pathfollowing

Path following is a control problem in robotics and autonomous systems in which a vehicle or agent is commanded to follow a predefined geometric path. The path may be a continuous curve in the plane or space, or a sequence of waypoints. The objective is to minimize deviation from the path while advancing along it, subject to the system's dynamics, actuation limits, and safety constraints. Path following assumes the path is given, differing from path planning which generates the path.

A common framework uses a path parameterization, typically arc length, and a path-relative coordinate frame such as the Frenet frame. The primary errors are cross-track error, the lateral distance to the path, and heading error relative to the path tangent. The control action blends feedback from these errors with optional feedforward terms based on path curvature to improve trackability.

Representative algorithms include Pure Pursuit, which steers toward a look-ahead point; the Stanley method, combining heading and cross-track errors; and more general approaches such as Model Predictive Control (MPC) or LQR-based trackers that optimize a cost function while enforcing constraints. Some systems also employ velocity profiles and dynamic re-planning when the path changes or obstacles appear.

Key implementation considerations include converting sensor measurements into a smooth, discrete path representation, respecting nonholonomic constraints, ensuring feasibility under acceleration and steering limits, and mitigating latency. Path following is frequently integrated with obstacle avoidance and real-time replanning in dynamic environments.

Applications span autonomous road vehicles, mobile robots, aerial drones, ships, and industrial manipulators. Evaluation uses metrics such as maximum cross-track error, root-mean-square tracking error, along-path progress, and convergence time.