Robots in the real world

The zoo of robots: every family and what makes it special

14 min

You will learn

to place any robot in its family and to know the main challenge of each one.

Family	Movement	Examples	Main challenge
Serial arms	A chain of joints from a fixed base.	6-axis, SCARA, cobots, Cartesian gantries (pages of this site).	Singularities, flexibility, cost of a large workspace.
Parallel robots	Several chains in parallel link the base to one platform.	Delta, Stewart platform, flight simulators, fast pick and place.	Small workspace, direct-kinematic singularities.
Wheeled mobile robots	Differential, car-like, omnidirectional.	Vacuum robots, AGV/AMR, rovers (mobile and wheels pages).	Localisation, non-holonomic constraints, slip.
Tracked robots	Continuous tracks.	Bomb disposal, inspection, agriculture.	Skid steering is hard to model; wear.
Legged robots	Walk, trot, run on rough ground.	Quadrupeds (Spot, ANYmal), bipeds, hexapods.	Balance, contact planning, energy.
Humanoids	Biped with two arms and hands, made for human spaces.	Atlas, Digit, Optimus-type, Pepper.	Dynamic balance + dexterous manipulation + cost and reliability.
Aerial robots	Multirotors, fixed wings, hybrids.	Camera drones, delivery, inspection.	Short battery life, wind, regulation.
Underwater robots	Thrusters or gliders (ROV: cable, AUV: autonomous).	Pipeline inspection, ocean mapping, archaeology.	No GPS or radio, pressure, corrosion.
Space robots	Arms on stations, rovers, landers.	Canadarm2, Mars rovers.	Vacuum, radiation, delay, no repair.
Soft and continuum robots	Bend with flexible bodies (air, tendons, shape memory).	Soft grippers, endoscopes, snake robots.	Modelling and control of infinite DOF; low force.
Micro and nano robots	Magnetic, acoustic or chemical propulsion.	Targeted drug delivery, cell manipulation.	Physics of tiny scales, imaging, fabrication.
Medical and wearable robots	Surgical arms, rehabilitation, exoskeletons, prostheses.	da Vinci surgical system, walking exoskeletons.	Safety, human intent detection, regulation.
Cable-driven robots	Cables pull a platform over a very large area.	Stadium cameras, large facade painting.	Cables only pull: need redundancy and tension control.
Modular and swarm robots	Many small units assemble or cooperate.	Self-reconfigurable blocks, drone swarms.	Communication, scaling, self-assembly.

1.1 Two ideas that explain most families

Fixed or mobile base. A fixed-base arm knows exactly where its base is: kinematics gives the tool pose directly. A mobile robot must also find where its base is (localisation, see the “Perception” course).

Actuated or underactuated. A robot is underactuated when it has fewer actuators than degrees of freedom. A quadrotor has 6 DOF in space but only 4 motors: it cannot move sideways without first tilting. A walking robot is underactuated at the foot that touches the ground. It must be stabilised dynamically, which is why balance control is a whole field.

1.2 Flying: the quadrotor

To hover, the sum of the four thrusts equals the weight: T = m g / 4 per rotor. To tilt forward, speed up the rear rotors; to turn (yaw), speed up the two rotors that spin in one direction and slow the other two (the reaction torques no longer cancel).

Worked example

A 1.2 kg drone: weight 1.2 × 9.81 = 11.8 N, so 2.9 N per rotor to hover. To climb at 2 m/s² (acceleration of 0.2 g) the total thrust must be 1.2 × (9.81 + 2) = 14.2 N: 20 % more. Motors are therefore chosen to give at least twice the hover thrust (thrust-to-weight ratio of 2) to keep control margin in wind.

Fly a quadrotor in 3D and look inside it →

1.3 Walking: the support polygon

A legged robot is statically stable if the vertical projection of its centre of mass lies inside the support polygon (the area between its feet on the ground). A quadruped that always keeps three feet down moves with a very safe “static walk”; a trot or a run lifts feet, the polygon becomes a line or disappears, and the robot is only dynamically stable, like a human running. Walking controllers use simple models: the inverted pendulum (the body falls forward and the foot is placed to catch it) and the zero moment point (ZMP), then whole-body control or learned policies on top.

Walk a humanoid in 3D and look inside it →

Key terms

serial / parallel robot
legged robot
humanoid
underactuated
support polygon
ZMP
ROV / AUV
soft robot

Check yourself

A 2 kg quadrotor hovers. What thrust does each rotor give?
m g / 4 = 2 × 9.81 / 4 ≈ 4.9 N.
Why is a quadrotor “underactuated”?
6 degrees of freedom in space but only 4 independent motors.
When is a quadruped statically stable?
When the projection of its centre of mass is inside the polygon formed by its feet on the ground.

Wheels and mobile bases →

Mechanical design: stiffness, payload, reach, materials

13 min

You will learn

the specification of a robot arm and the first calculations a mechanical designer does.

