sends a burst of high-frequency sound and measures how long the echo takes to return; since sound travels at about \(343 \text{ m/s}\), an echo after \(3.2 \text{ ms}\) means a round trip of just over a metre, so the wall is about half a metre away. A LIDAR does the same with a laser pulse instead of sound. The measurement goes wrong when the signal does not come back the way the sensor assumes. A slanted hard surface reflects the pulse off to one side, so the sensor hears nothing and reports open space. A curtain or a heap of cloth absorbs it. A thin object slips past the beam and is never struck. And with sound, a change in air temperature quietly changes the speed the calculation depends on. The sensor is not broken in any of these cases — it is answering a slightly different question from the one you asked.

The infrared sensor

An infrared (IR) sensor shines infrared light and measures how much of it comes back. Close, pale, matt surfaces reflect strongly; distant or dark ones reflect weakly.

On a mobile robot this makes it the natural choice for two jobs. Pointed downwards at the floor, a pair of IR sensors distinguishes a dark line from a pale floor, which is the whole basis of line following. Pointed down at the very front edge, a single one detects the absence of floor — the edge of a step or a loading bay — and stops the robot before it drives off.

IR sensors are cheap, draw little power and respond quickly. Their weaknesses are that they work only over short distances, that bright sunlight or a strong lamp can swamp the reflected signal, and that they confuse colour with distance: a black object close by and a white object further away can produce the same reading.

LIDAR

Light detection and ranging (LIDAR) works on the same timing principle as the ultrasonic sensor, but with a laser pulse instead of sound, and usually with the beam swept rapidly around the robot. Each sweep returns hundreds of range readings at known angles, which together form an outline of the surroundings, as in Fig. 18.4-3.

Diagram

Fig. 18.4-3 – top view of a small room with a wheeled robot in the middle carrying a LIDAR unit. Thin rays drawn radiating outward at regular angular intervals, each ending in a dot where it meets a wall, a doorway edge or a table leg. The dots joined by a light dashed line to show the outline the robot has measured, with the open doorway appearing as a gap in that outline

This is a much richer measurement than a single distance. It tells the robot the shape of the space, not merely that something is ahead, and it is what lets a robot recognise a corridor, find a doorway, or match what it sees against a stored map.

LIDAR is fast, accurate over metres rather than centimetres, and unaffected by the darkness that defeats a camera. It is also the most expensive sensor on most robots, it can be confused by glass and polished metal, and smoke, fog and heavy dust scatter the beam — which matters, because those are exactly the conditions of the places rescue robots are sent into.

Cameras and contact sensors

A camera gives more information than any other sensor, but it arrives as an image that must be processed before it means anything, and it needs light to work at all.

At the other extreme sits the humble touch or bump sensor: a switch on the bumper that closes when the robot strikes something. It tells the robot nothing until the collision has already happened, which is why it is never the primary sensor. It is the backstop — and every failure mode listed above is the reason a well-built robot still carries one.

Compare Table

Every range above is a typical figure for a common module and varies considerably between manufacturers and models; the datasheet for the exact part is the only authority.

18.4.3 Sensing the Robot’s Own Motion

Counting the wheels

The simplest proprioceptive sensor is an encoder on a drive wheel, which produces a fixed number of electrical pulses for every rotation. Counting pulses gives the angle the wheel has turned, and multiplying by the wheel’s circumference gives the distance it has rolled. Estimating position this way is called odometry.

Example 18.5

Distance travelled from encoder counts

Given: A robot has wheels of diameter \(D = 65 \text{ mm}\). Each wheel carries an encoder producing \(20\) pulses per revolution. During one run, a wheel’s encoder produces \(300\) pulses.

Find: The distance that wheel has rolled, and the distance represented by a single pulse.

Method: One revolution rolls the robot forward by the wheel’s circumference, \(C = \pi D\). The number of revolutions is the pulse count divided by the pulses per revolution, and the distance is the revolutions multiplied by the circumference.

\[C = \pi D = \pi \times 0.065 \text{ m} = 0.2042 \text{ m}\]

\[n = \frac{300}{20} = 15 \text{ revolutions}\]

\[d = n \times C = 15 \times 0.2042 \text{ m} = 3.063 \text{ m}\]

Distance represented by one pulse:

\[\frac{C}{20} = \frac{0.2042 \text{ m}}{20} = 0.0102 \text{ m} = 10.2 \text{ mm}\]

The wheel has rolled about \(3.06 \text{ m}\), and the finest movement this encoder can report is about \(10.2 \text{ mm}\).

Check: Is that sensible? A 65 mm wheel travels about 20 cm per turn, so 15 turns giving roughly 3 m is consistent. Note also that no amount of careful programming will let this robot measure a 3 mm movement; the hardware sets that floor.

Odometry has one fatal weakness, and it is worth stating bluntly. It measures what the wheel did, not what the robot did. Every slip on a wet tile, every scuff during a turn, every millimetre of tyre wear puts the estimate wrong — and because each reading is added to the last, the errors accumulate rather than cancelling. If the wheels slip by three per cent, the robot believes it has travelled \(3.06 \text{ m}\) when it has really covered about \(2.97 \text{ m}\), and the gap only widens as the run goes on. This steady accumulation of error is called drift.

Inertial sensors

A gyroscope measures the rate at which the robot’s body is rotating, and an accelerometer measures its linear acceleration. Packaged together on one small module, they form an inertial measurement unit (IMU).

For a mobile robot the IMU answers questions the wheels cannot. It reports how far the body has actually turned, which catches the case where one wheel spun on a wet patch and the robot did not turn as commanded. It reports tilt, which tells the robot it is on a ramp or close to toppling. A two-wheeled balancing robot stays upright on gyroscope and accelerometer readings alone, correcting its lean many times a second.

The IMU drifts too, and for the same reason. It measures rates and accelerations, and a heading has to be built up by adding those measurements over time, so a tiny constant error becomes a large one after a minute of driving.

18.4.4 Sensing Position in the Wider World

Odometry and the IMU both answer the question “how far have I come since I started?” Neither can answer “where am I?” — and after enough drift, the first answer stops being a usable substitute for the second.

Outdoors, a global positioning system (GPS) receiver answers it directly. By receiving timing signals from several satellites, the module reports the robot’s latitude and longitude on the Earth’s surface. This is an absolute position, so it does not drift: an error made an hour ago does not affect the reading taken now.

That makes GPS essential for outdoor work — a delivery robot crossing a campus, or a field machine that must cover every row of a plot without missing one.

Its limitations are equally clear. A standard receiver is accurate to a few metres, which is fine for choosing a street and useless for staying in a lane. It updates slowly, often about once a second, which is far too slow to steer by. And it needs a clear view of the sky, so it degrades under dense trees, fails between tall buildings where the signals bounce, and does not work indoors at all — which rules it out for exactly the warehouses and hospitals where most mobile robots work.

18.4.5 Sensor Integration and Sensor Fusion

Set the last three subsections side by side and a pattern appears. Odometry is fast, smooth and steadily wrong. GPS is slow and coarse but never drifts. The IMU catches rotations the wheels miss, but drifts itself. LIDAR gives shape but not identity; a camera gives identity but needs light.

No single sensor is adequate — and, crucially, the weaknesses are not the same weaknesses. That is the opportunity sensor fusion exploits.

Definition

Sensor fusion is the combining of readings from two or more sensors to produce a single estimate that is more reliable than any of the individual readings taken alone.

Theory Snapshot

Sensor fusion Statement: When several sensors measure related quantities with independent error characteristics, an estimate computed from all of them together carries less error than the estimate from any one of them alone. In words: Sensors that fail in different ways can cover for each other. Why it holds: Each sensor’s error is bounded in a different respect. Odometry is precise from one instant to the next but drifts over minutes; GPS is coarse at any instant but does not drift at all. Running on odometry between GPS readings, and correcting the estimate whenever a GPS reading arrives, keeps the smoothness of the first and the absolute reference of the second. Used for: Position and heading estimation on almost every autonomous mobile robot, and for obstacle detection, where an ultrasonic reading is confirmed against a camera or LIDAR before the robot acts on it. Watch out: Fusion assumes the errors are independent. Smoke blinds a camera and a LIDAR together, and a jolt that makes both wheels slip corrupts odometry on both sides at once. Where two sensors fail in the same way at the same time, combining them adds confidence without adding correctness — the most dangerous result of all.

Integration is a hardware problem too

Integration covers more than the arithmetic. Getting several sensors to work together on one moving machine raises four practical problems, and each has cost somebody a working robot.

Placement and field of view come first. A sensor perceives only where it points and only as wide as its beam. An ultrasonic sensor mounted high on a mast will not see a low kerb, and one mounted behind a projecting bumper spends its life measuring the robot’s own frame.

Timing comes second. An encoder can be read thousands of times a second, an ultrasonic sensor perhaps fifteen times, a GPS module once. Readings taken at different instants describe different situations, and a fused estimate has to allow for that rather than pretending they all arrived together.

