基于调整步长牛顿法的Stewart并联机构位置正解

针对采用牛顿或拟牛顿迭代算法求解Stewart并联机构接近奇异位姿的位置正解时存在计算结果不收敛以及采用牛顿下山迭代算法求解时间较长的问题,提出了将调整步长牛顿法应用于并联机构位置正解。首先设计基于调整步长牛顿法的Stewart并联机构位置正解流程;然后,采用遗传算法以步长矩阵初值及等比参数为变量,以Stewart并联机构64种极限位姿正解所需迭代步数为目标,得到步长矩阵初值及等比参数最优值。通过数值算例,设置机构杆长绝对误差为0.01mm,对64种极限位姿进行正解,牛顿法与拟牛顿法共6种位姿正解不收敛;牛顿下山法10种位姿正解时间大于2.0ms;调整步长牛顿法正解时间均小于2.0ms。调整步长牛顿法为Stewart并联机构位置正解的实时应用提供了理论指导。

Forward kinematics of Stewart parallel manipulator based on step-adjusting Newton method

Forward kinematics of the near singular position of the Stewart parallel manipulator based on the Newton method or quasi-Newton method are not converge; Newton downhill method is time-consuming, sometimes. To resolve the situation, a method of applying the step-adjusting Newton method to a parallel manipulator is proposed. Firstly, the process of forward kinematics of the Stewart parallel manipulator based on the step-adjusting Newton method was designed. Then, the fewest iterative steps in the forward kinematics of sixty-four kinds of utmost poses was used as the objective function. The initial values of the step matrix and geometric parameters were taken as design variables by genetic algorithm to obtain the optimal values. Numerical examples show that when the absolute error of the rod length was set as 0.01 mm, in solving the forward kinematics of sixty-four kinds of utmost poses, the Newton method or quasi-Newton method did not converge on six kinds of utmost poses. The Newton downhill method takes longer than 2.0 ms on ten kinds of utmost poses, while the time taken by the step-adjusting Newton method was less than 2.0 ms. The step-adjusting Newton method provides theoretical guidance for the forward kinematics of the Stewart parallel manipulator in real-time occasions.