6-UPS并联机器人快速正向运动学研究

Fast Forward Kinematics of 6-UPS Parallel Robot with Representative Points

根据平面平台型6-UPS并联机器人的结构特点,选取3个代表点的空间坐标作为参数来描述动平台的位置和姿态,结合3个代表点之间的约束条件,建立9个参数的一次与二次多项式方程组,通过对方程组进行消元处理,最终得到6个未知数表示的二次多项式方程。针对所获得的二次多项式方程组特点,改进传统牛顿-拉夫森数值迭代算法,并将其用于并联机器人的一般六维二次多项式方程数值求解,迭代算法收敛并可得到唯一解。数值算例表明,在同等条件下,传统旋转矩阵方法的计算时间为1. 42～2. 67 ms,所提代表点算法计算时间为0. 14～0. 23 ms,大大减少了计算时间,提高了收敛速度和计算效率,为并联机器人高性能闭环实时控制奠定了良好基础。

According to the structural characteristics of the planar 6-UPS parallel robot, the position and orientation of the mobile platform were described by choosing the spatial coordinates of three representative points as parameters. Combination of the constraint conditions during three representative points, nine quadratic polynomial equations with nine parameters were obtained. Finally, six quadratic polynomial equations, including six unknown parameters were obtained by eliminating three parameters of the nine equations. Aiming at the characteristics of the obtained quadratic polynomial equations, the traditional Newton Raphson numerical iteration algorithm was improved and used to the numerical solution of general six-dimensional quadratic polynomial equations of parallel robots. The iterative algorithm was converged and an unique solution was obtained. The numerical example demonstrated that the time consumptions of the proposed algorithm was 0.14~0.23 ms and the traditional method of rotation matrix was 1.42~2.67 ms respectively under the same conditions. The proposed algorithm of representative points greatly reduced the computational time, improved the convergence speed and computational efficiency and laid a better foundation for the closed-loop real-time control with high-performance of the six DOFs planar parallel robot.