Chapter 14: Batteries and Power Requirement of Various Components

In July 1997 a machine roughly the size of a microwave oven rolled down a ramp onto the red dust of Mars. It was called Sojourner, and it was the first wheeled robot to drive on another planet. It carried a camera, a chemical analyser and six small wheels. What it did not carry was a power cable.

Across its top deck lay a flat solar panel. Beneath it sat a lithium battery that could never be recharged — once its energy was spent, it was gone for good. Everything the rover did had to be paid for out of these two sources. Driving cost energy. Warming the electronics cost energy. Sending pictures home cost energy.

So the engineers planned each day the way you might plan a journey with a fixed amount of money in your pocket. The rover moved a few metres, stopped, and let the sunlight rebuild what it had spent. Instructions were written to fit the energy available, not the other way round.

Sojourner was designed to survive about seven Martian days. It kept working for nearly three months.

Photograph

Fig. 14.0-1 – the Sojourner rover on the Martian surface, photographed from the lander; the flat solar panel across its top deck and at least two of its six wheels must be clearly visible, with the dusty terrain around it in frame. Sourcing note: use a NASA/JPL public-domain mission image; a modern artist’s rendering, a museum replica or a cropped close-up that hides the top deck is unusable, because the solar panel is the point of the picture.

Every robot you build faces a smaller version of Sojourner’s problem. The battery on your workbench holds a fixed amount of energy, can deliver only so much current at once, and will one day refuse to hold charge at all. Learning to work within those three limits is what this chapter is about.

Curiosity Corner

Q1. Why can a battery that is still almost fully charged make a robot reset the instant its motors start? Q2. The pack in your laboratory is marked 2200 mAh. What does that number actually tell you, and what does it not tell you? Q3. Two batteries give the same voltage, but one is chosen for a drone and the other for a heavy floor robot. What is the difference between them? Q4. Why should a servo motor never take its power from the microcontroller board’s own 5 V pin? Q5. If you know how much current every part of your robot draws, how do you work out how big a battery it needs — and why is the answer never exactly that number?

This chapter will answer all five of these questions.

14.1 The Robot’s Own Power Source

Every other subsystem of a robot spends energy. The sensors spend it to listen to the world, the controller spends it to think, and the motors spend it to move. None of them makes energy. Something has to supply it, and on a mobile robot that something is carried on board.

This makes the power system a subsystem in its own right, as deliberately designed as the chassis or the control program. It has to hold enough energy for the job, deliver current fast enough when the robot suddenly demands it, survive being charged and discharged hundreds of times, and do all this without adding so much mass that the robot can barely move itself.

Diagram

Fig. 14.1-1 – block diagram of a robot’s power system in relation to its other subsystems: a battery pack block on the left; an arrow labelled “electrical power” from it to a power distribution block; from that block, three arrows labelled “power” going to a controller block, a sensor block and a motor driver block; a further arrow labelled “power” from the motor driver to a motors block; thin arrows labelled “signal” running from sensors to controller and from controller to motor driver, drawn in a different line style to show that signal paths are not power paths

Notice in Fig. 14.1-1 that power and signal follow different paths. A sensor sends the controller a small signal, but it draws its power from the same source the motors do. Much of the practical trouble in robotics comes from forgetting that these two paths meet inside one battery.

14.1.1 Why a Mobile Robot Cannot Be Plugged In

An industrial arm bolted to a factory floor does not carry a battery. It is wired into the building’s supply through a control cabinet, and it will run for years without anyone thinking about energy storage at all. Its work envelope is fixed, so a permanent cable costs it nothing.

A mobile robot has no such luxury. A cable that follows it would snag on shelving, twist as the robot turned, limit how far it could travel and trip anyone walking past. A drone cannot trail a cable at all. The moment a machine has to move freely, its energy has to move with it.

Carrying energy changes the engineering completely. The battery has mass, and that mass must be lifted, accelerated and braked by the very motors it powers. It occupies volume that could have held a sensor. It sets a hard limit on how long the robot can work before it stops. Sojourner’s engineers planned a Martian day around the energy available; you will plan a workshop session around the pack on your bench in exactly the same spirit.

Batteries also supply direct current (DC) — current that flows steadily in one direction — which is what almost every robotic component expects. The mains supply in a building is alternating current, and converting it safely is a task for equipment designed and certified for the purpose, not for a school workbench.

Safety Note

All practical work in this chapter is done at battery voltages, typically between 3.7 V and 12 V. Never connect any part of a robot to a mains socket, and never open, modify or repair a mains-powered charger or adaptor. Mains voltage is high enough to be fatal, and the risk is not reduced by care or experience.

What the power system must guarantee

Three separate promises are being made when a battery is chosen, and a battery can keep one of them while breaking another.

The first is energy: enough stored to finish the task. The second is current: enough delivered at the instant the motors start, without the voltage collapsing. The third is life: enough charge and discharge cycles that the pack is still usable next term. A pack that stores plenty of energy but cannot supply a sudden surge is as useless as a pack that has gone flat.

14.1.2 Cells, Batteries and Packs

Everyday speech treats “cell” and “battery” as the same thing. In engineering they are not, and the distinction matters as soon as you start joining them together.

A cell is the single electrochemical unit — one anode, one cathode, one electrolyte — and its voltage is fixed by the chemistry inside it, not by its size. A large cell and a small cell of the same chemistry give the same voltage; the large one simply holds more charge.

Definition

A cell is the basic electrochemical unit of a battery, consisting of a positive electrode, a negative electrode and an electrolyte, whose voltage is determined by the chemistry of the materials used.

A battery is properly a set of cells joined together, and in robotics the assembled unit — cells, casing, connector and any protective circuit — is usually called a battery pack. The 2200 mAh pack in your laboratory is not one cell. It is several, wired in a particular arrangement and sealed into one block.

Joining cells in series and in parallel

Cells are joined in two ways, and each way changes something different.

Joining cells in series — positive terminal of one to negative terminal of the next — adds their voltages. Two cells of 3.7 V in series give 7.4 V. The charge that flows through the string is the same charge flowing through every cell, so the capacity does not change.

Joining cells in parallel — all positives together, all negatives together — keeps the voltage the same and adds the capacity. Two cells of 1100 mAh in parallel behave as one cell of 2200 mAh at the same voltage, and they can also share the current between them.

Diagram

Fig. 14.1-2 – two cell arrangements drawn side by side, each cell shown as a standard cell symbol with its positive and negative terminals marked. Left: two cells in series, positive of the first joined to negative of the second, with the pack terminals labelled and annotated “3.7 V + 3.7 V = 7.4 V, capacity unchanged at 1100 mAh”. Right: two cells in parallel, both positives joined and both negatives joined, annotated “voltage unchanged at 3.7 V, 1100 mAh + 1100 mAh = 2200 mAh”. Below both, a third small drawing of four cells as two parallel pairs joined in series, labelled 2S2P

Packs are described by how many cells are in series and how many in parallel. A pack written as 2S is two cells in series; 3S is three in series; 2S2P is two parallel pairs joined in series, four cells in all. The S number tells you the voltage, and the P number tells you how the capacity was built up.

Example 14.1

voltage and capacity of a 2S2P lithium-ion pack

Given: four identical lithium-ion cells, each of rated voltage 3.7 V and capacity 1100 mAh, wired as 2S2P.

Find: the pack voltage and the pack capacity.

Method: cells in parallel keep the voltage of one cell and add capacities; cells in series add voltages and keep the capacity of one branch. Deal with the parallel pairs first, then the series connection between them.

Each parallel pair: voltage \(= 3.7\ \text{V}\), capacity \(= 1100 + 1100 = 2200\ \text{mAh}\).

Two such pairs in series: voltage \(= 3.7 + 3.7 = 7.4\ \text{V}\), capacity \(= 2200\ \text{mAh}\).

Answer: the pack is rated 7.4 V, 2200 mAh. Check: the arrangement uses four cells, so the total stored energy must be four times that of one cell. One cell holds \(3.7 \times 1.1 = 4.07\ \text{Wh}\), so four hold \(16.28\ \text{Wh}\); the pack figures give \(7.4 \times 2.2 = 16.28\ \text{Wh}\). The two agree, which confirms that no charge or voltage has been counted twice.

Common Error

expecting a series connection to increase capacity What students do: wire two 1100 mAh cells in series and record the pack as 7.4 V, 2200 mAh. What happens: the robot runs for about half the time expected, and a runtime calculation based on 2200 mAh is wrong by a factor of two. The fix: series adds voltage only, so the pack is 7.4 V, 1100 mAh. Capacity is added by parallel connection, because only then does the load current divide between two paths.

14.1.3 Voltage, Current, Capacity and Energy

Four quantities describe everything a battery does, and confusing any two of them will ruin a design. It helps to picture water in a pipe before naming them.

Voltage is like the pressure pushing the water along. Current is the rate at which water actually flows. A tank’s contents are like the stored charge — a fixed amount that runs down as it is used. And the useful work the water can do depends on both how much there is and how hard it is pushed.

Voltage, measured in volts (V), is the electrical push a source provides. Current, measured in amperes (A) or milliamperes (mA), is the rate of flow of charge. A component’s demand is always stated as a pair: an operating voltage it must be given, and a current it will draw at that voltage.

Table

Power is the rate at which a component consumes energy, and it depends on both the voltage across it and the current through it:

\[P = V \times I\]

where \(V\) is in volts, \(I\) is in amperes and \(P\) is in watts. A sensor at 5 V drawing 20 mA is consuming \(5 \times 0.020 = 0.1\ \text{W}\). A motor at 6 V drawing 0.5 A is consuming 3 W — thirty times as much, which is why the motors, not the sensors, decide the size of a pack.

Capacity is charge, not energy

The number printed on a pack — 1000 mAh, 2200 mAh, 7 Ah — is its capacity, and this is the quantity students most often misread.

Definition

The capacity of a battery is the total charge it can deliver before it is discharged, measured in ampere-hours or milliampere-hours, quoted for a stated discharge rate and stated end-of-discharge voltage.

An ampere-hour is simply one ampere flowing for one hour. So 2200 mAh means 2.2 A for one hour, or 1.1 A for two hours, or 0.22 A for ten hours. Note the conditions in the definition: pull the charge out much faster than the manufacturer’s stated rate and you will get less than the printed figure, because some of the energy is lost as heat inside the cells themselves.

Capacity alone does not tell you how much energy a pack holds, because it says nothing about voltage. Energy is found by multiplying capacity by the pack’s rated voltage:

\[E = V \times Q\]

where \(Q\) is in ampere-hours and \(E\) is in watt-hours. The 7.4 V, 2200 mAh pack from the worked example above therefore stores \(7.4 \times 2.2 = 16.28\ \text{Wh}\), which is usually written as about 16.3 Wh.

This is worth holding on to, because it explains a comparison that looks strange at first sight. A 12 V lead-acid battery rated 7 Ah stores \(12 \times 7 = 84\ \text{Wh}\), more than five times the energy of the 16.3 Wh lithium-ion pack — and yet, as the next sections will show, nobody puts it on a drone.

Curiosity Corner

Q2. The pack in your laboratory is marked 2200 mAh. What does that number actually tell you, and what does it not tell you?

A. It tells you the charge the pack can deliver in total — 2.2 A for one hour, or 1.1 A for two hours, measured at the manufacturer’s stated discharge rate. It does not tell you the energy stored, because that also needs the voltage: at 7.4 V the same 2200 mAh is 16.3 Wh, while at 11.1 V it would be 24.4 Wh. It does not tell you how much current the pack can safely deliver at any one instant, which is a separate rating. And it does not tell you how long your robot will run, because that depends on what your robot draws.

14.2 Characteristics That Describe a Battery

A battery is not chosen by its name. It is chosen by a handful of numbers on its label and in its datasheet, each of which answers a different question a designer has to ask.

How much push does it give? How much can it store, and how heavy is that store? How fast can it give it up? How many times can it be refilled? And what does it cost — in money, in mass and in risk? The characteristics in this section are the standard answers to those questions, and they are the language in which every battery, of any chemistry, is described.

14.2.1 Nominal Cell Voltage and Pack Voltage

A cell’s voltage is not a single fixed number. It is highest when the cell is full, falls steadily as charge is drawn out, and drops sharply near the end. Plotting terminal voltage against how much charge has been removed gives the cell’s discharge curve, and it is the honest picture of what the cell actually does.