2.1 The data sheet

Specification	Meaning	Watch out for
Payload	Mass that can be carried by the flange.	It includes the gripper; it is given at a given reach and speed. A longer tool lowers it.
Reach	Maximum distance from the base axis to the wrist centre.	The tool adds to it, but the payload is given at the wrist.
Degrees of freedom	Number of axes.	6 for a general task, 4 for pick and place on a plane (SCARA), 7 to be redundant.
Repeatability	How close the robot returns to the same point (ISO 9283).	Typical ±0.02 to ±0.1 mm. It is not the absolute accuracy.
Speed and acceleration	Maximum joint speeds, tool speed.	The cycle time depends on accelerations more than on top speed.
Mass	Mass of the robot.	The payload / mass ratio: a cobot carries about 1/10 of its mass, an industrial robot up to 1/3 to 1/2.
Protection (IP) and environment	Dust and water ratings (IP54, IP67), cleanroom class, explosion-proof (ATEX), temperature.	Washdown for food, cleanroom for semiconductors.

2.2 First sizing: the torque at the base of the arm

The shoulder torque is a weight times its distance. For a quick estimate, take the payload at full reach plus half the weight of the arm (its centre of mass is about halfway):

τ ≈ ( m_payload + ½ m_arm ) g L

Worked example

A 5 kg payload at L = 0.8 m, with an arm of 8 kg: τ ≈ (5 + 4) × 9.81 × 0.8 ≈ 71 N·m at the shoulder, before any acceleration. With an acceleration of 3 rad/s² and a total inertia of about 5 kg·m², add 15 N·m. With a 100:1 gearbox of efficiency 0.8, the motor must give 86 / (100 × 0.8) ≈ 1.1 N·m at peak: a larger motor than the wrist ones. This shows why shoulders are heavy and why big robots have counterbalance springs.

2.3 Stiffness: why accuracy is not repeatability

Links bend. For a beam fixed at one end, the deflection under a force F at the free end is:

δ = F L³ / (3 E I)

with E the Young modulus of the material (aluminium 70 GPa, steel 200 GPa, carbon fibre 100 to 200 GPa) and I the second moment of area (for a tube I = π (D⁴ − d⁴) / 64). Note the cube: doubling the length multiplies the deflection by 8.

Worked example

An aluminium tube, outer diameter 40 mm, inner 36 mm, length 0.5 m, with a load of 20 N at its end: I = π (0.04⁴ − 0.036⁴) / 64 = 4.3·10⁻⁸ m⁴ and δ = 20 × 0.5³ / (3 × 70·10⁹ × 4.3·10⁻⁸) ≈ 0.28 mm. The robot is repeatable (it bends the same way every time) but the tool is 0.28 mm away from where the encoders say: that is a typical origin of the difference between repeatability and accuracy.

2.4 Design choices

Topic	Choices
Materials	Aluminium (light, cheap, easy to machine), cast iron or steel (stiff, heavy, base), carbon fibre (very stiff and light, expensive), magnesium, 3D-printed plastic or metal for prototypes and complex shapes.
Structure	Hollow tubes and ribbed shells for stiffness per mass; large bearings (cross-roller) for joints that carry moments.
Transmission	Gearboxes (lesson 2 of the control course), belts, cables, linear screws and rails for prismatic axes.
Balancing	Springs, gas cylinders or counterweights reduce the gravity torque on the shoulder: smaller motors and less energy; used on large robots.
Cables and sealing	Hollow wrists to pass cables, dress packs, rotary seals. Cable fatigue is a classic cause of failure.
Joint limits and brakes	Mechanical stops and software limits; holding brakes on joints that carry gravity.
Maintenance	Grease or oil changes, belt tension, battery for absolute encoders, easy access.

Key terms

payload
reach
repeatability
stiffness
deflection
counterbalance
IP rating
cross-roller bearing

Check yourself

A beam is made twice as long. By what factor does its end deflection change?
Multiplied by 2³ = 8.
Why is a robot repeatable to 0.02 mm sometimes 0.3 mm inaccurate?
Because of deflection, geometric errors and backlash, which are the same each time (repeatable) but not in the model.
What does a counterbalance spring do on a big robot?
It cancels part of the gravity torque on the shoulder, so the motor can be smaller and use less energy.

End effectors and grasping: grippers, suction, tools

13 min

You will learn

the main end effectors, how much force a grasp needs, and how the tool frame (TCP) is defined.

