1. Introduction
1 What is a Robot?
The word robota (meaning “work” or “forced labour” in Slavic languages) entered engineering vocabulary through Karel Čapek’s 1920 play Rossum’s Universal Robots (R.U.R.), in which artificial human-like creatures are built as cheap workers. Isaac Asimov later formalised behavioural rules in I, Robot (1950) — the Three Laws of Robotics:
- A robot may not injure a human being or, through inaction, allow a human being to come to harm.
- A robot must obey orders given to it by human beings, except where such orders would conflict with the First Law.
- A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.
A working engineering definition: Robotics is the science studying the intelligent connection between perception and action (Siciliano et al.). More broadly, robotics is concerned with machines that can replace human beings in the execution of a task, as regards both physical activity and decision-making.
2 Robot Systems
Every robot, regardless of application, is built from four interacting subsystems.
2.1 Mechanical system
The essential component is the mechanical system, which provides the physical structure: a locomotion apparatus (wheels, crawlers, legs) and/or a manipulation apparatus (arms, end-effectors, hands). Its design draws on articulated and continuum mechanics and materials engineering.
2.2 Actuation system
The actuation system animates the mechanical structure. It converts stored energy into motion and force. The two dominant technologies are:
- Electric actuators (DC motors, brushless motors): compact, precise, easily controlled; the standard choice for manipulation.
- Hydraulic actuators: very high force and power density; used when large forces are needed (e.g. heavy-duty industrial arms, legged robots).
The design of an actuation system falls within motion control: servomotors, drives, and transmissions.
2.3 Sensory system
The sensory system gives the robot perception. Sensors fall into two classes:
- Proprioceptive sensors measure the robot’s own internal state — joint encoders, IMUs, motor current.
- Exteroceptive sensors measure the environment — force/torque transducers, lidar, stereo cameras, tactile arrays.
Realising a sensory system involves signal conditioning, data processing, and information retrieval.
2.4 Control system
The control system connects perception to action. It executes a task plan, closes feedback loops around the sensors, and compensates for modelling uncertainties:
“The realisation of such a system follows the same feedback principle devoted to control of human body functions, possibly exploiting the description of the robotic system’s components (physical model).” — Siciliano et al.
The control problem draws on cybernetics, artificial intelligence, and computational architecture.
The diagram below summarises the relationship between the four subsystems and the course scope:
| Subsystem | Key discipline | This course? |
|---|---|---|
| Mechanical | Articulated mechanics | ✓ |
| Actuation | Motion control | ✓ (modelling) |
| Sensory | Signal processing | ✓ (strain sensing) |
| Control | Feedback control | — |
3 Robot Mechanics
Kinematics describes the motion of a robot with respect to a fixed reference frame, ignoring the forces and moments that cause the motion. Two problems are central:
- Direct kinematics: given joint positions, determine the end-effector position and orientation.
- Inverse kinematics: given a desired end-effector pose, find the joint positions that achieve it.
Differential kinematics extends this to velocities: the Jacobian matrix maps joint velocities to end-effector velocities. The Jacobian also connects end-effector forces to joint torques (statics) and is the foundation for dynamics and control.
4 Robot Planning
Planning specifies what motion the robot should execute. Two levels are distinguished:
- Trajectory planning: generate time-parameterised joint or end-effector trajectories from a concise task description (e.g. pick-up and release points, or a continuous path).
- Motion planning: find collision-free paths in a workspace with obstacles, formulated in configuration space. Solution methods include exact, probabilistic (e.g. RRT, PRM), and heuristic algorithms.
5 Robot Control
The trajectories generated by planning are reference inputs to the motion control system. The control problem is to compute the forces and torques that the joint actuators must deliver so that the robot tracks those references.
Because a manipulator is an articulated system, the motion of one link influences all others — the equations of motion contain coupling dynamic effects among the joints. These cannot be compensated from the model alone; feedback loops (using proprioceptive sensors) are essential to meet accuracy requirements.
6 Industrial Robots
6.1 Structured environments
Industrial robotics operates in structured environments whose geometric and physical characteristics are mostly known in advance. This limits the autonomy required and enables the design of highly accurate, repeatable machines.
Industrial robot manipulators are valued for their versatility, adaptability, accuracy, and repeatability. The first commercially deployed robot was the Unimate (1961), a hydraulic arm installed on a General Motors assembly line for die-casting operations.
6.2 Industrial applications
Typical industrial uses include manipulation (pick-and-place, machine feeding), assembly and packaging, spray painting and coating, arc and spot welding, laser cutting and welding, gluing and sealing, and mechanical machining (milling, drilling, deburring, grinding).
6.3 End-effectors
The end-effector is the part of the robot that interacts with the environment, typically mounted at the end of the kinematic chain. Its nature depends entirely on the task. For manipulation the most common end-effectors are grippers — fingered mechanical grippers or vacuum (suction-cup) devices. Specialised end-effectors include welding torches, spray nozzles, and force-controlled machining spindles.