Diagram

Fig. 14.2-1 – discharge curves: graph with “charge removed, from full on the left to empty on the right” on the horizontal axis and “terminal voltage per cell (V)” on the vertical axis. Two labelled curves drawn: a lithium-ion cell starting at about 4.2 V, staying nearly level near 3.7 V across most of the graph, then falling steeply to 3.0 V at the right-hand end; a lead-acid cell starting at about 2.1 V and sloping gently down to about 1.75 V. Each curve labelled with its chemistry, the flat middle region annotated “nominal voltage” and the right-hand end annotated “cut-off voltage”

Because the voltage varies, manufacturers quote a single representative figure taken from the flat middle of the curve. This is the nominal voltage, and it is what appears on the label.

Definition

The nominal voltage of a cell is the representative average voltage it supplies over most of its discharge, fixed by the chemistry of the cell and quoted under stated discharge conditions.

A lithium-ion cell has a nominal voltage of about 3.6 V to 3.7 V. It leaves the charger at roughly 4.2 V and must not be taken below about 3.0 V. A lead-acid cell has a nominal voltage of 2.0 V, which is why a car-type battery with six cells in series is called a 12 V battery.

The pack voltage is simply the nominal voltage of one cell multiplied by the number of cells in series. Two lithium-ion cells give 7.4 V, three give 11.1 V, and six lead-acid cells give 12 V. This is why robotic supplies come in the odd-looking values they do: they are not chosen, they are what the chemistry produces.

The lower end of the curve carries its own name. The cut-off voltage is the voltage below which a cell must not be discharged, and it is set by the manufacturer to protect the chemistry, not by how much energy is left. How far along the curve a pack currently sits is its state of charge, usually spoken of as a percentage of full.

Try Yourself

With a digital multimeter set to DC volts, measure the open-circuit terminal voltage of a fully charged lithium polymer pack and of one that has just been used, and compare both with the nominal voltage printed on the label. Record which reading is above the nominal figure and which is below, and by how much.

14.2.2 Capacity and Energy Density

Capacity, as section 14.1.3 established, is the charge a pack can deliver, and multiplying it by the nominal voltage gives the energy in watt-hours. For a mobile robot, though, the raw energy figure is only half the story. What matters is how much mass had to be carried to obtain it.

That ratio is the energy density, and it is the single characteristic that decides which chemistry flies and which one stays on the ground.

Definition

Energy density is the energy a battery stores per unit of its own mass, measured in watt-hours per kilogram (Wh/kg).

Typical figures at cell level are about 150 Wh/kg to 250 Wh/kg for lithium-ion, and about 30 Wh/kg to 50 Wh/kg for lead-acid. These are typical values and vary with the manufacturer and the exact chemistry; a finished pack, with its casing, connector and protective circuit, always works out somewhat lower than the bare cells.

Example 14.2

mass of battery needed to store the same energy in two chemistries

Given: a robot requires 100 Wh of stored energy. Typical energy densities are 200 Wh/kg for lithium-ion and 40 Wh/kg for lead-acid.

Find: the approximate mass of cells needed in each case.

Method: energy density is energy per unit mass, so mass \(= E / \text{energy density}\). The units confirm the arrangement: \(\text{Wh} \div (\text{Wh/kg}) = \text{kg}\).

Lithium-ion: \(m = \dfrac{100\ \text{Wh}}{200\ \text{Wh/kg}} = 0.5\ \text{kg}\)

Lead-acid: \(m = \dfrac{100\ \text{Wh}}{40\ \text{Wh/kg}} = 2.5\ \text{kg}\)

Answer: about 0.5 kg of lithium-ion cells, or about 2.5 kg of lead-acid cells. Check: the energy densities are in the ratio 200 : 40, that is 5 : 1, so the masses should come out in the ratio 1 : 5. They do — 0.5 kg against 2.5 kg. The magnitudes are also sensible: a 2.5 kg lead-acid block is about the size and weight of a small brick, which matches what a 12 V, 7 Ah battery actually feels like in the hand.

Two kilograms of difference is nothing to a robot rolling across a workshop floor. To a drone that must lift its entire mass off the ground continuously, it is the difference between flying and not flying.

There is a second, quieter point hidden in the capacity figure. The printed capacity is measured at a stated, fairly gentle discharge rate. Draw the charge out much faster and you will recover noticeably less than the label promises, because energy is lost as heat inside the cells. The effect is mild in lithium-ion cells and pronounced in lead-acid ones, so a lead-acid battery discharged rapidly delivers well below its rated ampere-hours.

14.2.3 Discharge Rate and the C-Rating

Capacity tells you how much charge is stored. It says nothing about how quickly that charge may be taken out, and a robot’s motors take charge out in sudden bursts.

Discharge rates are therefore expressed as multiples of the pack’s own capacity, using the C-rating. A rate of 1C is a current numerically equal to the capacity, so a 2200 mAh pack discharged at 1C is supplying 2.2 A and would in principle empty in one hour. A rate of 10C is ten times that current for one-tenth of the time.

Definition

The C-rating of a battery is its maximum permitted discharge current, expressed as a multiple of the numerical value of its rated capacity; a current of 1C empties a fully charged pack in one hour.

Table

Table 14.2 – maximum continuous discharge current for a 2200 mAh pack at different C-ratings, showing how the same stored charge can be released at very different rates | C-rating | Multiplier applied to 2.2 Ah | Maximum continuous current | Time to empty at that current | |—|—|—|—| | 1C | \(1 \times 2.2\) | 2.2 A | 1 hour | | 2C | \(2 \times 2.2\) | 4.4 A | 30 minutes | | 10C | \(10 \times 2.2\) | 22 A | 6 minutes | | 20C | \(20 \times 2.2\) | 44 A | 3 minutes |

Read Table 14.2 carefully, because it is easy to draw the wrong conclusion from it. A high C-rating does not mean more energy is stored; every row of the table describes the same 2200 mAh. It means only that the pack is built to release that same charge more violently without harming itself.

Internal resistance and voltage sag

Why should there be any limit at all? Because no cell is a perfect source. Every cell has a small internal resistance — the resistance of its own electrodes and electrolyte — and the current the robot draws must pass through it.

When current flows, some voltage is lost across that internal resistance, so the voltage appearing at the terminals is lower than the voltage the chemistry is producing. This drop is called voltage sag, and it grows in proportion to the current drawn. A pack that reads 7.4 V with nothing connected may read 6.6 V the instant two motors start.

Diagram

Fig. 14.2-2 – voltage sag under a load pulse: graph with time on the horizontal axis and terminal voltage on the vertical axis. A steady line at 7.4 V labelled “no load”; at a marked instant labelled “motors switched on” the line drops sharply to about 6.6 V and stays low for the duration of a shaded band labelled “motor starting current”; when the band ends the line rises back to just below 7.4 V. The vertical gap between the two levels labelled “voltage sag”; a note alongside reading “sag increases with current drawn and with internal resistance”

A pack sold with a high C-rating is one built with low internal resistance, so it sags less under a heavy pulse. This single fact explains a great deal of unexplained robot behaviour, as later sections will show.

Curiosity Corner

Q1. Why can a battery that is still almost fully charged make a robot reset the instant its motors start?

A. because a reset is caused by voltage, not by stored charge. A motor draws several times its running current in the moment it starts turning, and that surge has to pass through the pack’s internal resistance. The voltage lost there is subtracted from what reaches the robot, so the supply sags — often by a volt or more. If it sags below the voltage the controller needs to keep running, the controller restarts, even though the pack is nearly full. A pack with a higher C-rating, which is a pack with lower internal resistance, sags less under the same surge.

14.2.4 Cycle Life and Self-Discharge

A battery is not consumed in one use; it is consumed slowly over many. Each full discharge and recharge is one cycle, and the number of cycles a pack survives before its usable capacity has fallen noticeably is its cycle life.

Definition

Cycle life is the number of complete charge and discharge cycles a battery can undergo before its usable capacity falls to a stated fraction of its original rating, commonly 80 per cent, under stated conditions of temperature and depth of discharge.

Typical figures are about 500 to 1000 cycles for lithium-ion and about 200 to 500 cycles for lead-acid, both depending heavily on how deeply the pack is discharged each time. That last condition is important enough to have its own name. The depth of discharge (DOD) is the percentage of the pack’s capacity removed before it is recharged, and shallow cycles are gentler than deep ones. A lead-acid battery routinely taken down to 80 per cent DOD will fail far sooner than one held to 50 per cent, which is why lead-acid systems are usually sized so that only about half the rated capacity is ever used.

Batteries also lose charge while doing nothing at all. This self-discharge is caused by slow internal chemical activity, and it is quoted as a percentage of capacity lost per month. Lithium-ion cells lose roughly 2 to 5 per cent per month and lead-acid cells roughly 3 to 5 per cent per month, both measured near room temperature; in a hot store room the rate rises steeply for either chemistry.

There is a further loss that has nothing to do with use. Lithium-ion cells age chemically whether they are cycled or not, so a pack bought three years ago and left on a shelf will hold less than its rated capacity even if it has never powered anything.

Common Error

running a lithium pack until the robot stops What students do: keep testing until the motors slow, stall and the robot finally goes dead, then put the pack on charge. What happens: the cells have been taken below their cut-off voltage. The pack may refuse to charge afterwards, and even if it does, its capacity is permanently reduced and its internal resistance permanently raised. The fix: stop the run while the robot is still behaving normally, and treat the cut-off voltage — not “the robot stopped” — as the end of the discharge, because the sharp fall at the end of the discharge curve gives almost no warning.

14.2.5 Weight, Safety and Cost

Three characteristics remain, and none of them appears in an equation. They decide as many designs as the electrical figures do.

Weight follows directly from energy density, but its consequences are mechanical. A heavy pack raises the torque the drive motors must produce, lengthens the braking distance, raises the load on the bearings and, if mounted high, makes the robot easier to topple. On a flying machine it is subtracted directly from the payload the robot could otherwise carry. On a large ground robot that has to be stable anyway, a heavy pack low in the chassis is closer to a benefit than a cost.

Safety concerns the ways a battery can fail dangerously rather than merely stop working. Lithium cells store a great deal of energy in a small, light package, and that is exactly what makes overcharging, short-circuiting, crushing or puncturing them hazardous: the stored energy comes out rapidly as heat, and the cell can vent, swell or catch fire. Lead-acid batteries contain metallic lead and sulfuric acid, so their hazards are chemical — leakage, corrosion and the flammable gas released during charging. Neither chemistry is unsafe when handled as intended, and both are unforgiving when it is not.

Safety Note

A pack that is swollen, dented, punctured or has damaged leads must never be charged or connected to anything. Hand it to your teacher for isolation and safe disposal. Never store a pack loose among metal objects such as screws or tools, because anything bridging its terminals creates a short circuit through a source able to supply tens of amperes.

Cost is usually quoted per watt-hour of storage rather than per battery, since that is what allows two very different packs to be compared fairly. Lead-acid is markedly cheaper per watt-hour, which is why it survives in applications where mass does not matter. For a school laboratory, cost also has a second face: a chemistry that tolerates rough handling and simple charging equipment is cheaper in practice than one that demands a specialised charger and careful supervision, whatever the label price says.

These three characteristics are where engineering judgement enters. The electrical figures can be compared arithmetically; weight, safety and cost have to be weighed against what the robot is actually for.

14.3 Lithium-Ion Batteries

If you have charged a phone, flown a drone or seen an electric scooter at a charging point, you have already met this chemistry. The lithium-ion battery (Li-ion) is the default choice wherever energy has to be carried rather than merely stored, and it earned that position by scoring well on the one characteristic mobile machines care about most: energy per unit mass.

14.3.1 Working Principle

The name is a good description of the mechanism. A lithium-ion cell works by moving lithium ions back and forth between its two electrodes, and nothing is used up in the process — which is precisely why the cell can be recharged.

The negative electrode, the anode, is usually made of graphite. The positive electrode, the cathode, is a lithium metal oxide. Between them sits the electrolyte, a liquid or gel that lithium ions can travel through, and a thin porous separator that keeps the two electrodes from touching while still letting ions pass.

When the cell discharges, lithium ions leave the anode, cross the electrolyte and lodge in the cathode. The electrons they leave behind cannot follow them through the electrolyte, so they travel the long way round — out through the external circuit, through the robot’s motors and sensors, and back to the cathode. That flow of electrons through the outside world is the current the robot uses.

