Robotics¶

Robotics is the integration of perception, planning, and control to enable physical systems to sense, reason about, and act in the real world. It's AI applied to embodied agents.

Key Concepts¶

Configuration Space¶

State: Position, orientation, joint angles (kinematics)
Configuration space: Space of all possible robot configurations
Free space: Configurations without collision
Workspace: Cartesian coordinates of robot end-effector

Kinematics¶

Forward kinematics: Configuration → end-effector position (straightforward)
Inverse kinematics: End-effector position → configuration (non-unique, hard)
Degrees of freedom: Independent directions of motion (6D for rigid body in 3D)

Core Algorithms¶

Localization & Mapping¶

Monte-Carlo-Localization (MCL): - Particle filter tracking robot position - Prediction: Propagate particles via motion model P(X'|X, v, ω) - Update: Weight by sensor likelihood (ray-casting) - Resampling: Focus particles on likely states - Handles global localization + multimodal uncertainty

Extended-Kalman-Filter (EKF): - Linearizes nonlinear models via Taylor expansion - Tracks belief as Gaussian (mean + covariance) - Works well with identifiable landmarks - Scales quadratically — practical for ~100s of landmarks

SLAM (Simultaneous Localization and Mapping): - Build map while localizing within it - EKF-SLAM: Augment state with landmark locations - Graph relaxation: For larger maps - Critical for autonomous exploration

Path Planning¶

Cell Decomposition: - Divide free space into cells - Regular grid: Simple but high-dimensional curse - Exact decomposition: Irregular cells matching boundaries - Hybrid A*: Continuous state per grid cell, smooth trajectories

Skeletonization: - Voronoi graph: Maximize clearance to obstacles - Probabilistic Roadmap: Sample-based, scales to high dimensions - RRT (Rapidly-exploring Random Tree): Quickly explore high-D spaces

Planning Under Uncertainty: - Compute policies (not single paths) for all states - MDP value iteration for navigation - Information-gathering actions to reduce uncertainty - Robust fine-motion planning for assembly

Control¶

Classical Controllers: - P (Proportional): a = K_P × error (causes oscillation) - PD (Proportional-Derivative): Add derivative term to dampen - PID (Proportional-Integral-Derivative): Add integral to eliminate steady-state error

Potential Fields: - Attractive force toward goal - Repulsive force away from obstacles - Real-time, no explicit planning needed - Risk: Local minima trap robot

Reactive Control: - Augmented Finite State Machines (AFSMs) - Direct sensor-to-action without explicit model - Emergent behavior from simple rules - Example: Hexapod walking with stuck detection

Perception¶

Sensor Types¶

Range: Sonar, LIDAR, radar, structured light, stereo
Imaging: Cameras (passive, rich but complex)
Proprioceptive: Encoders, accelerometers, gyroscopes, GPS
Tactile: Force/torque, contact

Sensor Models¶

Noise model: P(z|z*) — observed vs. expected reading
Ray-casting: Compute expected sensor values
Beam model: Accounts for correct readings, unexpected obstacles, failures, noise

Perception Challenges¶

Sensor noise: Requires probabilistic models
Partial observability: Infer hidden state
Data association: Match observations to landmarks
Multimodal distributions: Symmetry creates ambiguity
Dynamic environments: Moving obstacles, lighting changes

Machine Learning in Robotics¶

Adaptive Perception¶

Robot collects labeled training data via complementary sensors
Example: Autonomous car uses LIDAR to label terrain, trains vision classifier on color/texture
Enables fast feedback loops and domain adaptation

Low-Dimensional Embedding¶

Map high-D sensor streams to lower-D spaces (unsupervised)
Discover suitable internal representations while learning models

Reinforcement Learning¶

Policy search: Learn control policies for complex dynamics
Example: Autonomous helicopter acrobatics from 4 minutes of human flight data
Simulator + real-world deployment

Perception Learning¶

Terrain classification, object recognition, activity recognition
SVM, mixture models, neural networks on sensor data
Web-scale data enables large feature sets

Software Architectures¶

Type	Description	Strengths	Weaknesses
Subsumption	Layered reactive FSMs	Real-time, emergent	No planning, inflexible
Three-layer	Reactive + executive + deliberative	Combines reaction & planning	Complex integration
Pipeline	Parallel data flow: sensors → perception → control	Fast, robust, asynchronous	Uses stale sensor data

Application Domains¶

Manufacturing: Assembly, painting, welding
Transportation: Autonomous vehicles, warehouse robots, delivery drones
Healthcare: Surgical robots (da Vinci), rehabilitation, prosthetics
Exploration: Mars rovers, underwater mapping, drones
Services: Vacuum cleaners (Roomba), lawn mowers, tour guides
Hazardous: Nuclear cleanup, bomb disposal, mine clearing

Integration with AI¶

Robotics integrates: - Search & Planning — Find action sequences - Probabilistic-Reasoning — Handle uncertainty - Machine-Learning — Adapt to new environments - Control-Theory — Execute smooth, stable actions - Perception — Understand world state

Perception — Extracting information from sensors
Planning — Computing action sequences
Control-Theory — Executing smooth actions
Machine-Learning — Learning from experience
Reinforcement-Learning — Learning control policies

References¶

Russell & Norvig (2010): Chapter 25 - Robotics