Optimal path planning for a new type of 6RSS parallel robot based on virtual displacements expressed through Hermite polynomials

Abstract

The paper presents a method of determining the optimal trajectory of the characteristic point belonging to the end effector of a parallel robot with six degrees of freedom type 6RSS. The parallel robot is composed of a fixed plate and a mobile platform connected by six independent kinematic chains. Each of the six kinematic chains was part of one rotational actuating joint and two spherical joints. Based on the kinematic analysis, the motions of the end effector element were defined for manipulation operations using polynomial expressions of geometric parameters as time functions. By means of computational programs the polynomial variation of the motion parameters was determined. The data obtained were analysed on the basis of CAD programs through which the angular velocities of the actuating arms were determined when the end effector followed the trajectory described by the Hermite function. Using the same Hermite polynomials, two methods for optimizing the trajectory of the characteristic point were developed, the first intended to minimize its length and the second to minimize the runtime of the trajectory.