Electrical noise comes third. The drive motors are the noisiest things on the robot, and their switching currents couple into nearby signal wires. Sensor cables run alongside motor leads produce readings that jump every time the robot accelerates.

Power and grounding come fourth. Every sensor needs a supply within its rated voltage, and every sensor’s ground must be common with the control unit’s ground. Without a shared ground the sensor’s output voltage has no fixed reference, and its readings mean nothing at all.

Fig. 18.4-4 shows how the separate streams come together.

Diagram

Fig. 18.4-4 – block diagram of sensor fusion. Four input blocks on the left labelled “wheel encoders — fast, drifts”, “IMU — fast, drifts”, “GPS — slow, absolute, outdoors only” and “LIDAR or camera — shape and landmarks”, each with an arrow into a central block labelled “fusion in the control unit”. One arrow out of the central block into a block labelled “best estimate of position and heading”, and from there an arrow to a block labelled “planning and motor commands”

Common Error

Reading a sensor faster than it can answer What students do: They put an ultrasonic reading inside a fast loop and trigger a fresh pulse every few milliseconds, reasoning that more readings must mean better data. What happens: The distances jump about wildly. The echoes of the previous pulse are still bouncing around the room when the next pulse is sent, so the sensor times the wrong echo and reports objects that are not there. The fix: Leave enough time between pulses for the previous echoes to die away — around 60 ms is a common recommendation for ultrasonic modules — and read the fast sensors such as encoders in the quick loop, while reading slow sensors on their own slower schedule.

Try Yourself

Set an ultrasonic sensor on the bench and place a flat wooden board exactly 40 cm in front of it, square on. Record the reading. Now repeat three times: with the board turned to about 45 degrees, with a folded cloth draped over its face, and with only a pencil held upright at the same distance. Note which of the four situations gives the correct distance and which report a clear path, and explain each result from the sensor’s working principle.

18.5 Basic Design Principles

Designing a mobile robot is a chain of decisions, and each link in the chain constrains the next. Choose a heavier chassis and you need stronger motors. Stronger motors draw more current, so the battery must be larger. A larger battery is heavier, which brings you back to where you started.

That circle is not a flaw in the reasoning; it is the reasoning. A good design goes round it two or three times and settles. This section walks through the five subsystems in the order a designer actually meets them.

18.5.1 The Chassis

The chassis is the structural backbone of the robot. Everything else is fixed to it, and it decides where everything else sits.

Definition

The chassis is the structural frame of a mobile robot, which supports every other subsystem, protects the components mounted on it, and holds the sensors and actuators in fixed alignment with one another.

That last phrase carries more weight than it seems to. A robot’s program assumes that the ultrasonic sensor points straight ahead and that the two drive wheels are parallel. If a bracket flexes each time the machine starts, the sensor is no longer looking where the program believes, and no amount of clever software will fix a chassis that moves.

Where the mass goes

A chassis is also a decision about where the weight sits, and two rules govern it. Keep the heaviest item — almost always the battery — as low as possible, and keep the centre of mass inside the area bounded by the wheels. Fig. 18.5-1 shows a layout that follows both.

Diagram

Fig. 18.5-1 – top view and side view of a small differential-drive chassis. Top view: two driven wheels on a central axis, a castor at the front, the battery pack drawn as a shaded block placed centrally and slightly behind the drive axis, the control board and motor driver mounted forward of it, and the ultrasonic sensor bracket at the front edge; a dashed triangle joining the two wheel contact points and the castor contact point, labelled “support area”, with the centre of mass marked as a cross inside it. Side view: the same chassis showing the battery mounted low, close to the deck, with the height of the centre of mass marked by an arrow from the ground

Raise the centre of mass and the robot becomes easier to tip on a ramp or during a sharp turn. Push it outside the wheel base and the machine tips without any provocation at all. Neither is a subtle failure — the robot simply falls over the first time it is asked to work.

Choosing the material

The materials you met in the mechanical subsystem — MDF, acrylic, aluminum and steel — line up along one axis for this purpose: stiffness gained against mass added. MDF and acrylic are cheap, easily cut in a school workshop and quite adequate for a small indoor robot. Aluminum is far stiffer for its mass and is the usual choice once the machine has to carry a load. Steel is stronger still, but a steel chassis on a small robot is mostly a way of making the motors work hard for nothing.

The discipline to hold on to is this: every gram of chassis is a gram the motors must accelerate, the brakes must stop and the battery must move for the whole of its charge.

18.5.2 The Drive System

The drive system converts electrical energy into controlled motion. In a small robot it is a motor, a gearbox and a wheel, repeated on each driven side.

Sizing it is a question with a numerical answer, and the answer comes from the worst case the robot will meet — not the average one. For most machines the worst case is starting from rest, fully loaded, on the steepest slope it will ever have to climb.

Two forces resist that climb. Gravity pulls the robot back down the slope with a component \(mg\sin\theta\), and rolling resistance opposes the motion with roughly \(\mu mg\cos\theta\), where \(\mu\) is a rolling resistance coefficient for the wheel on that surface.

Example 18.6

Torque needed at each driven wheel on a ramp

Given: A robot of total mass \(m = 2.5 \text{ kg}\) with two driven wheels of radius \(r = 33 \text{ mm}\) must climb a ramp of slope \(\theta = 10^\circ\). Take \(g = 9.8 \text{ m/s}^2\) and a rolling resistance coefficient \(\mu = 0.05\), typical of small rubber wheels on a hard floor.

Find: The torque each driven wheel must produce.

Method: Add the gravitational component along the slope to the rolling resistance to get the total force the robot must overcome. Share it equally between the two driven wheels, then convert force at the rim to torque at the axle using \(\tau = F \times r\).

\[W = mg = 2.5 \text{ kg} \times 9.8 \text{ m/s}^2 = 24.5 \text{ N}\]

\[F_\text{slope} = W\sin\theta = 24.5 \text{ N} \times \sin 10^\circ = 24.5 \times 0.1736 = 4.25 \text{ N}\]

\[F_\text{roll} = \mu W\cos\theta = 0.05 \times 24.5 \text{ N} \times 0.9848 = 1.21 \text{ N}\]

\[F_\text{total} = 4.25 \text{ N} + 1.21 \text{ N} = 5.46 \text{ N}\]

Force at each wheel:

\[F_\text{wheel} = \frac{5.46 \text{ N}}{2} = 2.73 \text{ N}\]

\[\tau = F_\text{wheel} \times r = 2.73 \text{ N} \times 0.033 \text{ m} = 0.090 \text{ N·m}\]

Each driven wheel must produce about \(0.090 \text{ N·m}\), which is \(90 \text{ mN·m}\).

Check: Is that plausible? Small geared hobby motors of the kind used on school robots are rated in the region of a tenth of a newton metre, so the requirement is of the right order — but only just. A motor rated at exactly \(0.09 \text{ N·m}\) would have nothing left for acceleration or for a stiff wheel bearing, which is why designers size the drive for roughly twice the calculated figure.

Speed against torque

A motor on its own turns fast and pushes weakly. A gearbox trades one for the other: reduce the output speed by a factor and the available torque rises by roughly the same factor, less what is lost to friction inside the gears.

This is the single most common fix for a robot that cannot climb its ramp. The answer is usually not a bigger motor but a larger reduction ratio — accepting a slower robot in exchange for one that moves at all.

The choice also feeds directly into the next subsystem, because the current a motor draws rises with the torque it is asked to produce. A drive sized for the worst case must be powered for the worst case too.

18.5.3 The Power System

The power system supplies every other block. It has to meet two separate demands, and designs fail by forgetting the second one.

The first demand is energy: enough total charge to run the robot for as long as the task lasts. The second is peak current: the surge a motor draws in the instant it starts turning, which is several times its steady running current.

Sizing for endurance

A battery’s capacity is usually printed in milliampere hours, and the arithmetic for runtime is simple.

Example 18.7

How long a robot runs on one charge

Given: A robot is powered by a \(2200 \text{ mAh}\) lithium polymer pack. Measured over a typical task, the whole machine — motors, control board and sensors together — draws an average current of \(850 \text{ mA}\).

Find: The running time on one full charge.

Method: Capacity divided by current gives time, \(t = C/I\). With capacity in milliampere hours and current in milliamperes, the answer comes out directly in hours.

\[t = \frac{C}{I} = \frac{2200 \text{ mAh}}{850 \text{ mA}} = 2.59 \text{ h}\]

About \(2.6 \text{ h}\) in theory. In practice a pack is not run flat, both to protect the cells and to leave a margin, so a usable figure is roughly \(80\%\) of this, or about \(2.1 \text{ h}\).

Check: Does the magnitude make sense? The pack holds a little over twice the current the robot uses in an hour, so a runtime of a little over two hours is exactly what you should expect. Note also that \(850 \text{ mA}\) is an average — the motors will draw several times that during each start, and those surges are already included in the measured average.

