Speed Acceleration Jerk Limited 7-Phase Solution

Minimize the duration between two points given start and end velocity and acceleration, and limits on jerk, acceleration, and velocity.

Given points A and B separated by distance s, and given the start velocity & acceleration at A and end velocity & acceleration at B, obtain a trajectory from A to B that minimizes the duration and satisfies the limits in jerk, acceleration, and velocity. Such a trajectory can be obtained by applying the heuristic "Travel as fast as possible in the forward direction for as long as possible". The trajectory is constructed in the following 7 phases:

1. Jerk to accelerate.
2. Constant acceleration at acceleration cap.
3. Unjerk from acceleration.
4. Coast at constant velocity.
5. Jerk to decelerate.
6. Constant deceleration at deceleration cap.
7. Unjerk from deceleration.