Xie Zhengtai, Jin Long, Luo Xin, Sun Zhongbo, Liu Mei
IEEE Trans Neural Netw Learn Syst. 2022 Feb;33(2):615-628. doi: 10.1109/TNNLS.2020.3028304. Epub 2022 Feb 3.
For the existing repetitive motion generation (RMG) schemes for kinematic control of redundant manipulators, the position error always exists and fluctuates. This article gives an answer to this phenomenon and presents the theoretical analyses to reveal that the existing RMG schemes exist a theoretical position error related to the joint angle error. To remedy this weakness of existing solutions, an orthogonal projection RMG (OPRMG) scheme is proposed in this article by introducing an orthogonal projection method with the position error eliminated theoretically, which decouples the joint space error and Cartesian space error with joint constraints considered. The corresponding new recurrent neural networks (NRNNs) are structured by exploiting the gradient descent method with the assistance of velocity compensation with theoretical analyses provided to embody the stability and feasibility. In addition, simulation results on a fixed-based redundant manipulator, a mobile manipulator, and a multirobot system synthesized by the existing RMG schemes and the proposed one are presented to verify the superiority and precise performance of the OPRMG scheme for kinematic control of redundant manipulators. Moreover, via adjusting the coefficient, simulations on the position error and joint drift of the redundant manipulator are conducted for comparison to prove the high performance of the OPRMG scheme. To bring out the crucial point, different controllers for the redundancy resolution of redundant manipulators are compared to highlight the superiority and advantage of the proposed NRNN. This work greatly improves the existing RMG solutions in theoretically eliminating the position error and joint drift, which is of significant contributions to increasing the accuracy and efficiency of high-precision instruments in manufacturing production.
对于现有的用于冗余机器人运动学控制的重复运动生成（RMG）方案，位置误差始终存在且波动。本文针对这一现象给出了答案，并进行了理论分析，以揭示现有RMG方案存在与关节角度误差相关的理论位置误差。为弥补现有解决方案的这一弱点，本文提出了一种正交投影RMG（OPRMG）方案，通过引入一种理论上消除位置误差的正交投影方法，该方法在考虑关节约束的情况下解耦了关节空间误差和笛卡尔空间误差。利用梯度下降法并借助速度补偿构建了相应的新型递归神经网络（NRNN），并提供了理论分析以体现其稳定性和可行性。此外，给出了在固定基座冗余机器人、移动机器人以及由现有RMG方案和本文提出的方案合成的多机器人系统上的仿真结果，以验证OPRMG方案在冗余机器人运动学控制方面的优越性和精确性能。此外，通过调整系数，对冗余机器人的位置误差和关节漂移进行了仿真比较，以证明OPRMG方案的高性能。为突出关键要点，对冗余机器人冗余度求解的不同控制器进行了比较，以突出所提出的NRNN的优越性和优势。这项工作在理论上消除位置误差和关节漂移方面极大地改进了现有的RMG解决方案，这对提高制造生产中高精度仪器的精度和效率具有重要贡献。
