## Book Chapter: Chapter 9

Trajectory Generation

#### Chapter 9 Autoplay

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.

#### 9.1 and 9.2. Point-to-Point Trajectories (Part 1 of 2)

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.

#### 9.1 and 9.2. Point-to-Point Trajectories (Part 2 of 2)

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

#### 9.3. Polynomial Via Point Trajectories

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

#### 9.4. Time-Optimal Time Scaling (Part 1 of 3)

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.

#### 9.4. Time-Optimal Time Scaling (Part 2 of 3)

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

#### 9.4. Time-Optimal Time Scaling (Part 3 of 3)

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.