Robot Control

State, Dynamics, and Feedback

Robot control is the discipline of making physical machines behave purposefully through sensing and actuation. The fundamental elements are the state of the robot and its environment, the dynamics that govern how state evolves under actions, and feedback laws that compute actions from error.

Planners generate reference trajectories. Estimators recover hidden state from noisy sensors. Constraints (joint limits, obstacles, torque saturation) bound what is feasible.

This note builds directly on Newtonian mechanics (the plant) and signal processing (sensing and filtering), and supplies the runtime layer for higher-level robotics and embodied AI.

Stability, Controllability, and Optimality

Lyapunov theory gives rigorous conditions for stability. Controllability tells us what is achievable in principle. Optimal control (LQR, MPC) and sampling-based planning provide constructive methods with performance and completeness guarantees under stated assumptions.

What We Can Measure and Improve

Tracking error, settling time, control effort, and success rate under disturbance are the observables. Gains, model quality, sensor placement, and planning algorithms are the direct causal levers.

Core Procedures

PID tuning, receding-horizon MPC, and RRT-style sampling-based planning are the workhorse algorithms that turn theory into working robot behavior.

(See the YAML for detailed steps.)

Closed-Loop Dynamical Systems

A controlled robot is a classic stock-and-flow system with strong balancing feedback loops (error correction) and planning/replanning loops. Uncertainty acts as a persistent disturbance that good estimation and robust control must reject.

The Hard Engineering Reality

Making robots work reliably outside the lab is extremely difficult. Model error, sensing limitations, real-time constraints, and safety requirements dominate the design space. The substrate captures the essential objects and trade-offs that every robotics team must manage.