Sizing for the surge

The surge is where designs come apart. When a motor starts, its current climbs sharply, and that current has to come through the battery’s internal resistance and the wiring. The supply voltage dips for a few milliseconds.

If the control board is fed from the same rail, that dip can take its supply below the voltage it needs, and the board resets. The robot’s symptom is unmistakable and baffling to a beginner: the program restarts every time the motors start, so the machine twitches and never gets anywhere.

The remedies are standard. Give the logic its own regulated supply, or its own pack, so the motor surge does not reach it. Keep motor wiring short and thick. Fit decoupling capacitors close to the board. And whatever else is done, join the grounds — two supplies with no common ground give the signal wires no reference at all, and every reading and command between the boards becomes meaningless.

Exam Corner

Q. A robot works perfectly when its wheels are off the ground and resets the moment it is put down. What is the likely cause?

A. A supply that cannot meet the surge. With the wheels in the air the motors are unloaded and draw little current; on the ground they must produce real torque, the current jumps, and the shared supply voltage dips far enough to reset the control board. The clue is that the fault appears with load, not with any particular instruction in the program.

Safety Note

Lithium polymer packs store a great deal of energy in a soft pouch. Charge them only on the balance charger provided, on a non-flammable surface, and never leave a pack charging unattended or overnight. Never puncture, crush, bend or short a pack, never continue to use one that has swelled or been dropped hard, and store packs at part charge in a metal box rather than fully charged on the bench.

18.5.4 The Control Board and the Motor Driver

The control board is the decision-making core: a microcontroller board such as an Arduino UNO for simple robots, or a single-board computer such as a Raspberry Pi 5 where camera processing is needed. It reads the sensors, runs the program and issues commands.

What it cannot do is drive a motor.

Why the pin cannot do the job

A microcontroller output pin is a signalling device, not a power source. On a common ATmega328P-based board each pin is rated for a current of the order of twenty milliamperes, with limits on the total drawn across all pins together.

A small geared motor of the kind used on a school robot draws hundreds of milliamperes while running and considerably more at the instant it starts or when it is stalled against an obstacle. Ask the pin for that and, at best, the board’s protection intervenes and the robot behaves erratically; at worst the pin is destroyed.

There is a second reason, quite separate from current. A motor is a coil of wire, and switching the current in a coil produces a voltage spike as the magnetic field collapses. Those spikes are perfectly capable of damaging logic that is connected directly to them.

What the motor driver does

A motor driver sits between the two worlds. Its input side takes small logic signals from the control board; its output side switches the battery’s current through the motor. The board decides, the driver does the work, and the two are electrically separated except for a shared ground reference.

A driver such as the L298N contains an H-bridge for each motor — an arrangement of four switches that can connect the motor to the supply either way round, so the same driver reverses the motor as well as running it.

Speed is set by pulse width modulation (PWM): the driver’s enable input is switched on and off many times a second, and the fraction of each cycle for which it is on is the duty cycle. A higher duty cycle delivers more average power to the motor and turns it faster. On an Arduino board this comes from analogWrite() on a PWM-capable pin.

Fig. 18.5-2 shows the whole arrangement, and the single most important line in it is the ground.

Diagram

Fig. 18.5-2 – circuit: Arduino UNO driving two DC gear motors through an L298N motor driver module. From the UNO, pin 5 to ENA and pin 6 to ENB (both labelled “PWM, sets speed”); pins 7 and 8 to IN1 and IN2, pins 9 and 10 to IN3 and IN4 (labelled “direction”). On the driver, OUT1 and OUT2 to the left motor terminals, OUT3 and OUT4 to the right motor terminals. A 7.4 V battery pack: positive to the driver’s motor supply terminal, negative to the driver’s GND terminal. A separate supply feeding the UNO. A single heavy line drawn from the driver’s GND terminal to the UNO’s GND pin, labelled “common ground — without this the driver cannot read the control signals”. Each wire labelled with its pin name

Curiosity Corner

Q4. The small board that makes a robot’s decisions cannot drive its motors directly. Why not, and what sits between them?

A. Because a microcontroller pin is built to send information, not to deliver power. A typical output pin is rated at around twenty milliamperes, while a small drive motor needs hundreds of milliamperes running and more at stall — and a motor, being a coil, also throws voltage spikes back down the wire when its current is switched. A motor driver sits between them. Its input side listens to the logic signals from the control board, and its output side switches the battery’s current through the motor, so the heavy current never passes through the board at all. A driver such as the L298N uses an H-bridge for each motor, which lets it reverse the motor as well as run it, with speed set by pulse width modulation on the enable input. The two sides must share a common ground, or the driver has no reference against which to read the control signals.

Common Error

Powering a motor or servo from the board’s 5 V pin What students do: They connect the motor or servo supply to the 5V pin on the Arduino board, because it is the nearest source of five volts and the wire reaches. What happens: The board’s small on-board regulator cannot supply the current, so the rail sags every time the motor moves. The board resets, the program restarts mid-task, and in longer sessions the regulator overheats. The symptom looks like a software bug and is not one. The fix: Feed motors and servos from the battery pack through the motor driver, and use the 5V pin only for sensors and other light loads. Join the two grounds so the control signals still have a reference.

18.5.5 Control Algorithms and Closed-Loop Motion

The last design principle is not a component at all. It is the question of whether the robot checks its own work.

Send a motor a fixed command and hope for the best, and you have an open-loop system: the robot has no idea whether the wheel is actually turning at the speed asked for. Measure the result and correct the command from the difference, and the loop is closed.

Definition

A closed-loop control system measures the actual output, compares it with the desired value to obtain the error, and adjusts its command so as to reduce that error; the measurement fed back for this comparison is called feedback.

Compare Table

The structure of the closed loop is always the one drawn in Fig. 18.5-3, whatever the quantity being controlled.

Diagram

Fig. 18.5-3 – flow: desired speed (setpoint) → comparison point where the measured speed is subtracted, producing the error → controller block → command as a PWM duty cycle → motor driver → motor and wheel → actual speed, with a branch from the actual speed going to an encoder block and returning to the comparison point as the feedback line, closing the loop. The comparison point marked with a plus sign on the setpoint input and a minus sign on the feedback input

PID control

The most widely used controller for the block in the middle is PID, and each of its three letters answers a different question about the error.

Theory Snapshot

Proportional–integral–derivative (PID) control Statement: The correction applied to the actuator is the sum of three terms computed from the error between the desired and measured values — one proportional to the error now, one proportional to the accumulated error over past samples, and one proportional to the rate at which the error is changing. In words: React to how wrong you are, to how long you have been wrong, and to how fast things are getting worse. Why it holds: The proportional term does the bulk of the correcting but always leaves a small standing error, since a zero error would produce a zero command. The integral term accumulates that residue until it is driven out. The derivative term senses the error closing rapidly and eases off early, which damps the overshoot the other two would otherwise cause. Used for: Holding a motor at a set speed regardless of load, keeping a line-following robot centred on its line, driving a straight course when one wheel drags, and holding a two-wheeled robot upright. Watch out: The three terms have to be tuned for the particular machine, and badly chosen values are worse than no controller at all — too much proportional gain sets the robot oscillating, and the derivative term amplifies sensor noise, since noise is by definition a rapidly changing signal.

Algorithm

Closed-loop speed control of a drive motor Input: A target wheel speed in counts per sampling interval; the count from the wheel encoder; a fixed sampling interval; the three tuning constants for the proportional, integral and derivative terms. Output: A PWM duty cycle written to the motor driver’s enable input for that motor. Method:

1. Wait until the fixed sampling interval has elapsed since the last pass.
2. Read the encoder count accumulated during that interval; this is the
   measured speed.
3. error = target speed - measured speed
4. sum_of_errors = sum_of_errors + error
5. change_in_error = error - previous_error
6. correction = (Kp * error) + (Ki * sum_of_errors) + (Kd * change_in_error)
7. duty = duty + correction
8. If duty is above the maximum, set it to the maximum; if below zero, set it
   to zero.
9. Write duty to the motor driver's enable input.
10. previous_error = error
11. Reset the encoder count and repeat from step 1.

Why it works: Step 3 turns the physical question “is the wheel going too slowly?” into a number with a sign, so the same expression both speeds the motor up and slows it down. Steps 4 and 5 give the controller a memory of the recent past and a sense of the immediate future, which is what lets it settle on the target instead of hunting around it. Watch out: The interval in step 1 must be genuinely constant, because the integral and derivative terms both assume equal spacing between samples; a loop whose timing wanders is untunable. Step 8 also matters more than it looks — without the limit, the accumulated sum in step 4 keeps growing while the motor is already at full power, and the controller then takes a long time to respond when the load finally eases.

The practical lesson of this whole section is that the five subsystems are not independent. The chassis mass sets the motor torque, the torque sets the current, the current sets the battery and the driver, and the sensing decides whether any of it can be corrected when reality disagrees with the plan.