Diagram

Fig. 14.3-1 – cross-section of a lithium-ion cell during discharge: a rectangle divided into three vertical regions labelled “anode (graphite)”, “separator”, and “cathode (lithium metal oxide)”, with the surrounding space labelled “electrolyte”. Inside the cell, arrows labelled “lithium ions” run from anode to cathode through the separator. Outside the cell, a wire runs from the negative terminal through a labelled load block back to the positive terminal, with arrows labelled “electrons” showing the external flow. A caption arrow marked “discharge” indicates the direction; a second, dashed set of arrows in the reverse direction is labelled “charging”

Charging drives the process backwards. An external supply pushes current in the opposite direction, forcing the lithium ions out of the cathode and back into the anode, where they wait to be used again. Because the electrodes host the ions rather than being consumed by them, this can be repeated hundreds of times before the materials degrade appreciably.

14.3.2 Characteristics

The characteristics named in section 14.2 take particular values for this chemistry, and they hang together as a set rather than as a list.

Table

Reading Table 14.3 as a whole, three consequences stand out.

The first is the flat discharge curve already seen in Fig. 14.2-1. A lithium-ion cell holds close to its nominal voltage across most of its discharge, so a sensor or controller powered from it sees a nearly steady supply almost until the end. Circuits that misbehave as their supply drifts are therefore easier to design around.

The second is that the high cell voltage does useful work in the pack arrangement. Because one cell already gives 3.7 V, only two are needed for 7.4 V and three for 11.1 V. A lead-acid pack needs six cells to reach a comparable voltage, and every extra cell adds a connection that can fail.

The third is that high efficiency and low self-discharge together mean that most of the energy put in during charging is still available days later. A robot charged on Friday will very nearly be ready on Monday.

14.3.3 Applications

Lithium-ion packs are chosen wherever the mass of the power source is itself a problem, and each application chooses it for a slightly different reason.

Drones and other unmanned aerial vehicles (UAV) are the clearest case. Every gram of battery must be lifted continuously by the propellers, so the chemistry with the highest energy density gives the longest flight, and no other characteristic comes close in importance.

Autonomous mobile robots and automated guided vehicles (AGV) in warehouses use lithium-ion for a different reason: fast charging and high cycle life. A vehicle that can take a short top-up charge between tasks, rather than being taken out of service for hours, keeps working through the shift.

Service robots such as floor cleaners rely on the flat discharge curve and low self-discharge, so that the machine performs the same way at the end of a cleaning cycle as at the start, and still has charge after standing idle for a week.

Humanoid and research robots carry many motors, a substantial onboard computer and a great deal of sensing, all of which must be fed from a pack the machine itself carries and balances. Here the compactness matters as much as the mass.

Electric vehicles and self-driving platforms use the same chemistry at a much larger scale, and robotics has benefited from that: the cells, chargers and protection electronics developed for vehicles are what made small lithium-ion packs cheap and widely available.

14.3.4 Drawbacks

Everything that makes lithium-ion attractive comes from packing a lot of energy into a small, light space, and that is also the source of every drawback it has.

The most serious is thermal sensitivity. A cell that is overcharged, short-circuited, crushed or punctured can release its stored energy rapidly as heat, and the heat can accelerate further reactions inside the cell — a process called thermal runaway — leading to swelling, venting or fire. This is not a remote possibility to be mentioned and forgotten; it is the reason lithium packs are handled under the procedures set out in section 14.5.3.

Safety Note

A lithium pack that is swollen, dented, punctured or warm without having been used has failed and must never be charged or connected again. Report it to your teacher, do not attempt to open or discharge it yourself, and keep it away from anything flammable until it is disposed of through the school’s proper channel.

Because of this, a lithium-ion pack is rarely used bare. Almost every robotic pack includes a battery management system (BMS), a small protective circuit that disconnects the pack if it is overcharged, over-discharged or short-circuited, and that keeps the individual cells at matching voltages.

Exam Corner

Q. If all the cells in a pack are identical, why do they need to be balanced?

A. They are never quite identical. Small differences in manufacture, temperature and ageing make some cells accept and release charge slightly faster than others, and those differences accumulate over many cycles. The pack is then limited by its weakest cell: while the pack’s total voltage still looks correct, one cell may be pushed above its safe limit during charging or dragged below its cut-off during discharge. Balancing brings the cells back to the same state of charge so that no single cell is abused.

Two further drawbacks are less dramatic but shape planning. Lithium-ion cells age chemically whether they are used or not, so a pack loses capacity on the shelf, and the cut-off voltage must be respected absolutely — there is no equivalent of squeezing the last few minutes out of a torch battery. Finally, the chemistry costs more per watt-hour than lead-acid, and multi-cell packs require a charger designed to balance cells rather than any general-purpose supply.

System Profile

lithium-ion battery Working principle: lithium ions move reversibly between a graphite anode and a lithium metal oxide cathode through an electrolyte, while the electrons that balance them travel through the external circuit and do the useful work. Charging drives the ions back to the anode; the electrodes host the ions rather than being consumed, which makes the cell rechargeable. Components: anode, cathode, electrolyte, separator, cell casing or pouch, terminals, and a battery management system in the assembled pack. Advantages: high energy density, so long runtime for low mass; high cell voltage, so few cells are needed; flat discharge curve, giving a steady supply voltage; low self-discharge and high charge–discharge efficiency; fast charging and long cycle life. Limitations: risk of fire or venting if overcharged, punctured or crushed; requires protective circuitry and a balance charger; must never be discharged below its cut-off voltage; loses capacity with age even when unused; higher cost per watt-hour than lead-acid. Where it is used: drones and other unmanned aerial vehicles, autonomous mobile robots and automated guided vehicles, service robots, humanoid and research platforms, and electric and self-driving vehicles.

14.3.5 The Lithium Polymer Pack in the School Laboratory

The packs on your laboratory shelf, marked 1000 mAh and 2200 mAh, are almost certainly labelled lithium polymer (Li-Po). It is worth being clear about what that name means, because it is not a third chemistry standing alongside lithium-ion and lead-acid.

A lithium polymer cell is a lithium-ion cell. It uses the same lithium chemistry and gives the same 3.7 V nominal, the same 4.2 V full charge and the same 3.0 V cut-off. What differs is the packaging: instead of a rigid metal can holding a liquid electrolyte, the cell uses a gelled polymer electrolyte sealed inside a soft foil pouch.

That change of packaging buys two things. Removing the metal can removes mass, improving the energy stored per unit mass a little further. And a pouch can be made flat and rectangular in almost any proportion, so the pack can be shaped to fit the space a robot has rather than the other way round.

Pouch cells are also built with very low internal resistance, so they support high C-ratings and heavy current pulses without sagging badly. That is why they dominate quadcopters, racing models and any robot whose motors start abruptly.

Photograph

Fig. 14.3-2 – a lithium polymer pack of the type used in a school robotics laboratory, photographed against a plain background: the soft foil pouch construction must be visible, together with the two thick discharge leads ending in the main connector and the separate thin multi-wire balance connector. The printed label showing capacity in mAh, cell count and C-rating must be legible. Sourcing note: a stock or school-taken photograph of a plain, unbranded pack is preferred; images of swollen or damaged packs, or of packs connected to a charger, are unusable here as this figure is about identifying a healthy pack and its two connectors.

The costs of the pouch are mechanical. Without a metal can, the cell is easy to damage by bending, dropping or trapping under a chassis plate, and an over-stressed cell swells visibly. Cycle life is somewhat shorter, especially when the pack is regularly worked at a high C-rate. Charging must be done on a balance charger through the small connector visible in Fig. 14.3-2, which lets the charger see and correct each cell individually.

Common Error

connecting the balance lead to the robot What students do: plug the small multi-wire balance connector into the robot’s power input, because it fits the header on the board more neatly than the thick main connector does. What happens: the balance wires are thin, intended only for sensing individual cell voltages at very low current. Drawing motor current through them overheats the wiring, may melt the connector, and can short adjacent cells together inside the pack. The fix: the robot is always powered from the two thick discharge leads. The balance connector goes to the charger and to nothing else.

14.4 Lead-Acid Batteries

The lead-acid battery is the oldest rechargeable chemistry still in everyday use, and it has survived a century and a half of competition for two stubbornly practical reasons: it is cheap, and it can deliver enormous current on demand. Almost every vehicle on the road carries one, and so do a good many large ground robots.

It is the opposite of lithium-ion in almost every respect. Where lithium-ion is light, expensive and delicate, lead-acid is heavy, inexpensive and hard to hurt. Neither is better; they answer different questions.

14.4.1 Working Principle

A lead-acid cell has a positive plate of lead dioxide (\(\text{PbO}_2\)) and a negative plate of spongy lead (\(\text{Pb}\)), both immersed in a dilute sulfuric acid (\(\text{H}_2\text{SO}_4\)) electrolyte.

During discharge, both plates react with the acid. Each is converted to lead sulfate (\(\text{PbSO}_4\)), and water is produced, which means the acid becomes more dilute as the battery empties. Charging drives the reaction backwards, restoring the original plate materials and the original acid strength:

\[\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightleftharpoons 2\text{PbSO}_4 + 2\text{H}_2\text{O}\]

read left to right on discharge and right to left on charging.

Diagram

Fig. 14.4-1 – cross-section of a lead-acid cell during discharge: a container labelled “dilute sulfuric acid electrolyte” holding two vertical plates, the left labelled “negative plate — spongy lead (Pb)” and the right labelled “positive plate — lead dioxide (PbO2)”, with a thin separator drawn between them. Both plates annotated “converted to lead sulfate (PbSO4) on discharge”. Terminals rise from each plate; an external wire runs from the negative terminal through a labelled load block back to the positive terminal, with arrows marked “electrons” showing the external flow, and arrows inside the electrolyte marked “ion movement”. A dashed arrow pair labelled “charging reverses the reaction”

There is an important difference from lithium-ion here. In a lithium-ion cell the electrolyte only carries ions across; in a lead-acid cell the electrolyte is a reactant and is chemically changed by use. Because the acid becomes more dilute as the battery discharges, its density falls in proportion, and in the open type of battery the state of charge can literally be measured by testing the density of the liquid.

A single lead-acid cell gives a nominal 2.0 V, which is not enough for anything on its own. Practical batteries put six cells in series inside one case to give 12 V, connected by internal links you never see.

Diagram

Fig. 14.4-2 – cut-away view of a 12 V lead-acid battery: one rectangular case divided into six compartments drawn side by side, each labelled “cell, 2.0 V nominal”, with internal links joining the positive of each cell to the negative of the next drawn across the tops of the partitions. The two external terminals marked “+” and “−” at the ends, and the whole assembly annotated “6 cells in series = 12 V nominal”

The sealed type commonly used in laboratories and small robots holds its electrolyte absorbed in a mat rather than as free liquid. It does not need topping up with water and tolerates being mounted on its side, but it still releases gas under heavy charging and is still full of acid.

14.4.2 Characteristics

The characteristic figures for lead-acid tell a consistent story: modest storage, generous delivery.

Table

Two rows of Table 14.4 deserve attention because they pull in opposite directions.

The surge current capability is the battery’s outstanding property. Its plates are large and its internal resistance is very low, so it can supply hundreds of amperes for a few seconds without its terminal voltage collapsing. That is exactly what starting a motor demands.

The rated capacity, however, is quoted at a gentle discharge — typically the current that would empty it over twenty hours. Draw it much faster and you will recover distinctly less than the printed ampere-hours, because more of the energy is lost as heat inside the battery. A 7 Ah battery asked for 7 A will not last an hour.

Exam Corner

Q. A lead-acid battery stores less energy per kilogram than almost anything else, yet it can start a car engine. How?

A. Energy stored and current delivered are different properties. Starting an engine needs a very large current for two or three seconds, which is a small amount of energy but a huge rate. The battery’s low internal resistance lets it supply that rate without sagging. Its poor energy density only shows up when it is asked to supply a modest current for a long time — which is why the same battery that turns an engine over would be a poor choice for a drone.

14.4.3 Applications

Lead-acid finds its place wherever mass is not the limiting factor, and it is often chosen for reasons that have nothing to do with the electrical figures.

Large ground robots are the main robotic application. A floor-scrubbing machine, a heavy inspection platform or a material-handling robot already weighs a great deal, is designed to be stable, and gains nothing from shedding two kilograms. Mounted low in the chassis, the battery’s mass even helps by lowering the centre of gravity.

Prototypes and hobby projects use lead-acid because it is cheap and forgiving. Batteries recovered from scooters, inverters or vehicles can be reused for bench testing, and an inexpensive charger will do the job without balancing circuitry.

Backup power supplies and stationary robots use it because the duty is exactly what lead-acid is good at: sit fully charged for long periods, then deliver a large current when called upon. Laboratory emergency supplies work the same way.