End effector	Principle	Good for	Limits
Parallel two-finger gripper	Two jaws move in parallel (pneumatic or electric).	Rigid parts of known size.	Needs access on two sides; shape-specific fingers.
Angular / three-finger / adaptive	Fingers close around the object (underactuated, they adapt to the shape).	Round or irregular objects.	Less precise position.
Vacuum suction cup	Pressure difference × area holds the object.	Boxes, sheets, bottles: the standard of logistics.	Porous or rough surfaces, vacuum loss, hanging load.
Magnetic gripper	Electromagnet or permanent magnet.	Steel sheets and parts.	Only ferromagnetic parts; residual magnetism.
Soft gripper	Inflatable or flexible fingers.	Food, fragile or very varied objects.	Low force, wear.
Needle, Bernoulli, electroadhesion	Special principles for textiles, wafers, films.	Delicate or porous materials.	Specialised.
Dexterous hand	Several fingers and joints (up to 20+ DOF) with tactile sensing.	In-hand manipulation, humanoids, research.	Cost, control complexity, fragility.
Process tools	Welding torch, spray gun, screwdriver, drill, sander, glue dispenser, camera.	The robot positions, the tool works.	Cables, forces and weight at the wrist.
Tool changer	A quick coupling between flange and tool (air, electricity, signals).	One robot, several tools.	Extra weight and compliance.

3.1 How much force to hold an object?

Friction grip. Two fingers press with a normal force N each; the friction coefficient is μ. To lift a mass m with a safety factor SF that covers acceleration and uncertainty:

2 μ N ≥ SF · m g so N ≥ SF · m g / (2 μ)

Worked example

A 1 kg part, μ = 0.3 (steel on a dry finger pad), SF = 2: N ≥ 2 × 1 × 9.81 / (2 × 0.3) ≈ 33 N per finger. With a rubber pad (μ ≈ 1) only 10 N are needed: a good pad saves a gripper size. A form-closure grip (fingers shaped to the part, or a part held by a groove) needs almost no friction.

Vacuum. The holding force is the pressure difference times the cup area: F = ΔP × A. With a vacuum of 60 kPa and a cup of 30 mm diameter (A = 7.07·10⁻⁴ m²): F = 60 000 × 7.07·10⁻⁴ ≈ 42 N. With a safety factor of 4 for a horizontal suction (the load slides) or fast moves, one cup carries about 42 / (4 × 9.81) ≈ 1.1 kg. For a 10 kg box, use several cups, or a larger area.

3.2 The tool frame and TCP

The robot knows the pose of its flange (the mounting face). The point that works (the tip of a torch, the middle of the gripper fingers) is the tool centre point (TCP), described by a fixed transform flange → TCP (a frame, as in the modelling course). Programs are written in terms of the TCP, so it must be calibrated: the usual 4-point method touches the same fixed tip from four different orientations and the controller solves for the offset. A wrong TCP is invisible in joint moves but makes the tool “swing around” the wrong point when you reorient it. The payload data (mass, centre of mass, inertia) of the tool must also be entered: it feeds the dynamic model (control course).

Remember

The gripper is often the real limit of a robot project: choose it first, with the part, not last.
Test grasps with the real parts, at the real speed and acceleration.
Release is as important as grasp: pushing air to release a part, or a spring to open on power loss, avoids dropping or sticking.

Key terms

end effector
gripper
vacuum cup
friction grip
form closure
TCP
flange
tool changer

Check yourself

A 0.5 kg part, μ = 0.5, SF = 2. What normal force per finger with two fingers?
N = SF m g / (2 μ) = 2 × 0.5 × 9.81 / (2 × 0.5) ≈ 9.8 N.
Pressure difference 50 kPa, cup diameter 40 mm. What holding force?
A = π × 0.02² = 1.26·10⁻³ m²; F = 50 000 × 1.26·10⁻³ ≈ 63 N.
What does a wrong TCP cause when you reorient the tool?
The tool pivots around the wrong point, so the tip moves instead of staying in place.

End effectors on the robot pages →

Electronics and embedded systems: power, drivers, controllers, buses

13 min

You will learn

what electronics a robot contains, how to size the power supply, and which controller and bus to choose.

4.1 Power: batteries and supplies

Battery energy = voltage × capacity: a 24 V, 10 Ah pack stores 240 Wh. The runtime is the energy divided by the average power: 240 Wh / 60 W = 4 h. Keep 20 % in reserve.
Chemistries: Li-ion / LiPo (high energy density, needs a battery management system, BMS), LiFePO₄ (safer, longer life), lead-acid (cheap, heavy), NiMH.
Current: I = P / V. A 100 W motor at 24 V draws 4.2 A; at 12 V it draws 8.3 A, so thicker wires and bigger connectors. Higher voltage means less current and less loss (P_loss = R I²).
Peaks: motors draw several times their average current when accelerating; the supply and the wires must tolerate it, and braking can push energy back (use a brake resistor or a regenerative supply).

4.2 Drivers, controllers and buses

Layer	Options	Choose when
Motor driver	H-bridge (brushed), FOC driver (brushless, with current sensing and encoder input), stepper driver (microstepping), industrial servo drive.	Match the motor type, voltage and current; add protections.
Microcontroller (MCU)	Arduino, STM32, ESP32, Teensy.	Hard real time, low cost and power: fast loops, sensors, motor control.
Single-board computer	Raspberry Pi, Jetson (GPU), industrial PC.	Vision, planning, ROS 2, AI: high layers, with Linux.
PLC	Siemens, Beckhoff, Rockwell, Mitsubishi.	A robot in a production line: sequencing, safety, I/O, reliability.
Bus / network	I²C, SPI, UART (on a board); CAN / CAN-FD (robust, shared cable, 1 Mbit/s); EtherCAT (fast, synchronous, industrial); USB, Ethernet, Wi-Fi.	CAN for a few joints on a small robot; EtherCAT for many axes with tight timing.