6.4 Market trends
Global yearly installations of industrial robots have grown steadily, with the electronics and automotive sectors historically dominant. Recent growth is being driven by new sectors such as food handling, logistics, and e-commerce fulfilment.
7 Service Robots
Industrial robots perform specific, repetitive tasks with extreme precision. They are typically fixed to the ground, operate at high power, are isolated from human workers by safety cages, and require low autonomy.
Service robots, by contrast, perform professional or personal tasks in collaboration with humans and in unstructured environments. They must move (mobile robots), manipulate gently, be energy-efficient, and operate with high autonomy.
7.1 Application domains
Service robotics spans a wide range of domains:
- Space robotics: rovers (e.g. Perseverance on Mars) combine autonomy with remote control and must withstand extreme temperatures and radiation. Sending robots is far cheaper than sending humans and they can work continuously without life-support.
- Underwater robotics: ROVs and AUVs map ocean floors, monitor marine ecosystems, protect subsea infrastructure, and support naval operations. Soft robotic fish exploit passive compliance to swim efficiently using body deformation.
- Medical robotics: includes bionic limbs, rehabilitation exoskeletons, nursing assistants, and surgical robots. The da Vinci Surgical System is the benchmark for minimally invasive surgery — surgeons operate through a console, with the robot providing tremor filtering, motion scaling, and improved dexterity.
- Field robotics: mine exploration, de-mining, civil and naval construction, inspection and surveillance, fire-fighting, emergency rescue.
- Home and service: domestic cleaning (Roomba), lawn mowing, museum guides, agriculture, food industry.
7.2 Collaborative robots (cobots)
Cobots are designed for direct human-robot interaction, unlike traditional industrial robots. Key requirements:
- Safety and flexibility over raw speed and force.
- Mechanical compliance — more important than motion accuracy. Compliance can be physical (springs, compliant materials) or algorithmic (torque/force control via joint sensors).
- Lightweight materials, rounded edges, force-limited drives, and low operating speeds reduce inertial hazards.
Commercial examples include Universal Robots (UR series), ABB GoFa, and Franka Robotics — a 7-DOF arm with torque sensors at every joint, enabling force-sensitive manipulation and safe physical interaction.
7.3 Robotic hands
Anthropomorphic end-effectors for dexterous manipulation or active prostheses. Robotic hands are equipped with tactile sensors to improve human-like grasping and are typically tendon-driven (motors placed in the forearm or palm to reduce distal inertia). The Shadow Hand has 20 DOF driven by 20 motors.
Underactuated hands use fewer motors than DOF by harnessing passive mechanical compliance. The Pisa/IIT SoftHand actuates 19 DOF with a single motor, relying on adaptive synergies to conform to object shapes during grasping.
7.4 Legged robots
Legged robots use articulated limbs for locomotion, inspired by animal biomechanics (biomimetics). Advantages over wheeled platforms: greater versatility across uneven terrain, stairs, and obstacles. The cost is complex balance control and higher energy consumption.
- Hexapod robots: six legs; statically stable (centre of mass always supported by a triangle of feet), simpler balance control.
- Quadruped robots: four legs; dynamically stable gaits (e.g. Boston Dynamics Spot); widely used for inspection and surveillance.
7.5 Humanoids
The humanoid form factor is motivated by the vision of general-purpose robots operating in a world designed for humans — using the same tools, doors, staircases, and workspaces. However, bipedal locomotion is dynamically unstable and demands sophisticated balance and whole-body control.
Building a humanoid requires integrating all robot subsystems at high performance:
| Subsystem | Key technologies |
|---|---|
| Actuation | Electric motors, gears, springs (series elastic actuators) |
| Sensing | Encoders, IMUs, force/torque sensors, cameras, lidar |
| Mechanics | Lightweight links, compliant joints, dexterous hands |
| Control | Whole-body control, balance, planning algorithms |
| Power | High-energy-density battery packs |
8 Scope of These Notes
This course focuses on Robot Mechanics — the kinematic and static analysis of manipulator structures. The thread running through the material is the direct kinematics map
\[ \boldsymbol{x} = h(\boldsymbol{q}), \]
which relates the joint variables \(\boldsymbol{q}\) (the configuration in joint space) to the operational variables \(\boldsymbol{x}\) (the end-effector pose in task space). The notes cover how to build this map, how to differentiate and invert it, and how to ground it in physical actuators.
| Topic | Question answered |
|---|---|
| Rigid-body pose & rotation matrices | How is orientation represented? |
| Euler angles, axis/angle, quaternions | What are alternative orientation representations? |
| Homogeneous transformations | How are position and orientation combined? |
| Denavit–Hartenberg convention | How is a chain of links parameterised? |
| Direct kinematics | Where is the end-effector given the joints? |
| Inverse kinematics | What joints place the end-effector at a target? |
| Differential kinematics (Jacobian) | How do joint rates map to task rates? |
| Statics | How do end-effector wrenches map to joint torques? |
| Mobility (Grübler) | How many degrees of freedom does a mechanism have? |
| Actuators & gears | How is motion produced and transmitted? |
| Strain sensing | How is force/torque measured in practice? |