非冗余机械臂奇异路径跟踪算法

非冗余机械臂跟踪设定路径时 ,奇异点上 Jacobian矩阵降秩 ,基于 Jacobian逆的运动规划方法将失效。针对此问题提出一种精确跟踪奇异路径的算法 ,把路径跟踪问题化为非线性特征值问题 ,用数值方法求解路径跟踪方程 ,得到以扩展空间解曲线弧长为参数的逆运动学解 ,而关节轨迹可规划为弧长参数的任意函数。算法采用自适应步长和一阶模型预测方法 ,具有较低计算复杂性和较快收敛速度。给出一个仿真算例 ,说明了算法的有效性

Singular path tracking algorithm for non-redundant robot manipulators

In the execution of path tracking tasks of non redundant robot manipulators, the rank deficiency of the Jacobian matrix makes Jacobian based motion planning methods ineffective. A novel approach is presented to plan smooth joint trajectories to precisely track prescribed paths containing singularities. The singular path tracking is formulated as a nonlinear eigenvalue problem. The path tracking equation is solved numerically to find the inverse kinematic solution as a function of the parameter, the arc length of the solution curve to the path tracking equation in the augmented joint space. The joint trajectories can be generated as arbitrary functions of the arc length parameter. The algorithm was first order model prediction and adaptive step size adjustment techniques to speed up the numerical solution. Numerical simulations illustrate the effectiveness of the presented approach.