Dynamic rotational trajectory planning of a cable-driven parallel robot for passing through singular orientations

Abstract

This paper presents a dynamic trajectory planning scheme for passing through singular orientations of a three degree-of-freedom (DOF) rotational cable-driven parallel robot (CDPR) that uses a rigid link to restrict its translational DOFs. The kinematics, dynamics and actuation singularity loci of this CDPR are analyzed. Singularity loci divide the workspace into four independent parts, which significantly limit the motion performance of the mechanism. To this end, consistency conditions that can allow the robot to steadily pass through singular orientations are studied. The vector inner product form of consistency conditions is derived, which can simplify the determination of the conditions of a more complex parallel robot. A sequence of target orientations are reached by planning dynamic trajectories using the unit quaternion. A modified spherical linear interpolation with a fifth degree polynomial as the time function is used for the generation of a trajectory which does not contain a singular orientation. Moreover, a transition segment using a seventh degree polynomial is designed to merge into the fifth degree polynomial in order to satisfy the consistency conditions and pass through singular orientations. Simulations are provided to verify the proposed technique.