Trajectory

A trajectory is a time-parameterized sequence of robot states (joint angles or Cartesian poses) that describes how the robot moves from a start configuration to a goal. Trajectories can be generated by motion planners (planning a collision-free path then time-parameterizing it for smooth execution), by teleoperation recording (capturing the operator's motion at a fixed frequency), or predicted directly by a neural policy. Trajectory smoothness and velocity continuity are important for physical robot safety — abrupt discontinuities cause mechanical stress and can trigger safety stops. Trajectory representations include splines, dynamic movement primitives (DMPs), and discrete waypoint sequences.