Smooth Cubic Polynomial Trajectories for Human-Robot Interactions

With the growing importance of Human-Robot Interaction (HRI), the movement of the robots requires more and more attention to address the issues related to safety, efficiency and ergonomics. Trajectories are excellent candidates in the making of desirable motions designed for collaborative robots, because they allow to simply and precisely describe the motions. Despite the large number of works available for Online Trajectory Generation (OTG), there was, to our knowledge, no complete solution capable to simultaneously meet all the requirements of these new applications. In this paper we present a complete trajectory generation algorithm that build trajectories from arbitrary initial and final conditions, subject to general asymmetric bounds on jerk, acceleration and velocity. A review of the state of the art exposes the limits of the previous OTG works and reveals the difficult problem of non-linearity related with short motions. We explain how these non-linearities introduce discontinuities and we propose a solution based on sequences of segment of third degree polynomial functions.