A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation. (January 2017) - Yang, XiaoLong; Wu, HongTao; Li, Yao; Chen, Bai
Abstract: The forward kinematics is the basis of the design and control of the parallel robots. This paper aims to provide an efficient solution to the forward kinematics of a class of six-degrees-of-freedom parallel robots for real-time applications. With a unit dual quaternion used as the generalized coordinates of the robot system, the forward kinematic equations are derived to be a set of quadratic ones. An efficient algorithm is proposed to get the actual solution to them. The convergence and singularity problems of the new algorithm have been discussed. We have provided a convergence strategy and revealed the internal relation of the singularity with that of the parallel robot, proving the feasibility of the algorithm and giving the working condition in the practical applications. The new algorithm have been compared to the Newton's method for an 8-UP S parallel robot, resulting in the time consumptions of 0.2187 milliseconds and 14.25 milliseconds respectively. And then we perform a simulation of the state-feedback control for an 8-P US parallel robot. The two examples present the applications of the new algorithm and demonstrate its validity and efficiency. Highlights: A unit dual quaternion is introduced as the generalized coordinates of the six-DOF robotic system. An efficient algorithm is proposed to get the actual solution to the forward kinematic equations for real-time control. It is revealed that the algorithm is always valid in the singularity-free workspace of the robot in real- time control.