﻿ 考虑奇异摄动的船用水下机械臂轨迹自适应规划方法
 舰船科学技术  2024, Vol. 46 Issue (11): 50-53    DOI: 10.3404/j.issn.1672-7649.2024.11.009 PDF

Adaptive trajectory planning method for underwater robotic arms on ships considering singular perturbations
CAI Weiguo, GUO Shenghan, YUAN Wei, ZHANG Bozhi, WANG Shulin
School of Mechanical and Power Engineering, Dalian Ocean University, Dalian 116023, China
Abstract: To ensure that underwater robotic arms on ships can smoothly complete operational tasks in environments with singular perturbations, uncertainties, and dynamic characteristics, a trajectory adaptive planning method for underwater robotic arms on ships considering singular perturbations is studied. Divide the complex underwater robotic arm structure into slow subsystems and fast subsystems, analyze the state of the underwater robotic arm under singular perturbation, study the adaptive trajectory planning method for suppressing singular perturbation, design a trajectory planning objective function that minimizes the vibration of the robotic arm under the influence of singular perturbation, and use a wolf pack optimization algorithm to solve the joint angular displacement that satisfies this objective function angular velocity and angular acceleration planning scheme. Input the solved joint angular displacement, angular velocity, and angular acceleration into an adaptive fuzzy PID tracking controller to achieve adaptive generation of singular perturbation suppression trajectories. The experimental results show that this method can adaptively plan a stable operation trajectory for the robotic arm in a singular perturbation environment, and the end vibration displacement of the robotic arm is effectively suppressed.
Key words: singular perturbation     underwater robotic arm for ships     trajectory planning     wolf pack optimization algorithm     adaptive fuzzy PID     geometric trajectory generation
0 引　言

1 机械臂轨迹自适应规划方法设计 1.1 考虑奇异摄动的船用水下机械臂状态分析

 ${\bar {\ddot p}_s} = \bar N_{ss}^{ - 1}\left[ { - \bar C_{gs}^1{{\bar p}_s} - \bar G_g^1 - \bar F_g^1 + \bar v} \right] 。$ (1)

1.2 基于奇异摄动抑制的轨迹规划 1.2.1 轨迹规划目标设计

 ${\overline {\ddot q} _s}\left( {{{\boldsymbol{N}}_g}\ddot p + {{\boldsymbol{C}}_g}\dot p + {C_g}p + {{\boldsymbol{H}}_g}} \right) = {{\boldsymbol{N}}_{gs}}\ddot \alpha \times {\bar \ddot p_s} 。$ (3)

1）船用水下机械臂作业轨迹不存在断点，且满足单调递增或递减状态。

2）船用水下机械臂作业轨迹中，关节角速度与加速度曲线光滑不存在断点，并处于限定范围内。

1.2.2 基于狼群优化算法的轨迹规划路径求解

1.3 基于自适应模糊PID的轨迹生成方法

 图 1 自适应模糊PID跟踪控制器结构示意图 Fig. 1 Structural diagram of adaptive fuzzy PID tracking controller

 ${K_P} = {K_{P0}} + \Delta {K_P} ，$ (5)
 ${K_I} = {K_{I0}} + \Delta {K_I} ，$ (6)
 ${K_D} = {K_{D0}} + \Delta {K_D}。$ (7)

2 实验分析 2.1 实验设计

2.2 性能分析

 图 2 机械手的可达区域与轨迹规划结果 Fig. 2 The reachable area and trajectory planning results of a robotic arm

 图 5 本文方法规划轨迹前机械臂末端振动位移 Fig. 5 This article proposes a method for planning the end vibration displacement of a robotic arm before trajectory planning

 图 6 本文方法规划轨迹后机械臂末端振动位移 Fig. 6 The end vibration displacement of the robotic arm after trajectory planning using the method described in this article

3 结　语

1）提高了船用水下机械臂作业稳定性，抑制了机械臂因奇异摄动而出现的振动问题。

2）提高了船用水下机械臂在实际应用中的可靠性，在突发障碍物的工况中，也能平稳抓取目标物体。且采用了自适应控制方法，能够自适应地调整船用水下机械臂轨迹生成参数，减少了人工干预。

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