4.3 Signals and noise

ADC resolution: a 12-bit converter with a 3.3 V range has a step of 3.3 / 4096 ≈ 0.8 mV. A sensor of 10 mV per unit then has a resolution of 0.08 unit.
PWM: a motor is driven by switching the voltage at 10 to 20 kHz (above hearing); the duty cycle sets the average voltage.
EMC: motor drivers create electrical noise that corrupts encoder and sensor signals. Use shielded twisted-pair cables, a single ground point, separate power and signal cables, filters, and differential signalling (RS-422, CAN).
Protections: fuses or breakers, reverse-polarity and over-current protection, limit switches, temperature sensors on the motors and drivers.

Never forget the safety circuit

An emergency stop must not depend on the software. It cuts the power to the drives through certified relays or safe-torque-off inputs (see lesson 6). Test it every time you modify the robot.

Key terms

battery management system
motor driver
MCU
PLC
CAN bus
EtherCAT
EMC
PWM

Check yourself

A 12 V, 5 Ah battery powers a robot that draws 30 W on average. How long does it run, keeping 20 % in reserve?
Energy 60 Wh × 0.8 = 48 Wh; 48 / 30 = 1.6 h.
Why is a higher supply voltage often chosen for powerful motors?
For the same power the current is lower, so thinner wires and less loss (R I²).
Which bus would you pick to link 12 synchronised servo drives?
EtherCAT: fast, deterministic and synchronous.

Software and programming: ROS 2, simulators, robot languages

14 min

You will learn

the software stack of a robot and how robots are programmed, from the teach pendant to ROS 2.

5.1 Three worlds of programming

World	How	Who	Strength
Industrial robots	Teach pendant (move the robot, record points) and the manufacturer's language; offline programming in a simulator.	Technicians, integrators.	Robust, certified, fast to deploy for repeated tasks.
Cobots	Hand-guiding, graphical blocks on a tablet, plus scripting.	Operators, small companies.	No programmer needed for simple tasks.
Research and service robots	ROS 2 with C++ and Python; open libraries.	Engineers, researchers.	Flexible, huge ecosystem (navigation, vision, MoveIt).

The same joint move in the languages of four manufacturers (simplified syntax). The idea is the same: a target, a speed, a blending zone.

Universal Robots (URScript)   movej(q1, a=1.4, v=1.05, r=0.02)
ABB (RAPID)                   MoveJ p1, v1000, z20, tool0;
KUKA (KRL)                    PTP P1 C_PTP
FANUC (TP)                    J P[1] 100% CNT20

5.2 ROS 2 in one page

ROS 2 (Robot Operating System) is not an operating system but a middleware and a large set of libraries. A robot application is a graph of small programs called nodes that exchange data:

Concept	What it is	Example
Topic	A named stream of messages, publish / subscribe.	`/scan` (lidar), `/cmd_vel` (velocity command).
Service	A request and a reply (quick call).	“Reset the map”, “compute IK”.
Action	A long task with feedback and cancellation.	“Navigate to this pose”, “execute this trajectory”.
tf2	The tree of coordinate frames over time (the frames of the modelling course).	`map → odom → base_link → camera`.
URDF / Xacro	XML description of links, joints, masses and meshes.	The model that RViz, the simulator and MoveIt read.
ros2_control	Common interface between controllers and hardware drivers.	A joint trajectory controller on any arm.
Launch files, parameters, bags	Start many nodes together; configure them; record and replay all topics.	`rosbag` for debugging and datasets.

Ready-made packages cover most of the previous courses: Nav2 (navigation: costmaps, A*, controllers), SLAM Toolbox and Cartographer (mapping), MoveIt 2 (motion planning for arms), OpenCV / PCL (vision, point clouds), robot_localization (Kalman fusion).

5.3 Simulators and digital twins

Simulator	Strength
Gazebo	The classic ROS simulator; sensors, wheels, world files.
MuJoCo, PyBullet, Isaac Sim / Isaac Lab	Fast and accurate contact physics; GPU-parallel training for reinforcement learning (see the AI course).
Webots, CoppeliaSim	Easy to start; education and prototyping.
RoboDK, Process Simulate, manufacturer tools	Offline programming of industrial cells with real robot models and collision checking.

A digital twin keeps such a model in line with the real cell (same program, same layout) to test changes, estimate cycle times and train operators without stopping production. Remember the reality gap: a simulator always lacks some friction, flexibility or sensor noise; test on the real robot early.