Notice the pattern in all three cases. Lead-acid is chosen when the robot does not have to carry its power very far, or when what is really wanted is a cheap, robust source of large current.

14.4.4 Drawbacks

The first drawback is the one you feel when you pick the battery up. At 30 Wh/kg to 50 Wh/kg, storing a useful amount of energy takes several kilograms, and every kilogram must be pushed around by the drive motors, braked by them, and supported by the chassis. On anything that flies, or anything that must climb, this rules the chemistry out entirely.

The second is what the battery is made of. Lead is a toxic heavy metal and sulfuric acid is corrosive; a cracked case or an overturned battery is a chemical hazard as well as an electrical one. Charging also releases hydrogen, which is flammable.

Safety Note

Charge a lead-acid battery in a well-ventilated place, never in a closed cupboard, because charging releases hydrogen gas. Never lay a tool or a wire across the two terminals: the short-circuit current is high enough to melt metal and burst the case. Any battery with a cracked case, a leak or corroded terminals is taken out of service and disposed of through an authorised collection point, never in ordinary waste.

The third drawback governs how the battery is sized. Lead-acid does not tolerate being deeply discharged and recharged repeatedly; each deep cycle costs a disproportionate amount of its cycle life. Leaving it standing in a discharged state is worse still, because the lead sulfate on the plates hardens into a form that will not convert back — a failure called sulfation — and the battery permanently loses capacity.

The practical consequence is that a lead-acid battery is normally sized so that no more than about half its rated capacity is ever used.

Example 14.3

usable energy from a 12 V, 7 Ah lead-acid battery

Given: a sealed lead-acid battery rated 12 V, 7 Ah, of mass about 2.5 kg, to be operated at a maximum depth of discharge of 50 per cent to protect its cycle life.

Find: the rated stored energy, the usable energy, and the usable energy per kilogram.

Method: rated energy is \(E = V \times Q\). Usable energy is that figure multiplied by the permitted depth of discharge. Dividing by the mass gives the usable energy density.

Rated energy: \(E = 12\ \text{V} \times 7\ \text{Ah} = 84\ \text{Wh}\)

Usable energy at 50 per cent depth of discharge: \(84 \times 0.50 = 42\ \text{Wh}\)

Usable energy per kilogram: \(\dfrac{42\ \text{Wh}}{2.5\ \text{kg}} \approx 17\ \text{Wh/kg}\)

Answer: 84 Wh stored, of which about 42 Wh is usable, giving roughly 17 Wh/kg of usable energy. Check: the rated figure of \(84 \div 2.5 \approx 34\ \text{Wh/kg}\) falls inside the 30 Wh/kg to 50 Wh/kg range in Table 14.4, so the starting numbers are consistent. Halving it for depth of discharge halves the usable figure, as expected. Set against the 150 Wh/kg to 250 Wh/kg of lithium-ion cells, the gap in practice is wider than the raw table suggests.

Common Error

sizing a lead-acid pack by its rated capacity What students do: calculate that the robot needs 5 Ah and fit a battery rated 5 Ah. What happens: the robot runs for well under the expected time, and the battery loses capacity within a few weeks of use. Two effects have been ignored — only about half the rated capacity should be used, and the rated figure itself assumes a slow discharge. The fix: size the battery at roughly twice the ampere-hours the calculation gives, and check the manufacturer’s capacity figure at a discharge rate close to the one the robot will actually draw.

The last drawback is the mirror image of an advantage. Lead-acid performs best in applications with few, deep, infrequent cycles and long periods of rest. A robot that is charged and run several times a day — precisely the pattern of a school workshop or a warehouse shift — is asking the chemistry to do the one thing it does badly.

System Profile

lead-acid battery Working principle: a positive plate of lead dioxide and a negative plate of spongy lead react with a sulfuric acid electrolyte, both plates converting to lead sulfate and releasing electrical energy as the acid is diluted. Charging from an external supply reverses the reaction and restores the original materials. Components: positive plate of lead dioxide, negative plate of spongy lead, dilute sulfuric acid electrolyte, separators, cell partitions and internal links, case and terminals. Advantages: low cost per watt-hour; very high surge current capability from low internal resistance; mechanically and electrically robust, tolerating rough handling and simple charging; no balancing circuitry needed; long shelf life when stored fully charged. Limitations: low energy density, so heavy and bulky; contains toxic lead and corrosive acid, and releases hydrogen while charging; usable capacity limited to roughly half the rating to protect cycle life; capacity falls at high discharge currents; damaged permanently by sulfation if left standing discharged; unsuited to frequent charge and discharge cycles. Where it is used: large ground robots and heavy mobile platforms, prototypes and low-budget builds, stationary robots, and backup and emergency power supplies.

14.5 Choosing and Handling a Battery

You now know both chemistries the syllabus names, each on its own terms. The engineering question is not which is better — that question has no answer — but which one answers the demands of the machine in front of you, and how it must be looked after once it is fitted.

14.5.1 Lithium-Ion Compared with Lead-Acid

Set side by side, the two chemistries differ on almost every characteristic, and in opposite directions. Table 14.5 draws the comparison in the order the characteristics were introduced.

Compare Table

Read down the table and a single pattern emerges. Lithium-ion buys lightness and convenience at the price of money and care. Lead-acid buys cheapness and toughness at the price of mass and a narrower usable range.

That is why the choice is decided by the machine and not by the chemistry. Nothing in Table 14.5 says a drone must use lithium; what says so is that a drone must lift its battery continuously, and a fivefold mass penalty simply ends the design.

Curiosity Corner

Q3. Two batteries give the same voltage, but one is chosen for a drone and the other for a heavy floor robot. What is the difference between them?

A. energy density, and what follows from it. The lithium-ion pack stores roughly five times as much energy per kilogram, so for the same stored energy it weighs about a fifth as much. A drone must hold every gram of its battery in the air continuously, so the light pack is the only one that lets it fly at all, and its cost and its need for careful charging are accepted as the price. A floor robot rolls on a flat surface, is already heavy, and is more stable with mass low in its chassis, so the lead-acid battery’s weight costs it almost nothing while its low price, robustness and simple charging are real gains. The same voltage in each case; entirely different reasons for choosing it.

14.5.2 Matching the Battery to the Robot

A battery is not selected by picking a chemistry and then finding a pack. It is selected by asking, in order, what the robot demands, and letting the demands eliminate the options.

Algorithm

selecting a battery chemistry and pack for a robot Input: the robot’s supply voltage requirement, its largest instantaneous current, its average current, the running time required between charges, the mass it can carry, and the charging equipment available. Output: a chemistry, a cell arrangement and a pack rating that satisfies every one of these. Method:

1. Determine the supply voltage the drive and logic need, and the range
   they will tolerate between a full pack and an empty one.
2. Choose the number of cells in series that keeps the pack inside that
   range at both ends of its discharge.
3. Find the largest current the robot will ever draw, including motor
   starting and stall currents, not merely its running current.
4. Estimate the average current and multiply by the required running
   time to find the charge the robot will use in one session.
5. Ask whether the robot must lift or accelerate its own battery. If it
   flies, or must climb or move quickly, energy density decides and the
   choice is lithium-ion.
6. If mass is not a constraint, compare cost, robustness and the
   charging equipment available, which will usually favour lead-acid.
7. Size the pack: its capacity must cover the charge from step 4 within
   the usable fraction for that chemistry, and its C-rating multiplied
   by its capacity must cover the current from step 3.
8. Confirm that a suitable charger for that chemistry is available, and
   that the pack physically fits and can be mounted safely.

Why it works: the demands are applied in the order in which they can eliminate options. Voltage is fixed by the components and cannot be traded; mass is fixed by the mission; cost is the only one that bends. Sizing last, once the chemistry is settled, prevents the common mistake of choosing a pack and then discovering it cannot supply the starting current. Watch out: step 3 is the one most often skipped. A robot that draws 0.6 A while running may draw 5 A for a fraction of a second as its motors start, and a pack sized only on the average current will sag, reset the controller, or overheat.

Three robots, three answers

Consider a small quadcopter carrying a camera. It must lift everything it owns, continuously, for the whole flight. Nothing else in the specification matters as much, so the chemistry is decided at step 5 and the pack is a lithium polymer of the highest C-rating the budget allows.

Consider a floor-cleaning robot working a corridor. It is heavy by design, it must run for hours, and it is recharged in a store room overnight. Mass is not a constraint, so step 6 applies: lead-acid, sized generously so that only half its capacity is used each night.

Consider a robotic arm bolted to a bench, used in a school laboratory, with a mains-powered supply available. Here the honest answer is that it may need no battery at all, and a regulated bench supply is simpler, cheaper and safer than any pack. Recognising when a battery is not required is part of the same judgement.

14.5.3 Charging, Storage and Disposal

More packs are ruined between sessions than during them. The rules below are not housekeeping; they are what keeps a pack’s rated capacity available and, in the case of lithium, what keeps it safe.

Charging a lithium pack

A multi-cell lithium pack is charged by balance charging: the charger connects both to the main leads and to the balance connector, so that it can watch each cell in the string individually and bring them all to the same voltage rather than merely filling the pack as a whole. Without this, one cell can be driven past its limit while the total pack voltage still looks correct.

The charger must be the one intended for that pack, set to the correct cell count, and set to a charging rate of about 0.5C to 1C. Fig. 14.5-1 shows how a pack is set up on the bench for charging.

Photograph

Fig. 14.5-1 – a lithium polymer pack being charged correctly on a laboratory bench: the pack sits inside an open fire-resistant charging bag or a metal tray on a clear, non-flammable surface, with both its main discharge lead and its balance lead connected to a balance charger whose display is visible. Sourcing note: the frame must show the pack away from paper, cloth and other flammable material, with nothing stacked on top of it; images showing a pack charging unattended in a drawer, on a cluttered desk, or connected by main leads only are unusable, because this figure is the model of correct practice.

Two conditions apply that students often miss. A lithium pack must not be charged when it is cold — below about 0 °C the charging reaction damages the cell permanently — and it must not be charged immediately after a hard run, while it is still warm. Let it come back to room temperature first.

Safety Note

Charge lithium packs only under supervision, on a non-flammable surface, and never leave a charging pack unattended or overnight. Charge inside a fire-resistant bag or a metal tray, away from paper, cloth and bags. Disconnect the pack as soon as the charger reports the charge complete. If a pack becomes hot, swells or gives off any smell during charging, disconnect the charger at the mains socket if it is safe to reach, and tell your teacher immediately.

Charging a lead-acid battery

Lead-acid is charged more simply, because there is nothing to balance, but it takes far longer. A proper charge ends with a slow topping-up stage that may take several hours, and cutting it short leaves the battery permanently short of capacity.

The charger must be one intended for lead-acid, which holds the battery at a fixed voltage rather than driving a fixed current into it. Charging is done in a ventilated space and never inside a closed cabinet, because hydrogen is released towards the end of the charge.

Storage between sessions

The storage rules for the two chemistries are opposites, which is exactly why they are so often confused.

Compare Table

For long storage — the end of a term, for instance — a lithium pack is left at a partial charge rather than full, because sitting at full charge ages the cells faster. Most balance chargers have a storage setting that will bring a pack to the right point automatically. A lead-acid battery, by contrast, is stored full and topped up if it is to stand for months.

Disposal

Neither chemistry goes into ordinary waste. Lead is toxic and recovered lead is recycled through an established, regulated route; lithium cells retain enough energy to start a fire in a bin lorry even when they seem flat.

A pack that has reached the end of its life, or one that has been damaged, is handed to your teacher and passed to an authorised collection point. Do not attempt to open, discharge, puncture or bury a pack, and do not take a school pack home to dispose of it.

Common Error

judging a pack by whether the robot still runs What students do: keep using a pack until the robot becomes sluggish, then charge it and carry on, term after term. What happens: a lithium pack that has been repeatedly taken to the point where the robot slows is being taken past its cut-off, and a lead-acid battery treated this way is being deep-cycled every session. Both lose capacity permanently, and the robot’s runtime shortens month by month for reasons that look like a software problem. The fix: end the run while the machine is still behaving normally, and treat a shortening runtime as evidence about the pack’s health, not about the program.

14.6 Power Requirements of Robotic Components

A battery is only half of the power system. The other half is the collection of components hanging off it, each demanding a particular voltage and drawing a current that changes from moment to moment.

The syllabus asks you to understand how those demands vary with the type, the size and the function of the component, and the range is wider than most students expect. A limit switch on a robot’s arm draws less than a milliampere. A drive motor on the same robot, at the instant it starts, can draw five thousand times as much.

