An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines

This paper presents a new, highly effective approach for optimal smooth trajectory planning of high-speed pick-and-place parallel robots. The pick-and-place path is decomposed into two orthogonal coordinate axes in the Cartesian space and quintic B-spline curves are used to generate the motion profile along each axis for achieving C4-continuity. By using symmetrical properties of the geometric path defined, the proposed motion profile becomes essentially dominated by two key factors, representing the ratios of the time intervals for the end-effector to move from the initial point to the adjacent virtual and/or the via-points on the path. These two factors can then be determined by maximizing a weighted sum of two normalized single-objective functions and expressed by curve fitting as functions of the width/height ratio of the pick-and-place path, so allowing them to be stored in a look-up table to enable real-time implementation. Experimental results on a 4-DOF SCARA type parallel robot show that the residual vibration of the end-effector can be substantially reduced thanks to the very continuous and smooth joint torques obtained.