5.4 Good engineering habits

Version control (git) for code, parameters and robot programs; backups of the controller.
Test in layers: unit tests, simulation, hardware in the loop, then the real robot at low speed.
Logs and monitoring: record everything; failures are rare and hard to reproduce.
Error handling: every action can fail; define what the robot does then (retry, stop safely, call for help).
Security: a networked robot is a computer: passwords, updates, closed ports (IEC 62443).

Key terms

teach pendant
offline programming
ROS 2
node / topic
tf2
URDF
digital twin
reality gap

Check yourself

In ROS 2, which mechanism fits “navigate to this pose, with progress and the option to cancel”?
An action.
What is a URDF file?
An XML description of the links, joints, masses and shapes of a robot.
Why test on the real robot early even if the simulation works?
Because of the reality gap: friction, flexibility, delays and noise are never perfectly simulated.

Safety and standards: working next to robots

13 min

You will learn

the hazards of robots, the main standards, and the four ways of letting people and robots share a space.

Important

This lesson explains the ideas. A real installation needs a risk assessment by a competent person and compliance with the standards and laws of the country. Never rely on a course alone for safety decisions.

6.1 Where the danger comes from

Impact: a 100 kg arm moving at 1.5 m/s has a kinetic energy ½ m v² of 112 J, enough to injure seriously.
Crushing and trapping between the robot and a fixed object (quasi-static contact): the force does not stop at the first touch.
Tool hazards: sharp parts, hot welding torches, lasers, a gripper that releases its load, ejected parts.
Unexpected motion: a software error, a restart, a singularity (!), a person entering during a maintenance step.
Other: electrical, pneumatic and hydraulic energy, noise, cybersecurity.

6.2 The standards

Standard	Topic
ISO 12100	General principles of risk assessment and risk reduction for machines.
ISO 10218-1 / -2	Safety of industrial robots: the robot itself (-1) and the robot system, integration and cell (-2).
ISO/TS 15066	Collaborative robots: the four collaboration modes and the allowed contact forces and pressures.
ISO 13849-1 / IEC 62061	Safety-related control systems: performance levels (PL a to e) and categories; SIL.
ISO 13855 / 13857	Positioning of safeguards according to approach speed; safety distances to prevent reaching.
ISO 3691-4, ISO 13482, IEC 61508, IEC 62443	Driverless industrial trucks (AGV/AMR); personal care robots; functional safety; industrial cybersecurity.
EU Machinery rules, CE marking	A robot cell sold or used in the EU must be CE-marked under the Machinery Directive (replaced by the Machinery Regulation from 2027); other regions have equivalents (ANSI/RIA R15.06 in the USA).

6.3 Four ways to share a space

Mode (ISO/TS 15066)	How it works	Example
1. Safety-rated monitored stop	The robot stops when a person enters the zone and restarts when they leave; the power stays on.	An operator loads a part into a cell with a light curtain.
2. Hand guiding	The person moves the robot with a handle and an enabling device, at a safe limited speed.	Teaching a path by hand.
3. Speed and separation monitoring (SSM)	The robot slows down as a person comes closer and stops before contact; zones by a laser scanner or camera.	A fast robot in an open cell.
4. Power and force limiting (PFL)	Contact is allowed: force, pressure and speed are limited to values that do not hurt, per body part.	A cobot working next to people without a fence.

Worked example: the separation distance (mode 3)

The robot must stop before a person reaches it. The minimum protective distance is the sum of: the distance a person walks while the system detects and stops (S_h = K_h · (T_r + T_s), with the human speed K_h = 1.6 m/s in ISO/TS 15066), the distance the robot travels while stopping, the detection uncertainty and a margin. With a total reaction and stopping time of 0.5 s, the person covers 1.6 × 0.5 = 0.8 m before the robot stops: the scanner must trigger more than 0.8 m plus the robot stopping distance and margins away. A slower or faster-stopping robot allows a smaller separation.

6.4 The protective devices

Fences and interlocked doors, light curtains, laser scanners, pressure mats, safety cameras.
Emergency stop (red mushroom button, yellow background): stop categories 0 (immediate power removal), 1 (controlled stop then power removal), 2 (controlled stop, power kept). Enabling switch (three-position) on the pendant.
Safe functions in the drives: safe torque off (STO), safely limited speed (SLS), safe limited position, safe brake control. They are certified and independent of the standard software.
Operating modes: automatic, and manual reduced speed for teaching (limited to 250 mm/s at the tool in the “T1” mode).

Key terms

risk assessment
ISO 10218
ISO/TS 15066
performance level
speed and separation monitoring
power and force limiting
safe torque off
emergency stop

Check yourself

A person walks at 1.6 m/s. The system needs 0.7 s to detect and stop. How far does the person travel?
1.6 × 0.7 = 1.12 m.
Which collaboration mode allows contact with limited force and speed?
Power and force limiting (PFL).
Why must an emergency stop not depend on the robot software?
Software can crash or be wrong exactly when the stop is needed; the stop must work through independent, certified hardware.

