A ROBOT is a physical agent that performs tasks by manipulating the physical world, using SENSORS to perceive and EFFECTORS (actuators) to act. IT IS EXACTLY THE AGENT OF ACtE0901, with the environment being the physical world — which is, in the classification of the environment-types topic: PARTIALLY OBSERVABLE sensors are noisy and limited STOCHASTIC actions do not have their intended effect exactly SEQUENTIAL actions have lasting consequences DYNAMIC the world moves while you compute CONTINUOUS state, time, and action are all continuous often MULTI-AGENT people and other robots often partly UNKNOWN the environment must be mapped THAT IS THE HARDEST COLUMN OF THE ENVIRONMENT TABLE, every entry at once. Robotics is difficult because it gets no easy properties. THE CATEGORIES OF ROBOT: MANIPULATORS (robot arms) — anchored to a fixed base, moving objects within their reach. Industrial welding and assembly arms. MOBILE ROBOTS — moving through an environment: wheeled, legged, aerial (UAVs), underwater. MOBILE MANIPULATORS — both, which is far harder than either. HUMANOID ROBOTS — a mobile manipulator in human form. THE COMPONENTS: SENSORS PASSIVE — receive signals the environment emits: cameras, microphones, passive infrared ACTIVE — emit a signal and measure the return: sonar, lidar, radar, structured-light depth cameras PROPRIOCEPTIVE — measure the robot's own state: joint encoders, inertial measurement units, force sensors THE DISTINCTION MATTERS: active sensors give better range data and interfere with each other; proprioceptive sensors drift and must be corrected against external references. EFFECTORS each provides a DEGREE OF FREEDOM (DOF) — an independent direction of motion REVOLUTE joints rotate; PRISMATIC joints slide CONTROLLERS, and the power supply, which is a real design constraint for anything mobile. DEGREES OF FREEDOM — the arithmetic worth knowing: A rigid body in 3D space has SIX degrees of freedom: three of POSITION (x, y, z) and three of ORIENTATION (roll, pitch, yaw). THEREFORE A ROBOT ARM NEEDS AT LEAST 6 DOF to place its end effector at an arbitrary position AND orientation. A 7-DOF arm is REDUNDANT — it has more freedom than the task requires, so there are infinitely many joint configurations achieving the same hand pose. That redundancy is useful: it lets the arm avoid obstacles or joint limits while holding the hand still. THE CONFIGURATION SPACE (C-space) is the space of all possible joint settings. For a 6-joint arm it is 6-dimensional, and PLANNING HAPPENS IN CONFIGURATION SPACE rather than in physical space — because a path that is simple for the hand may be impossible for the joints. Obstacles in the world map to complicated forbidden regions in C-space, which is why motion planning is not just pathfinding on a map.

THE ROBOT'S CORE PROBLEMS, in the order they must be solved. 1. PERCEPTION UNDER UNCERTAINTY Sensors are noisy, so the robot never knows its state exactly. The standard treatment is PROBABILISTIC: maintain a BELIEF STATE — a probability distribution over possible states — and update it with each observation using Bayes' rule. THIS IS THE BELIEF-STATE MACHINERY OF ACtE0903, applied in real time. The KALMAN FILTER is the classic implementation for continuous state with Gaussian noise; PARTICLE FILTERS handle arbitrary distributions by representing the belief as a set of samples. 2. LOCALISATION — where am I? Given a map and sensor readings, estimate the robot's pose. Hard because odometry DRIFTS: wheel slip accumulates, so dead reckoning alone is worthless over distance, and external references are required. 3. MAPPING — what does the environment look like? Build a map from sensor readings, given known poses. 4. SLAM — SIMULTANEOUS LOCALISATION AND MAPPING Do both at once, with neither given. THE CHICKEN-AND-EGG PROBLEM OF ROBOTICS: you need a map to localise, and you need your location to build a map. The resolution is probabilistic — maintain a joint distribution over poses and map features, and correct both when a previously seen landmark is recognised (LOOP CLOSURE). SLAM is the enabling technology for autonomous vacuum cleaners, drones and self-driving cars. 5. MOTION PLANNING — how do I get there? Find a collision-free path in configuration space from the current configuration to the goal. APPROACHES: CELL DECOMPOSITION — divide C-space into cells and search the resulting graph. Suffers from the curse of dimensionality: a 6-DOF arm's C-space discretised at just 10 values per joint has 10⁶ = 1,000,000 cells, and at 20 values per