14.6.1 How a Component’s Demand Is Stated

Every component’s demand is a pair of figures: the voltage it must be supplied at, and the current it will draw at that voltage.

The voltage is the simpler of the two. It is stated as a value or a narrow range, and it is not negotiable. Too little and the component behaves erratically or not at all; too much and it overheats or fails.

The current is where the difficulty lies, because it is not one number. It depends on what the component is doing at that instant, and a component’s datasheet quotes several different values for it.

Table

The important habit to build is this: capacity is sized on the current a robot draws on average, and everything else — the pack’s C-rating, the driver, the wiring, the fuse — is sized on the current it draws at its worst. Use one figure for both jobs and something will be wrong.

Duty cycle and the average current

Very few components run continuously. A servo moves for a moment and then holds; an ultrasonic sensor measures ten times a second and idles in between; a pump runs for a few seconds each minute.

The duty cycle is the fraction of time a component spends active, usually written as a percentage. Multiplying the active current by the duty cycle, and adding the idle current for the rest of the time, gives the average current the pack actually has to supply.

Example 14.4

average current drawn by a servo that moves intermittently

Given: a servo draws 250 mA while moving and 8 mA while idle. In a sorting task it is moving for 12 seconds in every minute.

Find: the average current it draws.

Method: find the duty cycle as the active time divided by the total time. The average current is the active current multiplied by the duty cycle, plus the idle current multiplied by the remaining fraction.

Duty cycle: \(\dfrac{12\ \text{s}}{60\ \text{s}} = 0.20\), that is 20%

Active contribution: \(0.20 \times 250\ \text{mA} = 50\ \text{mA}\)

Idle contribution: \(0.80 \times 8\ \text{mA} = 6.4\ \text{mA}\)

Average current: \(50 + 6.4 = 56.4\ \text{mA}\)

Answer: about 56 mA on average. Check: the answer lies between the idle figure of 8 mA and the moving figure of 250 mA, and much closer to the low end, which is right for a component active only one-fifth of the time. Note that the pack must still be able to supply the full 250 mA at the moments the servo moves — the average tells you how long the pack will last, not what it must be capable of.

14.6.2 Motors

Motors are the largest single demand on almost every robot’s power system, and they are also the least constant.

14.6.2.1 DC Motors

A direct current motor for a small robot typically runs at 6 V to 12 V; the geared motors in a school kit are usually 3 V to 6 V, while motors for large platforms may need 24 V or more. The rule is unchanged from any other component: the supply must match the motor’s rated voltage, because running it above that rating overheats the windings and running it below leaves it without enough torque to move the robot at all.

The current is the interesting part. A motor’s current is not set by the motor; it is set by how hard the motor is being asked to work.

Why current rises with load

When a motor spins, it acts partly as a generator, producing a voltage that opposes the supply. This is the back EMF, and it grows with the speed of rotation. The current that flows is decided by the difference between the supply voltage and the back EMF, divided by the resistance of the windings.

Spinning freely, the motor turns fast, the back EMF is large, the difference is small, and the current — the no-load current — is low. Loaded, it turns more slowly, the back EMF falls, the difference grows and the current rises. Held so that it cannot turn at all, the back EMF vanishes entirely and the current is limited only by the winding resistance. That worst case is the stall current, and for a small motor it is commonly five to ten times the no-load figure.

Diagram

Fig. 14.6-1 – graph of motor current against mechanical load, with “mechanical load on the shaft” on the horizontal axis from zero at the left to “stalled” at the right, and “current drawn (A)” on the vertical axis. A single curve rising from a low value at the left to a high value at the right; three points marked and labelled along it: “no-load current” at the far left, “running current under normal load” near the middle, and “stall current” at the far right. A second, dashed curve on the same axes labelled “shaft speed” falling from high at the left to zero at the right, to show that speed and current move in opposite directions

Fig. 14.6-1 explains a great deal of practical robot behaviour. A robot climbing a ramp draws more current than the same robot on the flat. A wheel jammed against a wall draws stall current continuously, which is the situation most likely to destroy a motor driver, and it produces no motion at all to warn you.

Example 14.5

running and stall current of a small DC motor

Given: a DC motor rated 6 V with a winding resistance of 3.0 Ω. At its normal running speed it generates a back EMF of 4.5 V.

Find: the current it draws when running normally, and the current it would draw if the shaft were held still.

Method: the current is the voltage actually across the winding, divided by the winding resistance. When running, that voltage is the supply minus the back EMF. When stalled there is no back EMF, so the full supply appears across the winding.

Running: \(I = \dfrac{6.0\ \text{V} - 4.5\ \text{V}}{3.0\ \Omega} = \dfrac{1.5\ \text{V}}{3.0\ \Omega} = 0.5\ \text{A}\)

Stalled: \(I = \dfrac{6.0\ \text{V}}{3.0\ \Omega} = 2.0\ \text{A}\)

Answer: about 0.5 A running, and 2.0 A stalled — four times as much. Check: the stall figure is the larger of the two, as it must be. Here the stall current is four times the running current; measured against the smaller no-load current it would be a larger multiple still, which is where the familiar figure of five to ten comes from. Note that a driver rated for 0.5 A would survive normal running and fail the first time a wheel jammed.

Because of these currents, a motor is never connected directly to a controller pin. It is driven through a motor driver — a circuit such as the L298N module in your laboratory, which takes small control signals from the controller and switches the much larger motor current from the battery. The driver also lets the controller reverse the motor, which a single pin cannot do.

One practical detail is worth knowing before you measure anything. A driver of this type drops roughly one and a half to two volts across its own output stage, so a motor fed from a 7.4 V pack through an L298N actually sees rather less than 7.4 V. If a robot runs more slowly than the arithmetic predicted, this is often why.

Try Yourself

With a digital multimeter set to measure direct current and connected in series with one BO Motor straight from the kit, record the current with the wheel spinning freely. Then, with the wheel resting lightly against a wooden block so that it slows but keeps turning, record it again. Do not hold the shaft fully stopped for more than a second, and disconnect the supply before changing any connection.

14.6.2.2 Servo Motors

A servo is a small motor packaged with gearing, a position sensor and its own control circuit, so that it moves to a commanded angle and holds it. Most hobby servos run at 4.8 V to 6 V; some larger ones are designed for 7.4 V from a two-cell lithium pack.

The angle is commanded by a timing signal from the controller, using pulse width modulation (PWM), in which the length of a repeated pulse carries the instruction. That signal is separate from the servo’s power, and this separation is the source of most servo trouble: a single controller pin can comfortably produce the signal and cannot possibly supply the power.

A servo’s current follows a pattern of its own. Idle and unloaded, it draws only a few milliamperes. Moving, or holding a load against a force, a standard servo draws roughly 100 mA to 250 mA. A high-torque servo under heavy load, or one stalled against an obstruction, can draw one to two amperes. A humanoid or a walking robot with a dozen servos moving together may demand several amperes from the pack in the same instant.

The point that follows is a hard rule rather than a recommendation. The 5 V pin on a controller board is the output of a small regulator intended for the board itself and a few sensors, typically limited to a few hundred milliamperes in total. A servo asked to hold a load exceeds that on its own.

Curiosity Corner

Q4. Why should a servo motor never take its power from the microcontroller board’s own 5 V pin?

A. because that pin is the output of a small onboard regulator, rated for the board and a few sensors — a few hundred milliamperes at most. A servo draws 100 mA to 250 mA while moving and can draw well over an ampere when it is holding a load or stalled. Asking the regulator for that much makes it drop its output voltage or shut down on over-temperature, and the controller running from the same regulator resets in the middle of the task. The servo is instead fed from the battery through its own regulated supply, and only its signal wire goes to the controller pin — with the grounds joined, so that both are measuring the pulse against the same reference.

Common Error

powering a servo from the controller board What students do: connect the servo’s red and black leads to the board’s 5V and GND pins, because the three-wire servo plug fits neatly across three header pins. What happens: the servo works while unloaded on the bench. Under load it drags the 5 V rail down, and the board resets, restarts its program and drops whatever it was doing. The fault looks like a program bug and is not one. The fix: take the servo’s power from a separate regulated supply or a battery-fed converter rated for the servo’s peak current, run only the signal wire to the controller pin, and join the grounds of the two supplies.

14.6.3 Sensors

After the motors, sensors are a relief. Almost all of them run at 5 V or 3.3 V and draw currents measured in milliamperes, so on most robots the entire sensing system costs less than one motor.

Table 14.8 gives typical figures for the sensor types named in this course. They vary considerably between modules, so treat them as an order of magnitude rather than a specification.

Table

Two rows of Table 14.8 deserve comment.

A touch sensor is simply a switch, and a switch consumes nothing at all. The tiny current it costs is the current flowing through the resistor that holds the input at a known level, and it is negligible in any power budget.

Light detection and ranging (LIDAR), at the other end, is the exception that breaks the rule that sensors are cheap. A small scanning unit contains a laser, a detector, processing electronics and a motor to spin the assembly, and it can draw as much as a small drive motor. A robot that gains a LIDAR gains a real power problem along with it.

There is a second demand that sensors make, and it is not about current. Sensors need a clean supply. A supply that dips every time a motor starts produces readings that jump for no reason the program can see, which is one more argument for the distribution arrangements in section 14.6.6.

14.6.4 Actuators

Beyond wheels and servos, robots use actuators that produce straight-line force: an arm that extends, a gripper that closes, a plate that lifts. Their power demands differ from a motor’s in one important way — they are sustained.

A linear actuator converts rotation into straight-line motion through a screw, and typically runs at 12 V or 24 V, with smaller units at 6 V to 12 V. Current draw follows the load in the same way a motor’s does: around half an ampere unloaded, a few amperes working, and up to about five amperes stalled. Because the motion is slow, the actuator may be drawing several amperes continuously for many seconds, so the battery is asked for a sustained heavy current rather than a brief surge.

A hydraulic system does not consume electricity in its cylinders at all. It consumes it in the electrically driven pump that pressurises the fluid, and such pumps typically run at 12 V or 24 V and draw from about five to fifteen amperes depending on the pressure and flow required. Hydraulics appear where very large forces are needed, which is why they belong to industrial machinery rather than to a school workshop.

A pneumatic system is the same story with air. The cylinders are driven by compressed air, and the electrical demand belongs to the compressor, commonly a 12 V motor drawing several amperes while it runs, together with small solenoid valves that switch the air and draw a few hundred milliamperes each while energised.

The prescribed component list for this course includes one actuator of this family that you will actually handle: a small submersible pump, which runs from a low-voltage supply and draws a few hundred milliamperes. It is a useful reminder that a pump, unlike a sensor, runs for as long as the task lasts.

The design lesson from all three is the same. An actuator’s demand is judged by how long it holds its current, not by how high the peak is. A five-ampere surge lasting a fraction of a second is a question for the pack’s C-rating. Three amperes lasting thirty seconds is a question for its capacity, its wiring and its heat.

14.6.5 Microcontrollers and Single-Board Computers

The controller is usually the smallest electrical load on a robot and the one least tolerant of a poor supply.

A microcontroller board such as an Arduino UNO operates at 5 V and draws roughly 50 mA on its own, with larger boards of the same family drawing a little more. Those figures apply to the board alone; every module powered through it adds to the total.

An ESP32 board runs its processor at 3.3 V and draws only a few tens of milliamperes while computing — but it also contains a radio, and transmitting is expensive. Current rises into the hundreds of milliamperes in short bursts whenever the board sends data. A supply that copes with the average and not with the bursts produces a board that works until the moment it tries to communicate.

A single-board computer (SBC) such as a Raspberry Pi is a different class of load altogether. These boards run a full operating system, and they draw from several hundred milliamperes to well over an ampere at 5 V, rising further with a camera, a display or a heavy processing task; the most recent models specify supplies rated for several amperes. They are powered from a dedicated supply or converter, never from a microcontroller board’s regulator.

Table

Why the input regulator matters

A microcontroller board can be fed a higher voltage at its VIN pin and will regulate it down to 5 V itself. That is convenient, and it is also wasteful, because the regulator on such boards is a linear regulator: it produces the lower voltage by dissipating the difference as heat.

Example 14.6

energy wasted in a board’s linear regulator

Given: an Arduino UNO drawing 50 mA is powered at its VIN pin from a 12 V supply. Its onboard linear regulator produces 5 V.

Find: the power delivered to the board, the power dissipated in the regulator, and the efficiency of the arrangement.