How a cobot stays safe →

Calibration, accuracy and testing

12 min

You will learn

where robot errors come from, how they are measured, and how calibration reduces them.

7.1 Sources of error

Type	Examples	Typical size
Geometric	Link lengths and joint offsets different from the model (manufacturing tolerances, assembly, a collision that bent a link), axes not exactly perpendicular.	0.1 to 1 mm, the main cause
Elastic	Deflection of links and gearboxes under the load and gravity (lesson 2).	0.05 to 0.5 mm, depends on the pose and the payload
Backlash, friction	Free play in gears, hysteresis, stick-slip.	0.01 to 0.1 mm
Thermal	Expansion when the robot warms up (the first hour), room temperature.	0.05 to 0.3 mm
Sensor and control	Encoder quantisation and error, tracking error during motion, vibration.	0.01 to 0.2 mm
Environment	The workpiece position, the fixture, the tool wear, the calibration of the tool and base frames.	often the largest: 0.5 to several mm

Joint errors reach the tool through the Jacobian (dx = J dq, singularities course): the longer the arm, the larger the effect. An error of 0.01° on the shoulder joint is 0.01 × π/180 = 1.75·10⁻⁴ rad; at 1 m this is 0.17 mm at the tool. A well-conditioned pose keeps this amplification small.

7.2 Kinds of calibration

Calibration	What it finds	How
Mastering / zeroing	The encoder value at the reference pose of each joint.	Put each axis on a mark or a pin, store the zero. Required after a motor or encoder change.
Kinematic calibration	The true DH parameters (link lengths, offsets, twist angles).	Measure the tool position in many poses with a laser tracker or a touch probe; adjust the DH parameters by least squares until the model matches. Improves accuracy from about 1 mm to 0.2-0.3 mm.
Tool (TCP) and payload	The transform flange → tool and the mass data.	4-point method, load identification routine (lesson 3).
Base / work object	Where the table or the fixture is in the robot base frame.	Touch three points (origin, a point on x, a point in the xy plane) with the tool.
Camera	Intrinsics and hand-eye transform.	Checkerboard and marker views (perception course).
Dynamic identification	Masses, centres of mass, friction.	Excitation trajectories and least squares (control course).

Accuracy versus repeatability, again

Calibration improves accuracy, not repeatability. A robot that is repeatable to ±0.03 mm but 1 mm inaccurate can be taught points by hand and will return to them precisely (teach and repeat). It needs calibration when points come from a CAD model, a vision system, or when a robot is replaced: the program is then sent to a robot with different errors.

7.3 Testing: ISO 9283

The standard ISO 9283 defines how to measure a robot so that data sheets can be compared: the robot goes to the same pose many times (typically 30 cycles) from different directions, and a measuring instrument records where the tool really goes.

Measure	What it says
Pose accuracy (AP)	Distance between the commanded pose and the mean of the reached poses.
Pose repeatability (RP)	Spread of the reached poses around their mean (a sphere that contains them).
Path accuracy and repeatability (AT, RT)	The same along a programmed line or circle, at a given speed.
Settling time, overshoot	How long the tool takes to stabilise at the target.

Commissioning checklist

Mount the robot rigidly; check the levelling and the fixings.
Check the mastering, the payload and the tool frame (TCP).
Warm the robot up (one hour of motion) before accuracy-critical work.
Run at low speed first, then increase; watch the motor currents.
Test the safety functions (emergency stop, doors, scanners) and record the results.
Back up the program and the parameters.

Key terms

geometric error
kinematic calibration
mastering
laser tracker
work object
ISO 9283
warm-up
teach and repeat

Check yourself

The shoulder encoder is wrong by 0.02°. The tool is 1.2 m away. What is the error at the tool?
0.02° = 3.5·10⁻⁴ rad; × 1.2 m = 0.42 mm.
A robot has been taught its points by hand. Does it need kinematic calibration?
Not necessarily: repeatability is enough to return to taught points. Calibration matters when points come from CAD or vision, or the robot is replaced.
Why warm a robot up before a precise task?
Thermal expansion of links and lubricant changes the geometry in the first hour; a warm robot is more stable.

Applications and choosing a robot for a job

13 min

You will learn

where robots are used and a method to choose the right robot, gripper and cell for a task.