18.6 Navigation and Path Planning

Everything so far has been about a robot taking one step safely. This section is about the whole journey: choosing a route across a building, and holding to it while the building refuses to stay as it was mapped.

18.6.1 The Navigation Problem

Navigation breaks into three questions, and a robot must be able to answer all three.

Where am I? This is localisation, and section 18.4 supplied its raw materials — odometry that is smooth but drifts, and outside references such as GPS or LIDAR readings that pull the estimate back into place.

What does the world look like? The robot needs a map: a description of which parts of the space it can drive through and which it cannot.

How do I get from here to there? This is path planning, and it is the subject of the next four subsections.

Notice that these three are not answered at the same rate. A route across a warehouse is worked out once, in a few tens of milliseconds, before the robot sets off. Avoiding the trolley that appears in aisle four happens twenty times a second, all the way. Planning and avoiding are two different activities running on two different clocks, and confusing them is the commonest mistake in navigation design.

Definition

Path planning is the process of computing a route from the robot’s current position to a goal position, through a known map of the environment, while avoiding the regions marked as blocked.

18.6.2 Representing the Environment as a Graph

A planning algorithm cannot work on a floor. It works on a description of the floor, and the usual description is an occupancy grid.

The space is divided into square cells, and each cell is marked as free or occupied. A cell containing part of a rack, a wall or a pillar is occupied; the rest are free, and the robot may drive through them. Fig. 18.6-1 shows a warehouse floor treated this way.

Diagram

Fig. 18.6-1 – three panels of the same warehouse floor. Panel (a): a plan view with two storage racks, a pillar and a packing bench drawn as outlines, with a start point marked S and a goal marked G. Panel (b): the same plan overlaid with a square grid, cells containing any part of an obstacle shaded dark and labelled “occupied”, the rest left white and labelled “free”. Panel (c): the free cells redrawn as small circles (nodes) joined by short lines (edges) to their free neighbours, showing the grid as a graph, with S and G marked on the corresponding nodes

Once the floor is a grid, it is also a graph. Each free cell is a node — a place the robot can be. Each connection between neighbouring free cells is an edge — a move the robot can make. Every edge carries a cost, which is what the move actually costs the robot.

That last idea is where the engineering enters. Cost need not be distance. It can be travel time, energy used, or a penalty applied to routes that pass close to a doorway people walk out of. Whatever the planner is told to minimise, it will minimise, so choosing the cost is choosing the robot’s behaviour.

Common Error

Planning as though the robot were a point What students do: They mark a cell occupied only if an obstacle physically sits in it, and let the planner route the robot along the cells immediately beside a rack. What happens: The plan is legal for a point and impossible for a machine 400 mm wide. The robot clips the corner of the rack, or wedges itself in a gap that was free on the map and is not free in the aisle. The fix: Inflate the obstacles before planning. Mark every free cell within roughly the robot’s own radius of an occupied cell as occupied too, so that any route the planner returns has room for the whole machine, not just its centre.

18.6.3 Breadth-First Search

Breadth-first search is the simplest planner, and it is the one to understand first because the others are variations on it.

It works outwards in layers. From the start cell it looks at every neighbour; from those it looks at every neighbour again, and so on, so that all cells one step away are examined before any cell two steps away. The first time the goal is reached, it has been reached in the fewest possible steps.

Algorithm

Breadth-first search for a route through an occupancy grid Input: An occupancy grid with obstacles already inflated; a start cell; a goal cell. Output: A list of cells forming a route from start to goal, or a report that no route exists. Method:

1. Create an empty queue. Put the start cell in it and mark the start cell
   as visited, with no parent.
2. If the queue is empty, stop and report that no route exists.
3. Remove the cell at the front of the queue and call it the current cell.
4. If the current cell is the goal, go to step 7.
5. For each free neighbour of the current cell that is not yet visited:
      mark it visited
      record the current cell as its parent
      add it to the back of the queue
6. Repeat from step 2.
7. Starting at the goal, follow the recorded parents back one cell at a time
   until the start is reached. Reverse this list to give the route.

Why it works: Because cells are taken from the front of the queue in the order they were added, every cell at a given number of steps from the start is examined before any cell further away. The first path found to the goal is therefore a path with the fewest steps, and the parent records make it possible to recover that path afterwards without having stored every route tried. Watch out: Step 5 must mark a cell visited when it is added to the queue, not when it is later removed, or the same cell is added many times and the search slows to a crawl. Note also that “fewest steps” equals “shortest route” only when every move costs the same — which stops being true the moment a diagonal move or a slow surface appears.

The weakness of breadth-first search is that it treats every direction alike. Searching for a goal thirty metres to the east, it examines almost as much ground to the west, which is wasteful on any map of a realistic size.

18.6.4 Dijkstra’s Algorithm

Real floors are not uniform. A stretch of ramp costs more energy than level ground; a busy aisle costs more time than a clear one; a route past a doorway carries more risk. Once edges have different costs, “fewest steps” and “cheapest route” part company.

Dijkstra’s algorithm handles this. It keeps, for every cell it has reached, the total cost of the cheapest route found to that cell so far. At each turn it expands the unexpanded cell with the lowest such total, and it updates a neighbour’s total whenever the route through the current cell turns out to be cheaper than the route already recorded.

The guarantee that follows is strong: when the goal is finally expanded, the total recorded against it is the lowest achievable, so the route returned is genuinely the cheapest one on the map.

The cost of that guarantee is work. Like breadth-first search, Dijkstra’s algorithm spreads outwards in all directions — just in order of cost rather than of steps — and on a large map it examines a great many cells that lie nowhere near the goal.

18.6.5 The A* Algorithm

The A* algorithm keeps Dijkstra’s bookkeeping and adds one idea: a sense of direction.

For each cell it considers, A* adds to the cost already spent an estimate of the cost still remaining to the goal. That estimate is called a heuristic, and for a robot on a grid it is usually the straight-line distance from the cell to the goal — a figure that can be calculated instantly and needs no search at all.

The algorithm then expands whichever cell has the smallest total:

\[f(n) = g(n) + h(n)\]

where \(g(n)\) is the cost of the best route found so far from the start to cell \(n\), \(h(n)\) is the estimated cost from \(n\) onwards to the goal, and \(f(n)\) is the estimated cost of the whole journey through that cell.

The effect is that cells lying towards the goal look cheap and are examined early, while cells behind the robot look expensive and are left alone. A* therefore reaches the goal after examining a fraction of the cells Dijkstra’s algorithm would, and it returns the same cheapest route, provided the estimate never overstates the remaining cost. Straight-line distance satisfies that condition, because no real route can be shorter than the straight line.

Fig. 18.6-2 makes the difference visible on one map.

Diagram

Fig. 18.6-2 – three copies of the same occupancy grid side by side, each with the start S at the left, the goal G at the right and one obstacle block between them. In each copy the cells examined by the algorithm are lightly shaded and the route found is drawn as a bold line. Panel (a) labelled “breadth-first search”: shading spreads as a rough circle around S in all directions. Panel (b) labelled “Dijkstra’s algorithm”: similar spread, slightly distorted where a shaded strip marked “slow surface, higher cost” lies. Panel (c) labelled “A*“: shading forms a narrow band stretching from S towards G, with little shading behind S

Compare Table

Why the shortest route is often not the chosen one

The word “cheapest” has been doing quiet work throughout. Here is what it means in practice.

Example 18.8

Choosing between a short slow route and a long clear one

Given: A warehouse robot may take two routes to the packing station. Route A is \(30 \text{ m}\) long, but \(12 \text{ m}\) of it runs through a congested aisle where the robot must reduce speed to \(0.4 \text{ m/s}\); the remaining \(18 \text{ m}\) is clear and travelled at \(1.2 \text{ m/s}\). Route B is \(38 \text{ m}\) long and entirely clear, travelled at \(1.2 \text{ m/s}\).

Find: The travel time for each route, and which the planner should choose if cost is measured in time.

Method: Time equals distance divided by speed, \(t = d/v\), computed separately for each stretch travelled at a different speed and then added.

Route A:

\[t_\text{clear} = \frac{18 \text{ m}}{1.2 \text{ m/s}} = 15 \text{ s}\]

\[t_\text{congested} = \frac{12 \text{ m}}{0.4 \text{ m/s}} = 30 \text{ s}\]

\[t_\text{A} = 15 \text{ s} + 30 \text{ s} = 45 \text{ s}\]

Route B:

\[t_\text{B} = \frac{38 \text{ m}}{1.2 \text{ m/s}} = 31.7 \text{ s}\]

Route A takes \(45 \text{ s}\) and route B takes about \(32 \text{ s}\), so the planner should choose route B — the longer route — by a margin of some thirteen seconds.

Check: Is this sensible? The congested stretch is covered at a third of the normal speed, so those \(12 \text{ m}\) cost as much time as \(36 \text{ m}\) of clear floor would. Route A is effectively a \(54 \text{ m}\) journey in disguise, and route B at \(38 \text{ m}\) is comfortably shorter in the currency that matters.

