A dynamic optimal trajectory generator for Cartesian Path following

This paper considers a dynamic and adaptive trajectory generator for negotiating paths using S-curves. Applying constant jerk transitions between the constant acceleration and deceleration periods of the trajectory, the trajectory will optimally transition to the desired speed setting. Optimal is defined to be the minimum time to transition from the current speed to the set speed for the move segment when jerk and acceleration are limited. The S-curve equations will adapt to instantaneous changes in speed setting and path length. An integrated motion planner will determine allowable speeds and transitional profiles based on the remaining move distance.