Method: the same current passes through the regulator and the board. Power delivered is the board’s voltage times the current; power dissipated in the regulator is the voltage dropped across it times the same current. Efficiency is the ratio of the two.

Voltage dropped across the regulator: \(12\ \text{V} - 5\ \text{V} = 7\ \text{V}\)

Power delivered to the board: \(P = 5\ \text{V} \times 0.05\ \text{A} = 0.25\ \text{W}\)

Power dissipated as heat: \(P = 7\ \text{V} \times 0.05\ \text{A} = 0.35\ \text{W}\)

Efficiency: \(\dfrac{0.25}{0.25 + 0.35} = 0.42\), that is about 42%

Answer: 0.25 W reaches the board, 0.35 W is wasted as heat, and the arrangement is about 42% efficient. Check: more power is wasted than delivered, which is expected whenever a linear regulator drops more voltage than it passes. The magnitude is small enough to be harmless at 50 mA, but the same 42% applied to a load ten times larger would mean 3.5 W of heat in a small regulator, which is why heavier loads use a switching converter instead.

The alternative is a DC–DC converter, which produces the lower voltage by switching rather than by dissipating, and typically wastes only a small fraction of the energy passing through it. On any robot where the battery voltage is well above 5 V and the 5 V load is more than a few tens of milliamperes, a converter is the correct choice.

14.6.6 Distributing Power Within the Robot

The components have now been described one at a time. Putting them on the same robot introduces problems that none of them has alone.

Keep the motor current away from the logic

Motors draw large, sharply varying currents, and every wire has a little resistance. A large current through a shared wire produces a voltage drop along it, so the controller’s supply dips each time a motor starts. If the dip is deep enough the controller resets, a failure called a brownout — the supply falls too low to run the electronics but not low enough to switch them cleanly off.

The remedy is to give the motors their own path from the battery to the driver, and to feed the logic through its own converter, so that the two share only the battery itself. Fig. 14.6-2 shows the arrangement for a simple two-motor robot.

Diagram

Fig. 14.6-2 – circuit: power distribution for a two-motor robot. A 7.4 V two-cell lithium polymer pack at the left, its positive lead through an SPST rocker switch and then a 3 A fuse to a rail labelled “7.4 V battery rail”. From that rail, one branch to the L298N motor driver module’s motor supply terminal marked +12V, and a second branch to the input of a DC–DC converter module. The converter output labelled 5 V feeds the Arduino UNO 5V pin and the supply pins of two IR sensor modules. Control wiring drawn as thin lines: Arduino UNO D5 to L298N IN1, D6 to IN2, D9 to IN3, D10 to IN4; each IR sensor output to Arduino UNO D2 and D3. The L298N output terminals OUT1/OUT2 to the left BO motor and OUT3/OUT4 to the right BO motor. A single heavy horizontal line at the bottom labelled “common ground” joining the battery negative terminal, the L298N GND terminal, the converter ground, the Arduino UNO GND pin and the ground pin of each IR sensor. An annotation beside the fuse reading “fuse and switch in the positive lead, before any branch”

Join the grounds

Notice in Fig. 14.6-2 that every ground meets on one line. This is the common ground, and it is not optional.

A signal voltage means nothing by itself; it means something only relative to a reference. When the controller sends a 5 V pulse to the motor driver, the driver decides whether that is a high or a low by comparing it with its own ground. If the two grounds are not joined, the two circuits have no agreed reference, and the driver reads nonsense — sometimes working, sometimes not, in a way that is very difficult to diagnose.

The rule is simple: any two circuits that exchange a signal must share a ground connection, however they are powered.

Common Error

two supplies with no ground connection between them What students do: power the controller from a USB cable and the motors from a battery, and connect only the control wires between the board and the driver. What happens: the motors twitch, run at the wrong time, or do nothing, and the behaviour changes when anything is touched. The program is correct; the signals have no shared reference. The fix: run a wire from the battery’s negative terminal to a GND pin on the controller board. The grounds are joined; the signals now mean what they are meant to mean.

Protect, switch and size the wiring

Three further details finish the arrangement.

A fuse goes in the positive lead close to the battery, before any branch, chosen a little above the largest current the robot should ever draw. Its job is to open before a jammed motor or a short circuit can heat the wiring or the pack.

A main switch, also in the positive lead, lets the whole robot be isolated in one movement. On a machine with moving parts this is a safety device, not a convenience.

The wiring between the battery, the fuse, the driver and the motors carries the full motor current and must be thick enough for it; the signal wiring carries milliamperes and can be thin. A decoupling capacitor of a few hundred microfarads across the driver’s supply terminals, and smaller ones close to servos, helps by supplying the first instant of a current surge locally, so that the surge is not drawn all the way back down the wiring from the battery.

Safety Note

Disconnect the battery before changing any wiring, and switch off before picking the robot up. Secure the robot on a block so its wheels cannot touch the bench while you are testing, keep fingers, hair and sleeves clear of wheels and gears, and never hold a motor’s shaft to stop it — a stalled motor draws its full stall current and heats both itself and the driver within seconds.

Exam Corner

Q. The robot works perfectly on the bench with the wheels in the air, and resets as soon as it is put on the floor. Why?

A. In the air the motors are unloaded and draw their no-load current. On the floor they must move the robot’s mass, so the current rises sharply, and the starting surge is larger still. The extra current increases the voltage lost inside the pack and along the wiring, and the controller’s supply dips below the level it needs. Nothing in the program has changed; the load on the motors has.

14.7 Building a Power Budget

Everything in this chapter now comes together in one procedure. A power budget is a written account of what every part of a robot demands, added up and compared with what a battery can supply, and it is the calculation that decides whether a machine finishes its task or stops halfway through it.

The procedure is short. What makes it reliable is the discipline of doing every step, in order, and of being honest about the numbers that go in.

Algorithm

building a power budget for a robot Input: a complete list of the robot’s components, each with its supply voltage, its current when working and its duty cycle; the running time required between charges; the pack voltage chosen for the robot. Output: a required pack capacity and a required discharge capability, from which a pack can be selected. Method:

1. List every component that draws current, including the controller,
   the driver and anything left permanently powered.
2. For each one, record its supply voltage, its working current and
   the fraction of the time it is working.
3. Convert each component's demand to average power, allowing for the
   efficiency of any converter that feeds it.
4. Add the powers to get the robot's average power, and divide by the
   pack voltage to get the average current drawn from the pack.
5. Multiply the average current by the required running time to get the
   charge the robot will use.
6. Multiply by a safety margin to allow for surges, ageing and losses.
7. Add the largest current every component can draw at the same instant
   to get the peak demand, and divide by the capacity to get the
   C-rating the pack must have.
8. Choose a pack that meets the voltage, the capacity from step 6 and
   the C-rating from step 7, and that physically fits the robot.

Why it works: capacity answers the question “for how long?” and the C-rating answers the question “how hard?”. They are independent, and a pack is only suitable if it satisfies both. Watch out: step 3 is skipped more often than any other. If a 5 V load is counted as though its current came straight out of the pack, the budget is wrong, because a converter changes the current as it changes the voltage. Working in power rather than in current avoids the mistake entirely.

The rest of this section works the procedure through on one machine: an obstacle-avoiding robot built in a school workshop, with two driven wheels, a scanning sensor head and a required run of 45 minutes between charges.

14.7.1 Listing Every Load

The first step is the least mathematical and the most often botched. Every component that draws current goes on the list, including the ones that are easy to forget: the motor driver’s own electronics, a sensor that is powered even when it is not being read, an indicator that stays lit.

For each component, three things are recorded: the voltage it is supplied at, the current it draws while working, and the fraction of the time it works.

Table

Table 14.10 – load list for the obstacle-avoiding robot; currents are typical figures measured or taken from the component data | Component | Supply rail | Working current | Duty cycle | Average current on its own rail | |—|—|—|—|—| | Two BO Motor straight drive motors | 7.4 V, from the pack through the driver | 0.35 A each under normal load | 100% | 0.70 A | | L298N motor driver, own electronics | 7.4 V, from the pack | 20 mA | 100% | 0.02 A | | Scanning servo | 6 V, from a converter | 200 mA moving, 8 mA holding | 50% | 0.104 A | | Arduino UNO | 5 V, from a converter | 50 mA | 100% | 0.05 A | | Ultrasonic sensor | 5 V, from a converter | 15 mA | 100% | 0.015 A | | Two IR sensors | 5 V, from a converter | 15 mA each | 100% | 0.03 A |

The servo’s figure in the last column is the duty-cycle average calculated by the method of section 14.6.1: the head sweeps for half of each cycle and holds still for the other half, giving \(0.5 \times 200 + 0.5 \times 8 = 104\ \text{mA}\).

Notice that the table records the rail each component sits on, not just its current. The motors and the driver take their current straight from the pack. The servo and the 5 V devices are fed through converters, and their currents are therefore currents on the converter’s output side, which is not the same as the current they cost the pack.

14.7.2 Total Current and Required Capacity

Because the robot has three different supply rails, the loads cannot simply be added as currents. They are added as powers, and the total power is then converted into a current at the pack’s own voltage.

Each converter wastes a little of what passes through it, so the power a converter takes from the pack is the power it delivers divided by its efficiency. A typical small DC–DC converter module is around 85% efficient, and that figure is used here.

Example 14.7

average current and required capacity for the obstacle-avoiding robot

Given: the loads of Table 14.10; a 7.4 V pack; two DC–DC converters of 85% efficiency feeding the 6 V and 5 V rails; a required running time of 45 minutes.

Find: the average power, the average current drawn from the pack, and the charge the robot will use.

Method: find the average power on each rail as \(P = V \times I\). Divide the converter-fed powers by the converter efficiency to find what they cost the pack. Add all the powers, divide by the pack voltage to get the pack current, and multiply by the running time in hours to get the charge used.

Motors and driver, taken directly from the pack:

\(P = 7.4\ \text{V} \times (0.70 + 0.02)\ \text{A} = 7.4 \times 0.72 = 5.328\ \text{W}\)

Servo rail, delivered at 6 V:

\(P_{\text{out}} = 6\ \text{V} \times 0.104\ \text{A} = 0.624\ \text{W}\), so \(P_{\text{pack}} = \dfrac{0.624}{0.85} = 0.734\ \text{W}\)

Five-volt rail, delivered at 5 V to the controller and the three sensors:

\(P_{\text{out}} = 5\ \text{V} \times (0.05 + 0.015 + 0.03)\ \text{A} = 5 \times 0.095 = 0.475\ \text{W}\), so \(P_{\text{pack}} = \dfrac{0.475}{0.85} = 0.559\ \text{W}\)

Total average power drawn from the pack:

\(P_{\text{total}} = 5.328 + 0.734 + 0.559 = 6.621\ \text{W}\)

Average current from the pack:

\(I = \dfrac{P}{V} = \dfrac{6.621\ \text{W}}{7.4\ \text{V}} = 0.895\ \text{A}\)

Charge used in 45 minutes, that is 0.75 hours:

\(Q = I \times t = 0.895\ \text{A} \times 0.75\ \text{h} = 0.671\ \text{Ah} = 671\ \text{mAh}\)

Answer: the robot draws about 0.90 A on average and will use about 671 mAh in a 45-minute run. Check: the motors account for 5.3 W of the 6.6 W total — about four-fifths of the whole budget — which is what one expects on a wheeled robot and a useful sign that nothing has been mis-entered. The energy used, \(6.621 \times 0.75 = 4.97\ \text{Wh}\), is a plausible figure for a small robot running for three-quarters of an hour.

The dominance of the motors in that answer is worth pausing on. Every sensor, the controller and the driver together account for barely a fifth of the robot’s power, as Fig. 14.7-1 shows. Effort spent shaving milliamperes off the sensing while the motors run unnecessarily is effort spent in the wrong place.

Diagram

Fig. 14.7-1 – horizontal bar chart of average power drawn from the pack by each part of the obstacle-avoiding robot: bars labelled “drive motors and driver, 5.33 W”, “scanning servo including converter loss, 0.73 W”, and “controller and sensors including converter loss, 0.56 W”, drawn to scale on a common axis labelled “average power drawn from the pack (W)”; the total of 6.62 W marked at the end of the axis

14.7.3 Adding a Safety Margin

The figure of 671 mAh is the charge the robot uses if every number in Table 14.10 is exactly right and nothing unexpected happens. Neither condition is ever true.

Motors draw more on a rough floor than on a smooth one. Starting surges are not in the average. The pack has aged since it was bought and no longer delivers its rated capacity. The stated capacity itself was measured at a gentler discharge than this robot demands. And a pack run right down to its cut-off at the end of every session will not last many sessions.

