A dual quaternion approach to efficient determination of the maximal singularity-free joint space and workspace of six-DOF parallel robots. (November 2018) - Yang, XiaoLong; Wu, HongTao; Chen, Bai; Li, Yao; Jiang, SuRong
Highlights: We propose to determine the maximal singularity-free joint-space represented by a 6-cube and then determine the workspace defined on that joint-space for the first time. The scaled Jacobian matrices in terms of a unit dual quaternion are derived for singularity detection. We construct an efficient algorithm for detecting singularities in the joint space and the maximal singularity-free workspace is obtained simultaneously as the maximal singularity-free joint space is determined. A 6-UP S and a 6-P US parallel robots are presented to demonstrate the effectiveness of the new approach. Abstract: The avoidance of singularities is critical to design and control of parallel robots. This paper aims at efficient determination of the maximal singularity-free joint space and workspace of a class of six-DOF parallel robots with six kinematic chains of same type. We represent the singularity-free joint space by a 6-cube and determine it firstly. The singularity-free workspace is generated by continuous motion of all active joints in the singularity-free joint space. As a result, the boundary of the workspace can be obtained with simultaneous consideration of position and orientation of the mobile platform. The size relation between the maximal singularity-free joint space and workspace is discussed. To efficiently determine the singularity-free joint space and workspace, we propose dual quaternion-based Jacobian matrices and construct an efficient algorithm. The algorithm detects singularities in a given joint space and simultaneously calculates its corresponding workspace. The computational costs of the proposed algorithm and the traditional one are compared using a 6-UP S parallel robot, leading to 9 seconds and 458 seconds respectively. Finally, both the maximal singularity-free joint space and workspace of a 6-P US parallel robot are determined to further demonstrate the effectiveness of the new approach.