joint it is 6.4 × 10⁷. POTENTIAL FIELDS — attract to the goal, repel from obstacles. Fast and can get stuck in local minima. SAMPLING-BASED PLANNERS — RRT (rapidly-exploring random tree) and PRM (probabilistic roadmap): sample random configurations and connect them. THESE DOMINATE IN PRACTICE, because they avoid discretising the whole space, and they are PROBABILISTICALLY COMPLETE — they find a solution if one exists, given enough time, without guaranteeing an optimal one. THIS IS THE SEARCH SECTION'S MATERIAL, in a continuous high-dimensional space where exhaustive methods fail. 6. KINEMATICS FORWARD KINEMATICS: given the joint angles, where is the hand? A direct calculation, with one answer. INVERSE KINEMATICS: given a desired hand pose, what joint angles achieve it? HARDER — there may be NO solution (out of reach), ONE, SEVERAL (elbow up or elbow down), or INFINITELY MANY (a redundant arm). THE ASYMMETRY IS THE POINT: forward is a function, inverse is a relation, and inverse is what a task actually requires. 7. CONTROL Execute the plan despite disturbance. A PID controller (proportional, integral, derivative) on the error is the workhorse. Two philosophies: OPEN-LOOP: execute the plan blindly. Fails as soon as reality diverges. CLOSED-LOOP: measure the error and correct continuously. AND THE LAYERED ARCHITECTURE from ACtE0901 is mandatory here: a fast reactive layer for safety at ~10 ms, a slower planning layer at ~seconds, with the reactive layer able to override. The arithmetic in that topic — 200 reactive cycles during one replan — is a robotics fact before it is an architectural preference.

WHERE ROBOTS WORK, and the pattern is instructive: INDUSTRIAL MANUFACTURING — welding, painting, assembly, pick and place. Mature and enormously deployed. WHY IT WORKED FIRST: the environment is STRUCTURED and CONTROLLED. The part arrives in a known orientation, the lighting is fixed, and nothing unexpected walks past. Take away that structure and the same robot fails. WAREHOUSE AND LOGISTICS — mobile robots moving shelves, sorting parcels. Structured environment, engineered for the robots. SURGICAL ASSISTANCE — teleoperated systems that scale and steady a surgeon's motions. NOTE THAT THE HUMAN REMAINS IN CONTROL, which is the error-cost argument from the AI applications checklist. AGRICULTURE — autonomous tractors, weeding robots, harvesting. Semi-structured: rows are regular, plants are not. INSPECTION IN HAZARDOUS PLACES — pipelines, reactors, disaster sites, underwater, space. THE STRONGEST CASE FOR ROBOTS is where a human cannot go. DOMESTIC — vacuum cleaners are the success, and they succeeded by drastically simplifying the task: cover the floor, do not identify objects. AUTONOMOUS VEHICLES — the hardest deployed case, because the environment is unstructured, dynamic, multi-agent and safety-critical simultaneously. THE PATTERN ACROSS ALL OF THEM: ROBOTS SUCCEED IN PROPORTION TO HOW MUCH STRUCTURE THE ENVIRONMENT HAS — either naturally or because it was engineered for them. That is the single most useful predictive rule in the field. THE OPEN PROBLEMS: MANIPULATION OF UNKNOWN OBJECTS — grasping an arbitrary object is unsolved in general. Humans do it without thought; robots need the object modelled. DEXTERITY — human hands remain far beyond current actuators LEARNING FROM FEW EXAMPLES — a person shown a task once can do it; a robot typically needs many trials, and each trial in the physical world is slow and may break something SIM-TO-REAL TRANSFER — training in simulation is fast and safe, and policies learned there often fail on real hardware because the simulation's physics is approximate. Bridging that gap is an active research area. SAFE INTERACTION WITH PEOPLE — predicting what a human will do, and failing safely when wrong POWER AND ROBUSTNESS — batteries, and components that survive years of vibration and dust WHY ROBOTICS IS THE HONEST TEST OF AI, and it is worth ending the section on this: · you cannot ignore uncertainty — the sensors are actually noisy · you cannot ignore real time — the deadline is physical · you cannot ignore the cost of error — the robot breaks something · you cannot ignore the unmodelled case — the world supplies them constantly A TECHNIQUE THAT WORKS ON A BENCHMARK AND FAILS ON A ROBOT HAS BEEN TOLD SOMETHING TRUE ABOUT ITSELF. Every simplification that software permits — perfect information, unlimited time, reversible actions — the physical world withdraws, which is why robotics has been both the slowest-moving and the most informative part of AI.