为了实现超冗余机械臂的实时在线规划, 本文提出一种基于雅克比转置矩阵的人工势场轨迹规划方法。轨迹规划不仅要满足末端跟踪精度要求, 而且要满足关节速度和角度约束, 关节速度主要由轨迹规划算法的增益决定, 而增益的大小决定系统稳态性能的好坏, 通过优化势场函数和使用加权关节速度, 在避免关节限制的前提下减小关节速度范数, 从而能选择更大的增益。使用蒙特卡洛法建立最大关节速度与增益的关系, 从而确定增益范围。分别在点对点运动和轨迹跟踪运动中选取不同的增益证明算法的正确性和有效性, 并在轨迹跟踪运动中引入速度前馈, 通过李雅普诺夫稳定性定理证明算法稳定性。通过以超冗余机械臂为模型仿真验证, 得出在点对点运动下末端位置偏差小于10-4 mm, 姿态偏差小于1×10-5 rad; 轨迹跟踪运动的位置偏差小于10-3 mm, 姿态偏差小于1×10-4 rad。最后进行实验验证, 虽然实验过程中轨迹偏差相比于仿真增加一个数量级, 但仍符合实验任务需求。

Because their inverse kinematics do not have analytical solutions, hyper-redundant manipulators cannot be directly solved by the geometric method. To realize real-time planning, this study proposes an artificial potential field trajectory planning method based on the Jacobian transposition matrix. Trajectory planning must satisfy not only the requirements of end-tracking accuracy but also the joint velocity and angular constraints. The joint velocity is mainly determined by the gain of the trajectory planning algorithm. Through the optimization of the potential field function and use of weighted joint velocities, the joint speed norms can be reduced under the precondition of avoiding joint restriction. Thus, a larger gain can be selected to help the system achieve a better steady-state performance. The Monte Carlo method was used to establish the relationship between the maximum joint speed and gain, which is necessary to determine the gain range for selecting an appropriate gain. The correctness and effectiveness of the algorithm can be proved by selecting different gains in point-to-point and trajectory tracking motion. The study also introduces velocity feedforward in trajectory tracking motion and proves the stability of the two motion formal algorithms by the Lyapunov stability theorem. Results of a simulation verification of the hyper-redundant manipulator independently designed and manufactured by our laboratory revealed that the end position deviation and attitude deviation were less than 10-4 mm and 1×10-5 rad, respectively, based on the premise of ensuring rapid point-to-point movement. In addition, the trajectory tracking movement position deviation and altitude deviation were less than 10-3 mm and 1×10-4 rad, respectively. Finally, experimental verification revealed that although the trajectory deviation in the experimental process increased by an order of magnitude compared to the simulation, the requirements of the experimental task were still met.