Trajectory Planning

Deciding where a robot should be and how fast at every moment in time — a path plus a schedule.

Trajectory planning answers ‘where to be at what time, at what speed.’ Modern Robotics splits a trajectory into two parts: the path, a purely geometric sequence of configurations describing only which positions are visited; and the time scaling s(t), which specifies which point along the path to be at, at each moment. Together they form the trajectory θ(t), which must be smooth enough and respect the joint's velocity, acceleration, and torque limits. It is related to but distinct from path planning and motion planning: path planning focuses on finding a feasible route around obstacles without regard to time, while trajectory planning adds time and dynamics constraints on top of a route. Common techniques include polynomial time scaling, trapezoidal or S-curve velocity profiles, splines through waypoints, and time-optimal parameterization that accounts for actuator limits.

ExampleMoveIt's typical pipeline: a planner first produces a collision-free sequence of joint waypoints with no timing information, then time parameterization (mainly the TOTG algorithm, sometimes followed by Ruckig to limit jerk) adds timing based on joint velocity and acceleration limits, producing an executable trajectory.

Also called

Trajectory Generation

Related

Path Planning · Motion Planning · Time Parameterization · Time-Optimal Path Parameterization · Trapezoidal Velocity Profile · Trajectory Tracking

Sources

Lynch & Park, Modern Robotics (2017 preprint), Ch.9 Trajectory Generation
MoveIt Docs: Time Parameterization