张国庆,李宗道,吴剑雄,顾浩宇,李清都.基于同伦延拓的冗余机械臂逆运动学优化算法研究[J].包装工程,2024,45(7):197-204.
ZHANG Guoqing,LI Zongdao,WU Jianxiong,GU Haoyu,LI Qingdu.Inverse Kinematics Optimization Algorithm of Redundant Manipulator Based on Homotopy Continuation[J].Packaging Engineering,2024,45(7):197-204. |
| 基于同伦延拓的冗余机械臂逆运动学优化算法研究 |
| Inverse Kinematics Optimization Algorithm of Redundant Manipulator Based on Homotopy Continuation |
| 投稿时间：2023-07-10 |
| DOI：10.19554/j.cnki.1001-3563.2024.07.025 |
| 中文关键词: 冗余机械臂 逆运动学 Levenberg Marquardt 同伦延拓 二进制改进粒子群算法 |
| 英文关键词: redundant manipulator inverse kinematics Levenberg Marquardt homotopy continuation binary improved particle swarm algorithm |
| 基金项目:国家自然科学基金(92048205) |
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| 中文摘要: |
| 目的 针对偏置冗余机械臂的逆运动学，采用传统数值法存在依赖初始值、奇异位姿收敛性差等问题，提出一种改进数值法。方法 首先将非线性方程组转化为同伦方程组，引入同伦延拓算法能够有效避免依赖初始值的问题，同时能够获取逆运动学解空间。然后考虑奇异位姿，将同伦方程组转化为最小二乘问题，采用Levenberg Marquardt算法对同伦方程组进行路径追踪，以获取逆运动学解空间。最后将关节极限避免问题映射为解空间优化问题，引入二进制改进粒子群优化算法，获得最优逆运动学解。结果 实验结果表明，相较于传统数值法，文中所提数值法针对逆运动学求解具有更高的收敛率、更快的收敛速度，同时二进制改进粒子群算法能够有效避免关节极限问题。结论 采用文中所提数值法求解逆运动学的精度较高，能够满足实时性要求，对于机械臂用于包装作业具有一定的理论意义和工程应用价值。 |
| 英文摘要: |
| The work aims to propose an improved numerical method to solve problems of dependence on the initial value and poor convergence of singular poses in the traditional numerical method in terms of complex inverse kinematics of the offset redundant manipulator. First, the nonlinear equations were transformed into homotopy equations. The introduction of homotopy continuation algorithm could effectively avoid the initial value dependence problem, and at the same time obtain the inverse kinematics solution space. Then taking the singular pose into account, the homotopy equations were transformed into a least squares problem, and the Levenberg Marquardt algorithm was used to track the path of the homotopy equations to obtain the inverse kinematics solution space. Finally, the joint limit avoidance problem was mapped to a solution space optimization problem, and the binary improved particle swarm optimization algorithm was introduced to obtain the optimal inverse kinematics solution. The experimental results showed that the numerical method proposed in this paper had a higher convergence rate and faster convergence speed for inverse kinematics than the traditional numerical method, and the binary improved particle swarm optimization algorithm could effectively avoid the joint limit problem. This numerical method has high accuracy in solving inverse kinematics and can meet real-time requirements, and has certain theoretical significance and engineering application value for the subsequent use of the manipulator in packaging operations. |
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