A dynamic optimal trajectory generator for Cartesian Path following

Red, Edward, "A dynamic optimal trajectory generator for Cartesian Path following" (2000). All Faculty Publications. Paper 589. SUMMARY 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. INTRODUCTION Motion planning and trajectory generation lie at the heart of robotic and machine tool path control. New digital drive technologies and computational speeds are changing motion control paradigms that, in the past, relied on pre-processors to descretize, shape and buffer moves into a series of micro move segments passed to the controller. The path speeds were limited by how fast the descretized move segments could be processed by the controller, i.e. the block processing speed. Free-form shapes (NURBS, B-splines, etc.) now form the core of most modern CAD/CAM systems. The current movement is to develop dynamic interpolators that can process object shapes directly, rather than decomposing them into small linear segments. The challenge of modern motion planning and trajectory control is to process a series of macro moves dynamically and smoothly, while applying a set of limiting conditions such as speed, acceleration and jerk. This paper will show how this might be accomplished by proper motion planning and trajectory generation. An optimal approach is applied that adapts to instantaneous speed changes and increases in path length.