Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

This video introduces the concepts of paths, trajectories, and time scaling a path to get a trajectory. It also introduces representations of straight-line paths, constant screw paths, and paths that combine straight-line motion in Cartesian space with constant rotation.

This video introduces third-order polynomial, fifth-order polynomial, trapezoidal, and S-curve time scalings to turn a path into a trajectory.

This video introduces robot trajectories passing through via points based on cubic polynomial interpolation.

This video defines the problem of finding the time-optimal time scaling of a robot path that respects actuator force and torque limits. The dynamics of the robot are rewritten in terms of the path parameter s and its derivatives, and the actuator limits place limits on the path acceleration, the second time derivative of s.

This video continues the derivation of the time-optimal time-scaling algorithm for robot trajectories by interpreting the path acceleration constraints (due to actuator limits) as cones of feasible motions in the (s, s-dot) phase plane, where s is the path parameter. Time-optimal motions are either “bang-bang” (maximum acceleration followed by maximum deceleration) or they touch a

Building on the previous two videos, this video derives an algorithm for finding the time-optimal time scaling along a path that respects actuator limits. The result is the fastest possible motion along the pre-specified path.