Curiosity Corner

Q5. Once a robot knows where it is and where it has to go, how does it choose a route — and why is the shortest route not always the one it takes?

A. It turns the floor into a grid of free and occupied cells, treats each free cell as a node and each move between neighbours as an edge carrying a cost, and then searches that graph. Breadth-first search finds the route with the fewest steps, Dijkstra’s algorithm finds the route with the lowest total cost, and A* finds the same cheapest route far more quickly by adding an estimate of the distance still to go, expanding the cell with the smallest value of \(f = g + h\). The shortest route loses whenever cost is not distance. If a \(30 \text{ m}\) route runs through a congested aisle where the robot must crawl, and a clear \(38 \text{ m}\) route does not, the longer one arrives thirteen seconds sooner. Whatever quantity the designer puts into the cost — time, energy, or the risk of meeting people — is the quantity the planner minimises, and distance is only one candidate among them.

18.6.6 Avoiding Obstacles While the Robot Is Moving

Every route above was planned on a map, and every map is a description of how the building was, not how it is. A pallet has been set down in aisle three. Somebody is walking across the junction. The planned route is now wrong, and the robot is already driving along it.

This is why navigation is built in two layers. The global planner produces a route over the whole map, occasionally. The local behaviour keeps the robot out of trouble between one sensor reading and the next, continuously, inside the sense–plan–act loop. Fig. 18.6-3 shows the two working together.

Diagram

Fig. 18.6-3 – a plan view of an aisle with the globally planned route drawn as a bold dashed line running straight down its centre from S to G. An unmapped trolley drawn sitting on that line partway along. A solid line showing the robot’s actual track: following the dashed route, curving out around the trolley with the ultrasonic detection cone drawn at the point of departure, and rejoining the dashed route beyond it. Labels: “planned route, from the map” on the dashed line and “local avoidance, from the sensors” on the detour

Algorithm

Local obstacle avoidance while following a planned route Input: The next waypoint on the planned route; the obstacle flag and forward distance produced by the sensing method of section 18.4.5; a clearance threshold. Output: Drive commands to the motor driver. Method:

1. If the obstacle flag is false, steer towards the next waypoint and drive
   forward. Go to step 8.
2. Stop the drive motors.
3. Reverse a short fixed distance, so the robot is clear of the obstacle.
4. Turn in place a small angle to the left and read the forward distance;
   turn in place a small angle to the right and read the forward distance.
5. If neither side gives a distance greater than the clearance threshold,
   report the cell blocked to the planner, request a new route, and wait.
6. Turn towards the side with the greater distance.
7. Drive forward until the robot is past the obstacle, then steer back
   towards the next waypoint.
8. Repeat from step 1 on the next pass of the control loop.

Why it works: The planned route supplies the long-term direction and the sensors supply the short-term veto, so the robot keeps its overall goal while treating anything unexpected as a temporary deviation rather than a failure. Step 3 matters because a robot that has already stopped close to an obstacle usually cannot turn without striking it. Watch out: This method can trap the robot. In a dead end or a U-shaped recess it will turn towards whichever side is momentarily clearer, drive a little way, and be blocked again — repeating indefinitely without ever escaping. Step 5 is the escape hatch: once no direction is clear, the local behaviour must give up and hand the problem back to the global planner, which can mark the region blocked and route around it on the map.

Exam Corner

Q. If the map goes out of date so easily, why not simply replan the whole route on every pass of the control loop?

A. Because a full search over a large grid takes far longer than the few tens of milliseconds a control loop allows, and a small robot’s controller has other work to do in that time. The standard compromise is to replan only when something has actually changed — when the robot marks a new cell blocked, when it strays far from its route, or when the goal itself changes — and to leave the fast reflexes to the local behaviour in between.

18.7 Applications of Mobile Robots

Three settings show what the last five sections were for. In each of them, look for the same thing: the problem that made a mobile robot worth building, and the design decisions that problem forced.

18.7.1 Logistics and Warehouse Automation

Start with the problem, because the solution is surprising only if you skip it.

In a conventional warehouse, an order picker walks to the shelf holding each item, takes it, and walks on to the next. Across a shift in a large building that adds up to many kilometres of walking, and almost all of the picker’s time is spent travelling rather than picking. The bottleneck is not the person’s hands; it is the distance between the shelves and the packing bench.

The mobile robot’s answer inverts the whole arrangement. Instead of sending the worker to the shelf, send the shelf to the worker. Low, flat robots drive underneath a movable rack, lift it a few centimetres, and carry the entire rack to a picking station where a person stands still and picks from rack after rack as they arrive. Fig. 18.7-1 shows the layout.

Diagram

Fig. 18.7-1 – plan view of a fulfilment area. A dense block of movable racks drawn as squares in a grid with narrow lanes between them; three picking stations drawn along the left edge with a person symbol at each; several low robots drawn as small rectangles, two under racks and moving along lanes with arrows showing their direction, one empty and returning; a charging bay drawn at the bottom edge. Labels: “movable racks”, “robot carrying rack to station”, “picking station”, “charging bay”

Every design choice follows from the building. The floor is flat, swept and indoors, so wheels are the obvious locomotion and tracks would only waste charge. The load is heavy and the robot must pass under a rack, so the chassis is wide, low and carries its battery at the very bottom. The routes are fixed lanes, so the planner works on a grid that matches the lane layout exactly.

Localisation is handled in a way worth noticing. Rather than fit every robot with an expensive sensor to work out where it is, the operator marks the floor with a regular pattern of coded markers that a downward-facing camera on each robot reads. The building has been engineered for the robot, which is far cheaper than engineering the robot for an arbitrary building.

Exam Corner

Q. Why not simply give each warehouse robot a LIDAR and let it work out its own position, as a delivery robot must?

A. Because the operator controls the building and can choose the cheaper option. A LIDAR costs many times what a downward camera and a floor marker cost, and multiplied across a fleet of hundreds the difference is decisive. It is also more reliable: a coded marker read from 30 cm away in controlled lighting gives an exact position every time, while a LIDAR trying to recognise an aisle full of identical racks can genuinely mistake one aisle for another.

The real problem is traffic, not navigation

With one robot, path planning is section 18.6 and nothing more. With three hundred robots in the same lanes, two of them will plan routes that cross at the same instant, and two more will meet head-on in a lane wide enough for one.

This is why a fleet is run by a fleet management system: a central computer that assigns tasks, reserves sections of lane in advance, and releases them once a robot is through. Individual robots keep their own reflexes for anything unexpected, but the routing decisions are made centrally so that they can be made consistently.

System Profile

Warehouse transport robot Working principle: A low wheeled robot navigates fixed lanes between movable racks, locating itself from coded markers set into the floor and read by a downward-facing camera. On reaching an assigned rack it raises a lifting platform to take the rack’s weight, carries it to a picking station, waits while items are removed, and returns it to a storage position. A central fleet management system assigns the tasks and reserves the lanes. Components: Low-profile chassis, driven wheels and motors, lifting platform and its actuator, downward camera for marker reading, obstacle sensors, control board and motor driver, battery pack, wireless link to the fleet management system. Advantages: Removes the picker’s walking time, so orders are completed far faster; allows racks to be packed densely because no aisle need be wide enough for a person; runs through the night without supervision; the fleet’s throughput can be raised by adding robots rather than rebuilding the floor. Limitations: Works only in a purpose-built facility with a flat, clean, marked floor; a robot that stops with a fault blocks the lane and disrupts the robots behind it; the whole operation depends on the central system and the wireless link; energy and floor space are given up to charging bays; the capital cost is only recovered at large volumes. Where it is used: Order fulfilment centres, parts warehouses and distribution hubs. Systems of this kind have been in commercial use since Kiva Systems introduced them in the mid-2000s, and several manufacturers now supply comparable fleets.

18.7.2 Transportation and Last-Mile Delivery

The economics of a delivery are lopsided. Moving a parcel a thousand kilometres by rail or road is cheap per parcel, because thousands travel together. Moving that same parcel the last kilometre — from a local depot to one doorstep — is expensive, because it is carried alone. This final stretch is called last-mile delivery, and it is where mobile robots are being tried.

A pavement delivery robot is a small, slow, insulated box on six wheels. It travels at roughly walking pace, carries a single order, and crosses roads at marked crossings. Fig. 18.7-2 shows one at a kerb.

Photograph

Fig. 18.7-2 – a small six-wheeled pavement delivery robot on a public footpath, photographed from the side at low height, with its wheels, its sensor mast or camera housing and its cargo lid all visible, and pedestrians or a kerb in the frame to give scale. Sourcing note: the robot must be in genuine outdoor public use, not a trade-show stand or a rendering; images cropped so the wheels or the surroundings are lost are unusable, because the point is the machine’s size relative to the pavement it shares.

The environment sets every requirement, and it is a far harder environment than the warehouse.

