On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation

Abstract

In robotics and automated manufacturing, motion functions for parts of machines need to be designed. Many proposals for the shape of such functions can be found in the literature. Very often, time efficiency is a major criterion for evaluating the suitability for a given task. If there are higher precision requirements, the reduction in vibration also plays a major role. In this case, motion functions should have a continuous jerk function but still be as fast as possible within the limits of kinematic restrictions. The currently available motion designs all include assumptions that facilitate the computation but are unnecessary and lead to slower functions. In this contribution, we drop these assumptions and provide an algorithm for computing a jerk-continuous fifteen segment profile with arbitrary initial and final velocities where given kinematic restrictions are met. We proceed by going systematically through the design space using the concept of a varying intermediate velocity and identify critical velocities and jerks where one has to switch models. The systematic approach guarantees that all possible situations are covered. We implemented and validated the model using a huge number of random configurations in Matlab, and we show that the algorithm is fast enough for online trajectory generation. Examples illustrate the improvement in time efficiency compared to existing approaches for a wide range of configurations where the maximum velocity is not held over a period of time. We conclude that faster motion functions are possible at the price of an increase in complexity, yet which is still manageable.