Computationally efficient implementation of the Gauss–Newton method for solving the forward kinematics of redundant cable‐driven parallel robots

Abstract

AbstractCable‐driven parallel robots (CDPRs) are parallel robots in which cables are used instead of rigid connecting elements. An important task here, as in other areas of robotics, are kinematic calculations. The state of the CDPR can be described either in Cartesian workspace coordinates as a pose or in the joint space via the cable lengths. The calculation of the cable lengths from a given platform pose is relatively simple for CDPRs. In contrast, the forward kinematics, that is, the calculation of the pose from the cable lengths, is complex due to the parallel topology and often cannot be solved analytically. In addition, CDPR systems are often designed redundantly, with more cables than Cartesian degrees of freedom. This redundancy causes that the solution of the forward kinematics can be considered as a fitting problem, where for measured cable lengths, the solution with minimum error norm is sought. In this paper, an approach based on the Gauss–Newton method is presented. It is described how a computationally efficient implementation is possible when using quaternions under consideration of the unit quaternion constraints.