The robot is outdoors, so it fuses GPS for absolute position with odometry and an inertial measurement unit for the metres between fixes. It meets kerbs and driveway ramps, so its wheels are relatively large and its drive is geared for torque rather than speed. It travels among people who have not been trained to expect it, so it is deliberately slow, gives way rather than asserting priority, and stops for anything ambiguous.

That last habit produces the design’s most interesting feature. A robot that stops whenever it is unsure will stop often — at an unmarked obstruction, a crowd, a parked vehicle across the path. Rather than trying to program an answer for every case, operators keep human staff at a remote console who take control of any robot that has stopped, drive it through the difficulty, and hand it back to autonomy. One person can supervise many robots precisely because each needs help only occasionally. This is the shared control of section 18.3 turned into a business model.

System Profile

Pavement delivery robot Working principle: The robot plans a route over a map of local footpaths and drives it autonomously at walking pace, fusing GPS with odometry and inertial sensing to know where it is, and using cameras and short-range sensors to detect pedestrians, kerbs and obstructions. Where a situation is beyond its programming it stops and a remote operator takes control until the difficulty is passed. Components: Wheeled chassis with an insulated locking cargo compartment, drive motors and gearboxes, cameras, short-range obstacle sensors, GPS receiver, inertial measurement unit, control computer, battery pack, mobile data link to the operations centre. Advantages: Cuts the cost of the most expensive leg of a delivery; runs on electricity rather than fuel; frees delivery staff from short repetitive trips; can operate at times of day that suit the customer rather than the driver. Limitations: Defeated by steps, deep snow and heavy rain; GPS degrades badly among tall buildings; carries only a small load over a short range; needs permission to use public footpaths, which differs from city to city; must share space with pedestrians, wheelchair users and prams, whose convenience matters as much as the robot’s. Where it is used: Campus and neighbourhood delivery of food and parcels in several countries, generally under specific local permissions and within a defined service area.

18.7.3 Search and Rescue

After an earthquake, an explosion or a mine collapse, rescuers face a problem that no amount of courage solves. The structure that has already fallen once may fall again, the air inside may not be breathable, and the voids in the rubble where survivors are most likely to be trapped are frequently too small for a person to enter at all.

A search-and-rescue robot is sent in to answer questions, not to lift anything. Is anyone in this void? Is the air safe? Where does this passage lead? Every answer it brings back shapes what the rescue team does next, and every hour saved matters, because survival rates fall steeply with time.

The design follows from rubble. Locomotion is tracked or legged, because there is no continuous floor. The body is sealed against dust and water and built to survive being dropped down a hole. Many such robots are designed to keep working whichever way up they land.

The payload is a set of senses borrowed for a human being: a camera with its own lighting, a thermal camera that finds body heat in the dark, a gas detector that reports whether the void is breathable, and a two-way audio link so that a rescuer can speak to anyone found and hear the reply. Fig. 18.7-3 shows the arrangement.

Diagram

Fig. 18.7-3 – cross-section through a collapsed slab structure. A void beneath broken concrete slabs, with a tracked robot part way along it, drawn with labelled payload: camera with lamp, thermal camera, gas detector, speaker and microphone. A cable drawn running from the robot back out of the rubble to an operator station outside, where a person is shown at a screen, labelled “tether: carries video out and commands in, and does not depend on radio through concrete”. A survivor position marked ahead of the robot in the void

Control is where these robots differ most sharply from the two above. The environment is unknown, unmapped and unrepeatable, so global path planning has almost nothing to work on, and the judgement needed at every turn is human. These machines are teleoperated or semi-autonomous, with the robot handling only what must be fast — holding a heading, refusing to drive off a drop — while a rescuer decides where to go.

Communication is the recurring failure. Radio does not pass reliably through reinforced concrete and earth, so many of these robots trail a tether that carries video out and commands in. A tether is a nuisance — it snags, it limits range, it must be reeled — and it is used anyway, because a robot that cannot report is worse than no robot at all.

System Profile

Search-and-rescue robot Working principle: A small tracked or legged robot is driven by a remote operator into voids and passages that are unsafe or too small for a rescuer. It carries sensing equipment in place of the operator’s own senses and relays what it finds back to the surface, so that the rescue team can decide where to dig. Components: Sealed rugged chassis, tracks or articulated legs, drive motors, camera with lighting, thermal camera, gas detector, two-way audio, tether or radio link, battery pack, operator control station. Advantages: Reaches places a person cannot enter safely or physically; keeps rescuers out of an unstable structure; works in darkness, dust and smoke; can be sent into a void that turns out to be empty at no risk to anybody. Limitations: Battery endurance is short, and a stranded robot may itself block the passage; the operator sees only a narrow camera view and quickly loses track of where the machine is; radio fails through rubble, and a tether snags; the robot finds and reports survivors but cannot free them. Where it is used: Collapsed buildings after earthquakes and explosions, mine and tunnel incidents, and inspection inside industrial plant that has been damaged.

Reading the three side by side

The three applications use the same five subsystems and arrive at three different machines, because they answer to three different environments.

Compare Table

One pattern runs through the whole table. The more the environment can be controlled, the more autonomy is worth building; the less it can be controlled, the more a human stays in the loop. That is the same conclusion section 18.3 reached from first principles, arrived at here from three real settings.

Mobile robots work in other fields too — carrying supplies through hospital corridors and moving through fields to monitor crops — and both of those are studied in detail in Class XII.

18.8 Summary

What a mobile robot is

A mobile robot carries its own locomotion mechanism and moves from place to place while performing a task, instead of working from a fixed base. It does not enlarge its reach; it takes its small workspace to wherever the work is.
Mobility is paid for four times over. The robot must carry its own energy, it no longer knows its position by construction and must estimate it from sensors, it cannot assume anything about the ground, and it shares its space with people.
Almost every mobile robot is built from five subsystems: the structure and locomotion system, the actuators, the sensors, the control unit and the power source. A communication link is added wherever a human operator is involved.
The subsystems work as a repeating cycle, the sense–plan–act loop: sense the surroundings and the robot’s own state, plan the next action from those readings and the goal, act through the actuators, then sense again — because the robot’s own action has changed the situation.
Latency is the delay between something changing and the robot’s response reaching its actuators. Between two passes of the loop the robot travels blind, a distance given by \(d = v \times T\), so a slow loop and a fast robot are a dangerous combination.

Types of mobile robots

Mobile robots are classified by locomotion into wheeled, tracked and legged machines. The three are three different bargains between simplicity, efficiency and the roughness of the ground.
Wheeled robots are the commonest, because rolling contact converts rotation into travel with few moving parts and little friction loss, making them simple and the most energy-efficient of the three. Differential drive steers by giving each driven wheel its own speed, with passive castors carrying the load.
A wheeled robot needs a firm, reasonably smooth surface, loses grip on loose or wet ground, and cannot climb a step approaching its own wheel radius.
Tracked robots circulate a continuous belt around a drive sprocket and idler, so their weight rests on a long strip of ground. Ground pressure, \(p = W/A\), is therefore low: the machine does not sink into soft surfaces and gains far more traction, and the belt lays itself over steps and gaps.
Tracks cost energy and wear, because skid steering drags the belts sideways across the ground, and they add mechanical complexity that can immobilise the robot if a belt is thrown.
Legged robots place each foot at a chosen point and lift it clear of everything between, so they can cross ground that offers no continuous path at all. They stand only while the centre of mass stays inside the support polygon formed by the feet in contact, so every step is a balancing calculation.
Legs demand two or three powered joints per leg, so they are mechanically complex, power-hungry, slow and expensive.
The design rule is to begin with the worst surface the robot will actually meet, and then choose the simplest locomotion that can cross it, since every step up in complexity is paid for again in battery capacity and maintenance.

Autonomy

An automatic machine repeats a fixed sequence regardless of its surroundings. An autonomous machine is given a goal, reads its surroundings and chooses the action that suits the situation it actually finds.
Autonomy is best located by asking which stage of the sense–plan–act loop the human occupies. In teleoperation the robot senses and acts while a person takes every decision; in full autonomy the whole loop closes on board and the person supplies only the goal.
An autonomous mobile robot decides route, obstacle avoidance and task steps for itself. It depends totally on its sensors, needs its goal expressed in terms the program can act on, and needs an environment predictable enough to plan in. Its limitation is that it can only handle situations its designers anticipated.
A semi-autonomous mobile robot divides the work: the robot takes the fast, continuous, low-level decisions, and a human operator takes those needing judgement. It depends on a communication link, and both the link delay and the operator’s reaction time add to the distance travelled before a command takes effect.
The degree of autonomy is chosen by four questions: how predictable the environment is, what a wrong decision costs, whether a reliable link is available, and whether a person can be present for the whole task.