A margin of 20% to 25% is standard practice, and it covers all of these together.

\[Q_{\text{required}} = 671\ \text{mAh} \times 1.25 = 839\ \text{mAh}\]

So the robot needs a pack rated at least about 840 mAh, not 671 mAh.

Curiosity Corner

Q5. If you know how much current every part of your robot draws, how do you work out how big a battery it needs — and why is the answer never exactly that number?

A. you add the average power of every load, allowing for the losses in any converter, divide the total by the pack voltage to get the average current, and multiply by the running time you need. That gives the charge the robot will use — 671 mAh in the example worked here. The answer is never exactly that number because the calculation assumes ideal conditions: it uses average currents and ignores starting surges, it assumes the floor and the load never get harder, it uses the pack’s rated capacity even though a pack delivers less as it ages and less again when discharged quickly, and it would leave the pack completely empty at the end of every run. Multiplying by a margin of 20% to 25% covers all of this. For a lead-acid battery a further allowance is needed, because only about half its rated capacity should ever be used.

Common Error

budgeting with stall currents What students do: look up the stall current of each motor, add those figures, and size the pack on the total. What happens: the pack comes out several times larger, heavier and more expensive than the robot needs, and on a small machine it may not fit at all. A robot does not run stalled; if it did, it would not be working. The fix: use average currents for capacity and peak currents for the C-rating. The two figures answer two different questions, and each belongs in its own step.

14.7.4 Checking Peak Demand Against the C-Rating

Capacity is settled. The second question is whether the pack can supply the current at the worst instant, which is the moment both motors start together while the servo is swinging.

Table

Table 14.11 – peak current tally for the obstacle-avoiding robot, taken at the instant both motors start | Load | Peak demand | Current drawn from the 7.4 V pack | |—|—|—| | Two drive motors starting | 1.2 A each at the moment of starting | 2.40 A | | L298N own electronics | 20 mA | 0.02 A | | Servo moving | 200 mA at 6 V through an 85% converter | 0.19 A | | Controller and sensors | 95 mA at 5 V through an 85% converter | 0.08 A | | Total peak | | 2.69 A |

Example 14.8

the C-rating the pack must have

Given: a peak demand of 2.69 A from Table 14.11, and a pack of capacity 1000 mAh, that is 1.0 Ah.

Find: the minimum C-rating the pack must carry, and whether a pack marked 2C would be acceptable.

Method: the maximum current a pack may supply is its C-rating multiplied by its capacity in ampere-hours. Rearranging, the C-rating required is the peak current divided by the capacity.

Required rating: \(\dfrac{2.69\ \text{A}}{1.0\ \text{Ah}} = 2.69\text{C}\)

A 2C pack could supply \(2 \times 1.0 = 2.0\ \text{A}\), which is less than 2.69 A.

Answer: the pack must be rated at least 2.7C, so a 2C pack is not acceptable. A pack of 10C or more is chosen in practice, to leave the peak well inside the pack’s capability.

Check: the answer is sensible in magnitude — a small pack asked for under three times its capacity in amperes is an ordinary demand, and lithium polymer packs sold for robotics are routinely rated far above it. Note also what happens if the pack is undersized here: the pack does not simply fail to deliver, it sags, and the controller browns out at the very moment the robot tries to move.

Choosing well above the minimum is not wasteful. A pack running far below its rated discharge has lower internal resistance in proportion to the current drawn, sags less, runs cooler and lasts more cycles.

14.7.5 Selecting the Pack

Three requirements have now been established, and a pack must satisfy all of them at once.

The voltage must suit the components. A two-cell lithium polymer pack gives 7.4 V nominal, ranging from 8.4 V charged to 6.0 V at cut-off. The L298N accepts this comfortably, and the converters feeding the 6 V and 5 V rails work across the whole range. Allowing for the driver’s own voltage drop, the 6 V motors see a little under their rating, which is acceptable and slightly reduces their top speed.

The capacity must be at least 840 mAh, from section 14.7.3.

The discharge capability must be at least 2.7C at that capacity, from section 14.7.4.

The 1000 mAh two-cell lithium polymer pack on the laboratory shelf satisfies all three, provided its printed C-rating is comfortably above 2.7C, which for a pack of this type it will be.

Confirming the choice

A selection is not finished until it is checked against the requirement it came from.

\[t = \frac{Q}{I} = \frac{1000\ \text{mAh}}{895\ \text{mA}} = 1.12\ \text{h} \approx 67\ \text{minutes}\]

That is comfortably beyond the 45 minutes required, and the difference is the margin doing its job rather than spare capacity going to waste.

Two further checks finish the selection. The pack must physically fit the chassis and be mountable where nothing can press into it, as section 14.3.5 required. And its mass — a pack of this size is well under 100 g — must be within what the robot can carry without changing the motor currents the budget assumed.

It is worth seeing how differently this ends if the same robot were built around lead-acid. The 840 mAh requirement at 7.4 V is about 6.2 Wh; allowing for the 50% depth-of-discharge limit, a lead-acid battery would have to be rated for roughly 12.4 Wh, and at 30 Wh/kg to 50 Wh/kg that is several hundred grams of battery for a robot that presently carries under a hundred. For a small mobile machine, the arithmetic makes the choice for you.

Exam Corner

Q. The budget says 45 minutes needs 671 mAh, and the pack holds 1000 mAh. Why not simply run it for 67 minutes every time?

A. Because doing so uses the margin that was put there for a reason. The extra charge is covering surges, a stiffer floor, an ageing pack and the capacity lost at heavier discharge, and it keeps the pack from reaching its cut-off at the end of each run. A pack routinely emptied to its last few per cent loses cycle life quickly, and the robot’s usable runtime then shortens month by month.

Try Yourself

Repeat the budget for the same robot with the running time raised from 45 minutes to 90 minutes, keeping the same average current and the same 25% margin. State the capacity now required, and say whether the 2200 mAh pack in the laboratory would meet it. Then say what happens to the peak-current check when the larger pack is used.

14.8 Summary

The power system

A robot’s power system is a subsystem in its own right. A stationary machine can take energy from a fixed supply; a mobile robot must carry its energy, and the mass of what it carries must then be moved by the very motors that energy feeds.
Batteries supply direct current, which is what almost every robotic component expects. All work in this chapter is done at battery voltages, never at mains voltage.
A cell is the single electrochemical unit, and its voltage is fixed by its chemistry. A battery pack is an assembly of cells with its casing, terminals and any protective circuitry.
Cells in series add their voltages and keep the capacity of one cell. Cells in parallel keep the voltage of one cell and add their capacities. A pack marked 2S2P has two parallel pairs joined in series.

The quantities

Voltage is the electrical push a source provides and is fixed by what the component requires. Current is the rate of flow of charge and is set by the load, not by the battery.
Capacity is charge, not energy. It is measured in ampere-hours or milliampere-hours, quoted at a stated discharge rate, and related to current and time by \(Q = I \times t\).
Energy stored is capacity multiplied by voltage, \(E = V \times Q\), in watt-hours. Two packs of the same milliampere-hour rating do not hold the same energy unless they are also the same voltage.
Power is the rate at which energy is used, \(P = V \times I\), in watts. Energy says how much there is; power says how fast it is being spent.

The characteristics a battery is described by

Nominal voltage is a representative figure from the flat part of the discharge curve, not the voltage the pack actually holds at any moment. A pack sits above it when full and below it when nearly empty, and the cut-off voltage is the limit below which it must not be discharged.
Energy density, in watt-hours per kilogram, decides how heavy a pack must be for the energy required. It is the characteristic that separates a chemistry that can fly from one that cannot.
The C-rating gives the maximum discharge current as a multiple of the capacity: for a 2200 mAh pack, 1C is 2.2 A. A high C-rating means the same stored charge can be released faster, not that more is stored.
Every cell has internal resistance, so drawing current makes the terminal voltage fall by that current multiplied by the resistance. This voltage sag depends on the current being drawn, not on the charge remaining, which is why a nearly full pack can still reset a controller.
Cycle life is the number of charge and discharge cycles before usable capacity falls to a stated fraction of the rating, usually 80 per cent, and it falls sharply as the depth of discharge increases. Self-discharge is the charge lost while standing idle, quoted per month and faster in warm storage.
Weight, safety and cost carry no equation, and they decide as many designs as the electrical figures do.

Lithium-ion

A lithium-ion cell stores and releases energy by moving lithium ions reversibly between a graphite anode and a lithium metal oxide cathode through an electrolyte, while the electrons that balance them travel through the external circuit and do the useful work. Nothing is consumed, which is why the cell is rechargeable.
Typical figures: 3.6 V to 3.7 V nominal per cell, about 4.2 V fully charged and about 3.0 V at cut-off, 150 Wh/kg to 250 Wh/kg, 500 to 1000 cycles, 2 to 5 per cent self-discharge per month, and above 90 per cent charge–discharge efficiency, with a nearly flat discharge curve.
It is chosen for drones and other unmanned aerial vehicles, autonomous mobile robots and automated guided vehicles, service robots, and humanoid and research platforms — in every case because weight or size is a binding constraint, and in spite of its cost.
Its drawbacks all follow from packing much energy into a small space: risk of thermal runaway if overcharged, punctured or crushed; the need for a battery management system and a matched balance charger; loss of capacity with age even when unused; and a high cost per watt-hour.
A lithium polymer pack is a lithium-ion cell in a soft pouch with a gelled polymer electrolyte. It is not a third chemistry. The pouch saves weight and allows flat shapes, and it offers almost no mechanical protection.

Lead-acid

A lead-acid cell works by a reversible reaction between a lead dioxide positive plate, a spongy lead negative plate and a dilute sulfuric acid electrolyte, in which both plates convert to lead sulfate and the acid is diluted. Unlike a lithium cell, the electrolyte is itself a reactant.
Typical figures: 2.0 V nominal per cell, so six cells in series give 12 V; 30 Wh/kg to 50 Wh/kg; 200 to 500 cycles; 3 to 5 per cent self-discharge per month near room temperature; a sloping discharge curve; and a rated capacity quoted at a slow discharge, which is not recovered at heavy currents.
Its outstanding property is surge current. Large plates and very low internal resistance let it deliver a very large current briefly without collapsing, which is what starting a heavy motor demands.
It is chosen for large ground robots and heavy platforms, prototypes and low-budget builds, and stationary and backup supplies — wherever mass is not a penalty and cost and robustness are gains.
Its drawbacks are mass and bulk, toxic lead and corrosive acid with regulated disposal, hydrogen released while charging, and permanent damage by sulfation if it is left standing discharged. Only about half its rated capacity should be used.

Choosing and handling

The chemistry is decided by the machine, not by the label. If the robot must lift or accelerate its own battery, energy density decides and lithium-ion follows. If mass is not a constraint, cost, robustness and available charging equipment usually favour lead-acid.
A multi-cell lithium pack is balance charged through its balance connector so that every cell is monitored individually, at about 0.5C to 1C, never unattended, and never while cold.
The storage rules for the two chemistries are opposites. A lithium pack is stored part-charged and cool; a lead-acid battery is stored fully charged and recharged as soon as it is used. Neither goes into ordinary waste.

What the components demand

A component’s rated voltage is not negotiable. Its current is quoted under four conditions — no-load, running, starting and stall — and each figure sizes something different.
Duty cycle is the fraction of time a component is actually working. Average current, found from the duty cycle, decides how long the robot runs; peak current decides whether it runs at all.
A motor’s current is set by its mechanical load, because the back EMF it generates falls as it is loaded and vanishes when it is stalled. Stall current is commonly several times the running current, and a motor is therefore always driven through a motor driver rather than from a controller pin.
A servo draws a few milliamperes when idle, 100 mA to 250 mA while moving or holding, and far more under heavy load or when stalled. It is never powered from the controller board’s 5 V pin, which is the output of a small regulator meant for the board itself.
Sensors are small loads individually — tens of milliamperes for infrared and ultrasonic modules, a fraction of a milliampere for a touch sensor — but they add up, and LIDAR is the exception, drawing as much as a small motor. Sensors also need a clean supply, because an analogue reading is measured against it.
Actuators demand sustained rather than momentary current, and the electrical load is often not the actuator itself but the pump or compressor that drives it.
A microcontroller board draws around 50 mA on its own; a single-board computer draws an ampere or more. A linear regulator makes its lower voltage by dissipating the difference as heat, so a DC–DC converter is used wherever the drop or the current is significant.