Sector	Typical jobs	Typical robots
Automotive	Spot and arc welding, painting, sealing, handling heavy parts, assembly.	Large 6-axis robots (100-500 kg payload).
Electronics	Fast placement, screwing, testing, wafer handling.	SCARA, delta, small 6-axis, cleanroom robots.
Logistics and warehouses	Palletising, picking, sorting, moving goods.	Palletising arms, suction-gripper arms, AMR, shuttles.
Food and packaging	Pick and place of products, packing, cutting, decorating.	Delta robots, washdown arms, soft grippers.
Pharma and laboratories	Handling samples, pipetting, sterile filling.	Small arms, gantries, isolator robots.
Agriculture	Harvesting, weeding, milking, spraying.	Mobile manipulators, field robots, drones.
Construction and mining	Bricklaying, drilling, surveying, 3D printing of buildings, remote machines.	Large gantries, legged robots, excavators.
Health care	Surgery, rehabilitation, hospital logistics, disinfection.	Surgical robots, exoskeletons, AMR, UV robots.
Inspection, energy and space	Pipes, tanks, wind turbines, nuclear sites, satellites, planets.	Crawlers, drones, legged and underwater robots, rovers.
Home, service and education	Vacuuming, lawn mowing, reception, delivery, teaching programming.	Mobile robots, small arms, educational kits.

8.1 A method to choose

Define the task in numbers: what is handled (mass, size, material, variety), how many per hour, what precision, what environment (dust, water, temperature, cleanroom, explosive atmosphere).
Choose the kinematics: 4 DOF pick and place on a plane → SCARA or delta; a box-shaped workspace → Cartesian gantry; any pose in space → 6-axis arm; moving across a site → mobile robot or mobile manipulator.
Check the numbers: payload (with gripper and a 30 % margin), reach (with the whole workspace inside it and away from singularities), repeatability (about one third of the tolerance), cycle time (estimate it; see below).
Decide the safety concept: fenced, light curtain, scanner, or collaborative (lesson 6). A cobot is slower: check that the cycle time is still enough.
Plan the whole cell: gripper, feeding of parts, fixtures, vision, PLC and software, safety, guarding, maintenance access.
Simulate the cell (reachability, collisions, cycle time) and test the risky step (the grasp, the vision) on a prototype before ordering.

8.2 Estimating the cycle time

Add the moves, the gripper actions and the waiting: a pick and place cycle is roughly 2 × (approach + grasp or release + retract) + transfer. A fast pick and place of 0.5 m with accelerations of 10 m/s²: time for a move with a triangle profile = 2 √(d/a) = 2 √(0.5/10) ≈ 0.45 s.

Worked example: payback of a robot cell

A palletising cell must handle 600 boxes per hour: a cycle of 3600 / 600 = 6 s per box (2 boxes at a time would give 12 s per gripper cycle).
Cost: robot 40 000 €, gripper, safety, conveyors and integration 80 000 €, total 120 000 €. Rule of thumb: the integration costs 1.5 to 3 times the robot.
Savings: two operators on two shifts replaced, 60 000 € per year, minus 6 000 € of maintenance: 54 000 € per year.
Payback = 120 000 / 54 000 ≈ 2.2 years. Include the non-financial gains: fewer injuries, constant quality, availability.

8.3 Why robot projects fail

The gripper or the feeding of parts was not tested with real, variable parts.
The variety was underestimated: the robot is good at the same task a million times, bad at everything that changes.
Integration and software cost more than the robot, and nobody planned the maintenance or the training.
The process was not ready for automation: a robot automates a good process, it does not repair a bad one.
The safety study was done too late, forcing a redesign.

Key terms

cycle time
palletising
systems integrator
payback
total cost of ownership
mobile manipulator
feeding

Check yourself

A line needs 900 parts per hour. What cycle time per part?
3600 / 900 = 4 s.
A cell costs 90 000 € and saves 36 000 € per year. What is the payback time?
90 000 / 36 000 = 2.5 years.
Which robot kinematics would you choose for very fast 4-DOF pick and place of light products on a conveyor?
A delta robot (or a SCARA): light, fast moving parts and a small dome-shaped workspace.

Where a Delta robot is used →

Your path: projects, tools, books and careers

12 min

You will learn

a roadmap from zero to hero: what to build, what to read, and which jobs it leads to.

9.1 The map of the field

Level	What you can do	Where to learn it here
0 · Curious	Name the parts of a robot and what they do.	Foundations (12 lessons)
1 · Beginner	Compute where a 2-axis arm is and which angles reach a point.	Maths and motion (8 lessons) + the robot pages
2 · Intermediate	Model any serial robot (DH, MGD, MGI, Jacobian) and trajectories.	Robot modelling (11 lessons)
3 · Advanced	Handle singularities, redundancy; model dynamics and tune control; choose motors.	Singularities and the Jacobian; Dynamics, actuators and control
4 · Expert	Build autonomy: perception, estimation, SLAM, planning, learning.	Perception, planning and AI
5 · Hero	Deliver a real, safe, calibrated robot system for an application.	Robots in the real world + your own projects

9.2 A ladder of projects

Servo arm (Arduino + 3 hobby servos): write the forward and inverse kinematics of a 2-3 axis arm and make it draw.
Line follower or balancing robot: your first PID, sensors and motor drivers.
Differential-drive rover with encoders and an IMU: odometry, then a Kalman filter.
ROS 2 in simulation: a TurtleBot in Gazebo with SLAM Toolbox and Nav2; then the same on a real robot with a cheap lidar.
Pick and place: a 5-6 axis arm (or a simulated UR5) with MoveIt, a camera and ArUco markers, hand-eye calibration included.
Learning: train a policy in simulation (MuJoCo / Isaac Lab) and test it on a small real robot; or learn from demonstrations.
A complete system: a mobile manipulator or a dual-arm cell with a safety concept, a risk assessment and documentation. This is the “hero” project.