Sensing and perception

Exteroceptive sensors report on the world outside the robot; proprioceptive sensors report on the robot’s own state. A mobile robot needs both, because commanding an action is not the same as achieving it.
An ultrasonic sensor times the echo of a sound burst, giving \(d = vt/2\) since the pulse travels out and back. It is defeated by smooth surfaces met at a slant, which deflect the echo away, and by soft surfaces, which absorb it; its beam is a cone of roughly fifteen degrees, and the speed of sound varies with temperature.
An IR sensor measures reflected infrared light. It is cheap and quick and suits line following and edge detection, but a dark surface reads like empty space and strong ambient light swamps the reflection.
LIDAR — light detection and ranging — times a laser pulse and usually sweeps it round, giving accurate distance and bearing and a full outline of the surroundings. It is expensive, produces a large volume of data, and is defeated by glass, mirrors, dust and smoke.
A bump switch detects an obstacle only by striking it and is the last line of defence, since every other sensor can miss something. Cameras give the richest picture but return images rather than decisions, and need processing power a small microcontroller does not have.
Odometry estimates position by counting wheel rotations, and dead reckoning keeps a running position from it without any outside reference. It is smooth and cheap but drifts, because the encoder counts what the wheel did rather than what the robot did.
A gyroscope measures rate of rotation and an accelerometer measures linear acceleration, including gravity, and so also tilt. Together they form an inertial measurement unit. Both must be added up over time, so both give excellent short-term answers that slowly become fiction.
A GPS receiver gives an absolute position outdoors that never drifts, but it is accurate only to a few metres, updates slowly, and fails indoors, in tunnels, under tree cover and among tall buildings.
Sensor fusion combines readings from two or more sensors to produce a more reliable estimate than any one alone. It is done either for redundancy, where two sensors measure the same quantity and agreement raises confidence, or for complementarity, where two sensors measure different quantities whose weaknesses do not overlap, as GPS and odometry do.
The design rule is to choose sensors whose failure modes differ. Integration is also physical: mounting height and position decide what a sensor can possibly see, overlapping ultrasonic cones cause cross-talk, sensor cables are routed away from motor leads, and any sensor on a separate supply must share a common ground with the control unit.

Basic design principles

The chassis supports every other subsystem, protects the components and holds the sensors and actuators in fixed alignment, which no software can compensate for if it flexes. The heaviest item is mounted low, and the centre of mass is kept inside the area bounded by the ground contacts.
Chassis materials trade stiffness against added mass: MDF and acrylic are cheap and adequate for small indoor robots, aluminum is far stiffer for its mass, and steel is strong but usually more weight than a small machine can justify.
The drive system is sized from the worst case, not the average — normally starting fully loaded on the steepest slope. The force needed is \(mg\sin\theta\) along the slope plus \(\mu mg\cos\theta\) of rolling resistance, and the torque each driven wheel must produce is \(\tau = F \times r\).
A gearbox trades speed for torque, so a robot that cannot climb usually needs a larger reduction ratio rather than a larger motor. Higher torque means higher current, which passes the problem straight to the power system.
A battery must meet two separate demands: enough energy for the task, with runtime \(t = C/I\), and enough peak current for the surge a motor draws as it starts. A surge that pulls the shared supply down resets the control board, which looks like a software fault and is not.
Lithium polymer packs are charged only on a balance charger, on a non-flammable surface and never unattended, are never punctured, crushed or shorted, are discarded once swollen or badly dropped, and are stored at part charge.
A microcontroller pin is a signalling device rated at around twenty milliamperes and cannot drive a motor drawing hundreds of milliamperes, quite apart from the voltage spikes a coil throws back when its current is switched.
A motor driver such as the L298N takes logic signals on its input side and switches the battery’s current on its output side, using an H-bridge to reverse the motor and pulse width modulation — the duty cycle — to set its speed. The driver and the control board must share a common ground.
An open-loop system never measures its output and drifts whenever the load or the surface changes. A closed-loop system measures the output, subtracts it from the desired value to obtain the error, and adjusts its command to reduce that error; the measurement fed back is the feedback.
PID control sums three terms computed from the error: proportional to the error now, to the accumulated error, and to the rate at which the error is changing. It must be tuned for the particular machine — too much proportional gain sets the robot oscillating, and the derivative term amplifies sensor noise.

Navigation and path planning

Navigation asks three questions: where the robot is, which is localisation; what the world looks like, which is the map; and how to get to the goal, which is path planning. The route is planned occasionally, while obstacle avoidance runs continuously inside the control loop.
An occupancy grid divides the space into cells marked free or occupied. Free cells become nodes, moves between neighbours become edges, and each edge carries a cost — which may be distance, time, energy or risk. Whatever is put into the cost is what the planner will minimise.
Obstacles are inflated by roughly the robot’s own radius before planning, because a route that is legal for a point is not legal for a machine with width.
Breadth-first search explores outwards in layers and returns the route with the fewest steps, which is the shortest route only when every move costs the same. It examines cells in every direction, including away from the goal.
Dijkstra’s algorithm expands the reached cell with the lowest total cost so far and returns the cheapest route when edges differ in cost, but it too spreads outwards in all directions.
A* adds a heuristic estimate of the cost still remaining and expands the cell with the smallest \(f(n) = g(n) + h(n)\). It returns the same cheapest route as Dijkstra’s algorithm while examining far fewer cells, provided the estimate never overstates what remains — a condition straight-line distance satisfies.
The shortest route is not always chosen, because cost need not be distance: a shorter route through a congested stretch can take considerably longer than a clear route that is physically further.
Navigation is therefore built in two layers. The global planner works on a map that is always slightly out of date; local avoidance uses the sensors to deviate around whatever the map did not know about, and rejoins the route. Local avoidance alone can trap a robot in a dead end, so it must be able to hand the problem back for replanning.

Applications

In logistics, mobile robots invert the picking problem by carrying movable racks to a stationary picker. The floor is engineered for the robot — flat, marked with coded position markers — and the real difficulty is traffic between many robots, which is why a central fleet management system assigns tasks and reserves lanes.
In transportation, small pavement robots address last-mile delivery, the most expensive leg of a journey. They fuse GPS with odometry and inertial sensing, travel slowly among pedestrians, stop whenever a situation is ambiguous, and are handed to a remote operator for the cases their programming cannot settle.
In search and rescue, tracked or legged robots enter voids that are unsafe or too small for a person, carrying a camera, a thermal camera, a gas detector and two-way audio in place of a rescuer’s senses. They are teleoperated or semi-autonomous, because the environment is unmapped and the judgement needed is human, and they often trail a tether because radio does not pass reliably through rubble.
One pattern runs through all three: the more the environment can be controlled, the more autonomy is worth building, and the less it can be controlled, the more a human stays in the loop.