Distribution and budgeting

Motor current is kept off the logic path, the fuse and main switch sit in the positive lead close to the pack, and every circuit returns to one common ground — without which a signal has no shared reference and the robot behaves unpredictably.
A power budget lists every load with its rail, its working current and its duty cycle; converts the loads to average power so that rails at different voltages can be added, allowing for converter efficiency; divides by the pack voltage to obtain the average current; and multiplies by the required running time to obtain the charge used.
A margin of about 20 to 25 per cent is then added, because the calculation assumes typical figures, an unchanging load, a pack that has not aged and a discharge gentler than a robot actually demands.
Finally the peak demand is tallied and divided by the capacity to give the C-rating the pack must carry. Capacity answers how long the robot will run; C-rating multiplied by capacity answers whether it will run at all, and a pack must satisfy both.

14.9 Key Terms

AGV (automated guided vehicle) — a wheeled robot that moves goods along a route in a warehouse or factory without a driver.
Back EMF — the voltage a spinning motor generates against its own supply, which grows with speed and so limits the current the motor draws.
Balance charging — charging a multi-cell pack through its balance connector so that the charger monitors and equalises every cell individually rather than the pack as a whole.
Battery — two or more cells joined together and used as one source.
Battery pack — a complete assembly of cells with its casing, terminals, leads and any protective circuitry, treated as a single component of the robot.
BMS (battery management system) — a protective circuit in a lithium pack that disconnects it if it is over-charged, over-discharged or short-circuited, and keeps the cells at matching voltages.
Brownout — a fall in supply voltage deep enough to stop the electronics working properly but not deep enough to switch them cleanly off, usually causing a controller to reset.
C-rating — the maximum discharge current a pack may supply, expressed as a multiple of its capacity; 1C empties a full pack in one hour.
Capacity — the total charge a battery can deliver before it is discharged, in ampere-hours or milliampere-hours, quoted at a stated discharge rate.
Cell — the single electrochemical unit of a battery, whose voltage is fixed by the chemistry of its electrodes and electrolyte.
Common ground — the single conductor to which every negative and ground connection in a robot is joined, giving all its circuits one shared reference for their signals.
Cut-off voltage — the voltage below which a cell must not be discharged without permanent damage.
Cycle life — the number of charge and discharge cycles a battery survives before its usable capacity falls to a stated fraction of its rating, commonly 80 per cent.
DC (direct current) — current that flows steadily in one direction, which is what batteries supply and what almost every robotic component expects.
DC–DC converter — a switching regulator that produces a lower supply voltage from a higher one with little energy wasted as heat.
Decoupling capacitor — a capacitor fitted close to a driver or servo that supplies the first instant of a current surge locally, steadying the supply rail.
Discharge curve — the graph of a cell’s terminal voltage against the charge removed from it, showing how the voltage falls as it empties.
DOD (depth of discharge) — the proportion of a battery’s rated capacity that has been drawn out, expressed as a percentage.
Duty cycle — the fraction of a repeating period during which a component is switched on or actively working.
Electrolyte — the medium inside a cell through which ions travel between the electrodes.
Energy density — the energy a battery stores per unit of its own mass, in watt-hours per kilogram.
Internal resistance — the resistance within a cell itself, across which voltage is lost whenever current is drawn.
Lead-acid battery — a rechargeable battery using lead dioxide and spongy lead plates in dilute sulfuric acid, cheap and capable of very high surge current but heavy.
LIDAR (light detection and ranging) — a sensor that measures distance using laser light, and the one sensor whose power demand rivals a small motor’s.
Li-ion (lithium-ion battery) — a rechargeable battery in which lithium ions move reversibly between a graphite anode and a metal oxide cathode, giving high energy density.
Li-Po (lithium polymer) — a lithium-ion cell using a gelled polymer electrolyte in a soft pouch instead of a rigid can, lighter and shapeable but mechanically fragile.
Linear regulator — a regulator that produces a lower voltage by dissipating the difference as heat.
Motor driver — a circuit that takes small control signals from a controller and switches the much larger motor current from the battery, and that can reverse the motor.
No-load current — the current a motor draws while running with nothing opposing its shaft.
Nominal voltage — the representative average voltage a cell supplies over most of its discharge, by which it is named and matched to a load.
Pack voltage — the nominal voltage of one cell multiplied by the number of cells in series in the pack.
Parallel — a connection joining all positive terminals together and all negative terminals together, which keeps the voltage of one cell and adds the capacities.
Power budget — a written account of every load on a robot, its current and its duty cycle, worked through to a required battery capacity and discharge capability.
Power system — the subsystem that stores, converts and distributes the electrical energy the rest of the robot spends.
PWM (pulse width modulation) — control of a motor or servo by switching the supply on and off rapidly, so that the width of the pulses sets the average delivered.
SBC (single-board computer) — a board running a full operating system, drawing an ampere or more at 5 V, far beyond a microcontroller’s demand.
Self-discharge — the slow internal loss of charge in a battery that is standing idle, quoted as a percentage per month.
Separator — the thin porous layer that keeps a cell’s two electrodes from touching while still allowing ions through.
Series — a connection joining the positive terminal of one cell to the negative terminal of the next, which adds the voltages and keeps the capacity of one cell.
Stall current — the current a motor draws when its shaft is held so that it cannot turn, the largest current it can draw.
State of charge — how much of a battery’s capacity remains, expressed as a percentage of full.
Sulfation — the hardening of lead sulfate on the plates of a lead-acid battery left standing discharged, causing permanent loss of capacity.
Surge current — a very large current supplied briefly, such as the current that starts a heavy motor.
Thermal runaway — a self-feeding process in which a damaged or overcharged lithium cell heats itself, the heat driving reactions that produce still more heat.
UAV (unmanned aerial vehicle) — an aircraft flown without a pilot on board, including the drones used in robotics.
Voltage sag — the fall in a pack’s terminal voltage while current is being drawn, equal to that current multiplied by the internal resistance.

14.10 Objective Questions

Give the full form of each of the following abbreviations used in this chapter: BMS, DOD, PWM, LIDAR, SBC, AGV.
Fill in the blanks.

A discharge rate of 1C for a pack rated 2200 mAh is a current of ____ A.
A lead-acid battery of six cells in series has a nominal voltage of ____ V.
Cells joined in parallel keep the ____ of one cell and add their ____.
The voltage lost inside a pack when current is drawn is equal to the current multiplied by the ____.

Two packs are both marked 2200 mAh. One is rated 7.4 V and the other 11.1 V. Which statement is correct?

Both store the same energy, because the capacity is the same.
The 11.1 V pack stores more energy, because energy is capacity multiplied by voltage.
The 7.4 V pack stores more energy, because a lower voltage discharges more slowly.
Neither stores measurable energy until a C-rating is stated.

Four lithium-ion cells, each 3.7 V and 1500 mAh, are wired as two parallel pairs joined in series. The resulting pack is rated:

3.7 V, 6000 mAh
7.4 V, 1500 mAh
7.4 V, 3000 mAh
14.8 V, 1500 mAh

State whether each of the following is true or false.

A lead-acid battery should be stored fully charged, and a lithium pack should be stored part-charged.
A high C-rating means a pack stores more energy.
A servo draws almost no current while holding a position against a load.
A linear regulator wastes the voltage it drops as heat.
Two circuits that exchange a signal must share a ground connection.

Match each item in the first list with the description in the second list that fits it best.

List I	List II
a. Sulfation	i. Charge lost by a battery standing idle
b. Thermal runaway	ii. Hardening of lead sulfate on plates left discharged
c. Self-discharge	iii. Fraction of the time a component is actually working
d. Duty cycle	iv. Self-feeding heating of a damaged or overcharged lithium cell

For the assertion (A) and reason (R) below, choose the correct option.

Assertion (A): A pack that is almost fully charged can still cause a controller to reset at the instant the motors start.

Reason (R): The terminal voltage of a pack falls by an amount equal to the current drawn multiplied by the pack’s internal resistance.

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.

14.11 Check Your Concepts

Define capacity and energy density, and state the unit in which each is measured.
State what is meant by depth of discharge, and explain why it governs the sizing of a lead-acid battery more strictly than that of a lithium-ion pack.
A motor spinning freely draws far less current than the same motor driving a robot up a ramp. Explain why, and state what happens to the current if the wheel is jammed and cannot turn.
Explain, with reasons, why a servo motor is never powered from a microcontroller board’s 5 V pin, and describe the correct arrangement for powering it.
Explain the working principle of a lithium-ion cell during discharge, with a labelled sketch, and state two drawbacks of the chemistry.
A robot draws an average of 0.75 A from its pack and must run for two hours between charges. Calculate the charge it will use, and the capacity the pack must be rated at if a margin of 25 per cent is allowed. Explain what that margin is covering.
A school is building two machines: a small camera drone, and a heavy trolley robot that carries equipment along a corridor and is charged overnight in a store room. Compare lithium-ion and lead-acid for each machine against mass, cost and charging arrangements, recommend a chemistry for each, and justify both recommendations.

14.12 Diagram, Circuit & Output Reading

Two discharge curves are plotted on the same axes of terminal voltage per cell against charge removed. Curve X begins at about 4.2 V, stays nearly level for most of the plot and then falls steeply to 3.0 V. Curve Y begins at about 2.1 V and slopes down steadily to about 1.75 V.

Identify the chemistry of each curve, giving your reason.
State the cut-off voltage shown by each curve.
Explain why the state of charge of the battery represented by curve X cannot be judged reliably from a voltmeter reading.

A student wires a robot as follows. The battery positive lead goes through a main switch and a fuse to the motor supply terminal of the motor driver. A separate 5 V regulated supply, plugged into a bench socket, feeds the microcontroller board. Four signal wires run from the board’s output pins to the driver’s input pins. The battery negative terminal is connected to the driver’s ground terminal. No other connection is made between the two supplies. On test, the motors twitch, run at the wrong moments and behave differently when the wiring is touched, although the program has been checked and is correct.

Identify the single fault in this wiring.
Explain why the fault produces exactly these symptoms.
State the one connection that must be added to correct it.

A robot requires a pack of at least 1200 mAh, must supply a peak current of 6 A, and cannot carry a pack heavier than 130 g. Three packs are available.

Pack	Nominal voltage	Capacity	C-rating	Mass
P	7.4 V	2200 mAh	2C	115 g
Q	7.4 V	1000 mAh	25C	78 g
R	7.4 V	1500 mAh	20C	122 g

Calculate the maximum continuous current each pack can supply.
State which pack meets all three requirements, and explain precisely why each of the other two fails.
State what would happen in practice if the pack you rejected on its C-rating were used anyway.

A pack reads 7.4 V on a multimeter with nothing connected. With the robot’s motors running and drawing 6.0 A, the reading at the same terminals falls to 6.5 V.

Calculate the internal resistance of the pack.
The controller’s regulator needs at least 6.8 V at its input to hold its output. State whether the controller will keep running, and why.
Suggest one change to the pack specification that would reduce the sag, and explain how it works.

14.13 Case-Based Questions

A school workshop is building a line-following robot for a one-hour demonstration session. Its loads are listed below. The two drive motors are fed from the 7.4 V pack through a motor driver. Everything else is fed from a DC–DC converter of 85 per cent efficiency that produces 5 V from the pack. The laboratory holds two-cell lithium polymer packs of 1000 mAh and 2200 mAh.

Load	Rail	Working current	Duty cycle
Drive motor, left	7.4 V pack	400 mA	90%
Drive motor, right	7.4 V pack	400 mA	90%
Microcontroller board	5 V	50 mA	100%
Five infrared sensors	5 V	15 mA each	100%

Calculate the average current the robot draws from the pack, referring the 5 V loads back to the pack through the converter.
Calculate the charge the session will use, and the capacity required if a margin of 20 per cent is allowed.
State which of the two laboratory packs should be issued for the session, and justify the choice using your figures.

A farm is testing a robot that sprays a field. The machine weighs about 40 kg, drives slowly across level ground for four hours at a stretch, and returns to a shed each evening where it stands overnight beside a mains socket. Its motors and pump together consume about 300 Wh in one working session. The farm wants the running cost kept low and does not want to buy specialised charging equipment.

Recommend a battery chemistry for this machine, and justify your recommendation against the mass, cost and charging requirements stated.
If a 12 V lead-acid battery is used and no more than 50 per cent of its rated capacity may be discharged, calculate the rated capacity in ampere-hours that the battery must have.
State two handling rules that must be followed when charging and storing the battery you have recommended, giving the reason for each.