9.3 Competitions and communities

Student and youth: FIRST Robotics, RoboCup and RoboCup Junior, World Robot Olympiad, Eurobot, VEX.
Research challenges: DARPA challenges, ICRA / IROS competitions, Amazon picking, RoboMaster, autonomous racing.
Communities: ROS Discourse, open-source robots, local makerspaces, university labs and clubs.

9.4 Reading list

Book	Why
K. Lynch and F. Park, Modern Robotics (free online)	Modern, geometric, with videos and code.
B. Siciliano et al., Robotics: Modelling, Planning and Control	The standard graduate textbook.
J. Craig, Introduction to Robotics: Mechanics and Control	Classic and clear; origin of the standard DH convention used here.
W. Khalil and E. Dombre, Modeling, Identification and Control of Robots	The modified DH (DHm) and the French school used in the modelling course.
P. Corke, Robotics, Vision and Control	Code-driven, includes vision.
S. Thrun et al., Probabilistic Robotics	Filters, localisation, SLAM.
S. LaValle, Planning Algorithms (free online)	Motion planning in depth.
R. Murray, Z. Li and S. Sastry, A Mathematical Introduction to Robotic Manipulation	Screw theory and grasping, for the mathematically inclined.

9.5 Careers

Role	What you do	Skills used
Mechanical / mechatronics engineer	Design arms, grippers, gearboxes, structures.	Lessons 2 and 3 of this course, CAD, materials, kinematics.
Electronics / embedded engineer	Design drivers, boards, firmware, buses.	Motors, control, real time, EMC.
Controls engineer	Tune and design the control laws, identify models.	Dynamics, control and actuators course.
Robotics software / perception / AI engineer	Navigation, vision, planning, learning, ROS 2.	Perception, planning and AI course; C++ and Python.
Systems integrator / application engineer	Design and commission robot cells for customers.	The whole last course, safety, PLC, programming.
Safety engineer, field service, researcher, teacher, entrepreneur	Certify, maintain, invent, teach, create a company.	All of the above, plus communication.

Final advice

Build things. A robot that wobbles on your table teaches more than ten chapters.
Simulate first, then test early on hardware, and keep a log of what failed.
Learn the maths and the hardware. The best roboticists can move between the equation, the code and the screwdriver.
Respect safety. Every robot you build can hurt someone; think about it from the first sketch.

Key terms

project ladder
hero project
RoboCup
open source
systems integrator
mechatronics

Check yourself

Which project teaches you PID, sensors and motor drivers at the same time?
A line-follower or a balancing robot.
Which two courses of this site would you follow before building a pick and place with a camera?
Robot modelling (kinematics) and Perception, planning and AI (vision, hand-eye calibration, motion planning).
Name three jobs in robotics that are not “software developer”.
For example mechatronics engineer, controls engineer, systems integrator, safety engineer, field service technician.

Glossary

All the words of the course in one place.

Term	Meaning
Support polygon	The area between the feet of a legged robot; it is stable if the centre of mass is above it.
Underactuated	Fewer actuators than degrees of freedom (a quadrotor: 4 inputs, 6 DOF).
Payload	The maximum mass the robot can carry at its flange, including the gripper in most data sheets.
TCP	Tool centre point: the working point of the tool, defined by a frame.
Force closure	A grasp that can resist any external force and torque.
Friction cone	The set of contact forces that do not slip: its half-angle is arctan μ.
FOC	Field-oriented control, the standard way of driving a brushless motor.
CAN / EtherCAT	Industrial communication buses between controllers, drives and sensors.
ROS 2	The open-source robotics middleware: nodes exchanging messages by topics, services and actions.
URDF	An XML file that describes the links, joints and shapes of a robot.
Digital twin	A simulation model kept in line with the real robot or cell.
Risk assessment	The structured study of hazards, their severity and probability, and the measures to reduce them.
Collaborative modes	The four ways of ISO/TS 15066: safety-rated monitored stop, hand guiding, speed and separation monitoring, power and force limiting.
Performance level (PL)	A rating (a to e) of the reliability of a safety function (ISO 13849).
Repeatability / accuracy	How well the robot returns to the same point / how close it is to the commanded point.
ISO 9283	The standard that defines how to measure the performance of industrial robots.
ROI / payback	The time needed for the savings to pay for the robot cell.
Systems integrator	A company that designs and installs a complete robotic cell around a robot.

You have the whole map of robotics!

Go back to the roadmap, pick the pages you skipped, and start your own robot. The best way to know a robot is to build one.

Back to the roadmap → Home page