18.9 Key Terms

A* algorithm — a path-planning method that expands the cell with the smallest total of cost already spent plus estimated cost remaining, reaching the goal far more quickly than Dijkstra’s algorithm while returning the same cheapest route.
Autonomous mobile robot — a mobile robot that decides its own route, avoids obstacles and carries out its task without a person taking those decisions.
Autonomy — a robot’s ability to decide its own actions from sensor readings in order to achieve a given goal, rather than being told what to do.
Breadth-first search — a path-planning method that explores outwards in layers from the start cell and returns the route with the fewest steps.
Chassis — the structural frame of a mobile robot, which supports every other subsystem and holds the sensors and actuators in fixed alignment.
Closed-loop control — control in which the actual output is measured, compared with the desired value, and the command adjusted to reduce the difference.
Cost — the value attached to a move between two cells in a plan, which may represent distance, time, energy or risk, and which the planner works to minimise.
Dead reckoning — keeping a running estimate of position from the robot’s own motion measurements alone, without any outside reference.
Differential drive — a steering arrangement in which two wheels on a common axis are driven at separately controlled speeds, so that no steering mechanism is needed.
Dijkstra’s algorithm — a path-planning method that always expands the reached cell with the lowest total cost so far, and so returns the cheapest route when moves differ in cost.
Duty cycle — the fraction of each switching cycle for which a pulse-width-modulated signal is on, which sets the average power delivered to a motor.
Edge — a connection between two neighbouring free cells in a planning graph, representing a move the robot can make.
Exteroceptive sensor — a sensor that reports on the world outside the robot, such as the distance to an obstacle.
Feedback — the measurement of a system’s actual output that is returned for comparison with the desired value.
Fleet management system — a central computer that assigns tasks to many robots and reserves routes for them, so that they do not obstruct one another.
GPS — global positioning system; a satellite-based system whose receiver gives an absolute outdoor position that does not drift, but only to within a few metres and only under an open sky.
Ground pressure — the force a machine presses onto the surface divided by its total contact area, which decides how far it sinks into soft ground.
H-bridge — an arrangement of four switches inside a motor driver that can connect a motor to the supply either way round, allowing its direction to be reversed.
Heuristic — an estimate of the cost still remaining from a cell to the goal, used by A* to direct its search; it must never overstate the true remaining cost.
IMU — inertial measurement unit; a gyroscope and an accelerometer packaged together, reporting the robot’s rate of rotation and its linear acceleration.
IR — infrared; light just beyond the red end of the visible range, emitted and detected by short-range reflective sensors used for line following and edge detection.
Last-mile delivery — the final short leg of a delivery, from a local depot to the customer’s door, which costs the most per parcel because each is carried alone.
Latency — the delay between something changing in the world and the robot’s response to it reaching its actuators.
LIDAR — light detection and ranging; a sensor that times the return of a laser pulse and usually sweeps it round, giving accurate distance and bearing for the surroundings.
Localisation — the process by which a robot works out where it is within its map.
Locomotion — the means by which a robot moves its whole body from place to place, using wheels, tracks or legs.
MDF — medium-density fibreboard; a sheet material that is cheap and easily cut, often used for the chassis of small indoor robots.
Mobile robot — a robotic system that carries its own locomotion mechanism, so that it can move through its environment while performing a task instead of working from a fixed base.
Node — a single free cell in a planning graph, representing a place the robot can be.
Occupancy grid — a map that divides the space into square cells, each marked as free or occupied.
Odometry — estimating how far and in what direction a robot has moved by counting the rotations of its wheels.
Open-loop control — control in which a command is issued without the result ever being measured, so nothing corrects an error once it appears.
Path planning — computing a route from the robot’s present position to a goal through a known map, avoiding the regions marked as blocked.
PID — proportional–integral–derivative; a controller whose correction is the sum of three terms computed from the error now, the accumulated error, and the rate at which the error is changing.
Proprioceptive sensor — a sensor that reports on the robot’s own internal state, such as wheel rotation or body tilt.
PWM — pulse width modulation; switching a supply rapidly on and off so that the fraction of time it is on sets the average power delivered.
Semi-autonomous mobile robot — a mobile robot in which control is shared, the machine handling fast low-level motion and a human operator taking the decisions that need judgement.
Sense–plan–act loop — the repeating cycle in which a robot senses its situation, plans its next action, acts on that plan, and then senses again to see what its action achieved.
Sensor fusion — combining readings from two or more sensors to obtain an estimate more reliable than any of them alone.
Skid steering — turning a machine by driving the belts or wheels on its two sides at different speeds, so that they drag sideways across the ground.
Support polygon — the shape drawn on the ground by joining the feet or wheels currently in contact; a machine stands only while its centre of mass falls inside it.
Teleoperation — control of a robot by a human operator at a distance, who receives its sensor data and issues its movement commands directly.
Traction — the grip available between a wheel or track and the ground before it slips.
Workspace — the set of points a robot’s end-effector can reach; on a mobile robot it travels with the machine instead of being fixed in space.

18.10 Objective Questions

A robot of fixed mass is rebuilt with tracks in place of its wheels, nothing else being changed. Which quantity falls?

Its weight
Its ground pressure
Its traction on loose soil
Its total contact area

A robot approaches a matt black board placed across its path and does not slow down. Which sensor is most likely to have reported open space?

Ultrasonic sensor
IR sensor
Bump switch
Wheel encoder

State whether each of the following is true or false.

Dead reckoning gives a position estimate that becomes more accurate the longer the robot drives.
A gearbox increases the torque available at the wheel while reducing its speed.
A GPS receiver gives a position that does not drift, but only to within a few metres.

Fill in the blanks.

The shape formed on the ground by joining the feet currently in contact with it is called the ______.
Turning a machine by driving its two sides at different speeds, so that they drag sideways across the ground, is called ______.

Match each item in column A with what defeats it in column B.

Column A	Column B
a. Ultrasonic sensor	i. A slipping wheel
b. IR sensor	ii. A glass partition
c. LIDAR	iii. A smooth wall met at a slant
d. Odometry	iv. Strong sunlight

Give the full form of each of the following abbreviations: LIDAR, IMU, PWM, PID, GPS.
Assertion (A): The control board of a mobile robot is never connected directly to a drive motor. Reason (R): An output pin of a common microcontroller board is rated for a current of the order of twenty milliamperes.

Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.

A robot travelling at a fixed speed has its control loop slowed from twenty passes per second to five. In one line, state what happens to the distance it covers between one decision and the next.

18.11 Check Your Concepts

Define latency, and state one consequence of high latency for a robot moving at speed.
Name the five subsystems from which almost every mobile robot is built, and state in one line what each of them does.
Differentiate between an exteroceptive sensor and a proprioceptive sensor, giving one example of each and stating what a robot would be unable to do if it carried only one of the two kinds.
A wheeled robot and a tracked robot have the same mass. Explain, with reference to ground pressure and traction, why the tracked machine crosses soft ground better, and state one price that is paid for this advantage.
A robot of total mass \(3.0 \text{ kg}\) has two driven wheels of radius \(40 \text{ mm}\). It must start from rest on a ramp of slope \(8^\circ\). Take \(g = 9.8 \text{ m/s}^2\) and a rolling resistance coefficient of \(0.04\). Calculate the torque each driven wheel must produce, and state, with a reason, whether a motor rated at exactly that torque should be selected.
A warehouse robot must plan routes across a large floor on which one section has a slow, congested surface. Compare breadth-first search, Dijkstra’s algorithm and A* against three criteria — the ability to handle moves of differing cost, the number of cells examined, and the route finally returned — and recommend one of them, justifying your choice.

18.12 Diagram, Circuit & Output Reading

A student wires a robot as follows. The battery pack’s positive terminal goes to the motor supply terminal of an L298N driver module and its negative terminal to the module’s GND terminal. Pin 5 of an Arduino UNO goes to ENA, and pins 7 and 8 go to IN1 and IN2. The left motor is connected to OUT1 and OUT2. The UNO is powered separately from a USB supply. The program is correct, but the motor does not respond to any command.

Identify the single connection that is missing.
Explain why its absence stops the driver from acting on the control signals.

The table below gives typical figures for three sensors being considered for an indoor robot.

Sensor	Typical range	Directional detail	Defeated by
Ultrasonic	0.02 m to 4 m	Cone of about 15°	Angled smooth surfaces, soft surfaces
IR	A few millimetres to under a metre	A single narrow spot	Dark surfaces, strong ambient light
LIDAR	0.1 m to about 10 m	Distance and bearing at every point	Glass, mirrors, dust and smoke

The robot must run along a corridor that has a glass door at one end and a dark rubber mat across the middle of the floor. a. State which single sensor from the table would be the worst choice on its own for this corridor, and why. b. Choose a pair of sensors for the robot and justify the pairing in terms of their failure modes.

An ultrasonic sensor on a stationary robot receives its echo \(5.8 \text{ ms}\) after transmitting. The air temperature is about \(20\ ^\circ\text{C}\), at which the speed of sound is \(343 \text{ m/s}\).

Calculate the distance to the surface ahead.
The robot then turns through \(30^\circ\) and the sensor reports no echo at all, although the wall in front of it is unbroken. Explain what has happened.

The grid below is an occupancy map. S is the start cell, G is the goal, a full stop is a free cell and a hash is an occupied cell. The robot may move only up, down, left or right, one cell at a time, and every move costs the same.

S . . # .
. # . # .
. # . . .
. . . # G

State the number of moves in the route that breadth-first search would return.
The obstacles are now inflated by one cell in each direction before planning, as they would be for a robot with width. State whether any route from S to G still exists, and give the reason for your answer.

18.13 Case-Based Questions

A school robotics club is building a small robot to carry printed papers along the corridor between the science block and the office. The corridor floor is smooth and level, but the doorway at the office end has a raised threshold \(25 \text{ mm}\) high. The design so far is as follows.

Item	Value
Total mass of robot	4 kg
Wheels	65 mm diameter, two driven, one castor
Battery pack	2200 mAh lithium polymer
Average current drawn during a trip	900 mA
Expected duty	40 trips per day, about 3 minutes each

State which locomotion type suits this corridor, and say with a reason whether the \(25 \text{ mm}\) threshold is likely to stop the robot as designed.
Calculate the running time available from one full charge, assuming that only about \(80\%\) of the pack’s capacity is usable, and state whether one charge will cover a full day’s trips.
The corridor has a glass display case along one wall and a dark rubber mat near the office door. Choose two sensors for obstacle detection and justify the pairing by referring to the conditions under which each of them fails.

A district disaster response team is deciding what to buy for use after building collapses. Two machines are offered. Machine P is a tracked robot with a camera, a thermal camera and a gas detector, driven by an operator over a tether. Machine Q is a wheeled robot that navigates autonomously from a map and reports what it finds. A typical incident involves a two-storey structure that has come down, leaving voids about \(0.5 \text{ m}\) high beneath thick concrete slabs, with a layout that nobody knows in advance, and a working window of about ninety minutes.

State which locomotion type suits this environment and justify the choice by reference to the surface the machine must cross.
Recommend a degree of autonomy for this task, justifying it in terms of how predictable the environment is and what a wrong decision would cost.
State one limitation of the machine you have recommended, and describe one practical step the team could take to work around it during an incident.