Trajectory Tracking

Keeping a robot's actual motion closely following a time-varying reference trajectory, driving the error toward zero.

Trajectory tracking is a control problem: given a reference trajectory qd(t), drive the actual state q(t) so that the error qd(t) − q(t) goes to zero over time. A typical approach is ‘feedforward plus feedback’: feedforward uses the model to precompute the velocity or torque needed along the trajectory, and feedback (e.g., PD) corrects based on the current error; computed torque control combines both. Performance is judged by steady-state error, overshoot, and settling time. It differs from path tracking, which only requires following a geometric curve and can adjust its own speed; trajectory tracking has a requirement at every point in time. A reference trajectory is best kept away from the actuators' hard limits, to leave margin for correction. A humanoid robot imitating human motion — ‘motion tracking’ — follows the same idea.

ExampleChapter 11 of Modern Robotics simulates the same joint trajectory three ways: feedforward alone or PID feedback alone both show noticeable error, while computed torque control (feedforward plus feedback) tracks best.

Also called

Trajectory Following

Related

Trajectory Planning · Proportional-Derivative Control · Feedforward Control · Computed Torque Control · Motion Tracking · Linear Quadratic Regulator

Sources

Lynch & Park, Modern Robotics (2017 preprint), Ch.11 Robot Control 与 13.3 Trajectory tracking (Chinese)
Russ Tedrake, Underactuated Robotics: Trajectory Optimization（沿轨迹的 LQR 稳定） (Chinese)