多机械臂系统的区域最优覆盖控制

韩俊贤; 于晋伟; 杨卫华

doi:10.19304/J.ISSN1000-7180.2022.0527

多机械臂系统的区域最优覆盖控制

doi: 10.19304/J.ISSN1000-7180.2022.0527

太原理工大学数学学院, 山西晋中 030600

基金项目: 山西省自然科学基金（20210302124546）

详细信息

作者简介:
韩俊贤：男,（1998-）,硕士研究生.研究方向为机器人控制、非线性系统

杨卫华：男,（1984-）,博士,教授,博士生导师. 研究方向为图论及其应用、非线性系统

通讯作者:
男,（1989-）,博士, 讲师.研究方向为动力学与控制、非线性系统. E-mail：tyut_math_y@163.com

中图分类号: TP241
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- 被引次数: 0
出版历程
- 收稿日期: 2022-09-01
- 修回日期: 2022-10-26

Regional optimal coverage control of multi-manipulator systems

College of Mathematics, Taiyuan University of Technology, Jinzhong 030600, Shanxi, China

摘要

摘要:
针对具有强非线性特点的机械臂覆盖控制问题,基于Voronoi图理论,提出了一种多机械臂系统的区域最优覆盖控制算法. 首先,通过计算各个机械臂末端执行器的位置,将目标区域进行Voronoi划分；其次,根据凸优化理论,通过定义的描述区域覆盖控制效果的目标代价函数来衡量多机械臂系统关节以及末端执行器的移动是否最优；最后,结合机械臂系统特殊的动力学特性,给出了多机械臂系统的分布式区域最优覆盖控制器. 利用Lyapunov稳定性理论对该算法进行了稳定性分析,数值仿真实验表明了算法的实际有效性,即所提算法可以使得多机械臂系统的末端执行器在代价函数值最小的情况下到达相应Voronoi区域质心并且速度渐近收敛到零,形成对目标区域的最优覆盖. 特别地,该算法以机械臂为研究对象,丰富了现有的覆盖控制智能体模型研究,此外基于机械臂的非线性结构特性,算法中所设计的任务空间覆盖控制律,还可以应用到二阶系统智能体的覆盖控制研究中,拓宽了现有的基于一阶系统的覆盖控制研究.
- 多机械臂系统 /
- 覆盖控制 /
- Voronoi划分 /
- Euler-Lagrange系统
Abstract:
Aiming at the coverage control problem of the manipulator with strong nonlinear characteristics, based on Voronoi diagram theory, a region optimal coverage control algorithm for multi-manipulator systems is proposed. Firstly, the target region is divided into Voronoi regions by calculating the position of the end effectors of each manipulator; Secondly, according to the convex optimization theory, the optimal movement of the joints and the end effectors of the multi-manipulator systems are measured by the defined objective cost function that describes the effect of area coverage control; Finally, combined with the special dynamic characteristics of the manipulator system, the distributed area optimal coverage controller of the multi-manipulator systems is given. The Lyapunov stability theory is used to analyze the stability of the algorithm. Numerical simulation experiments show that the algorithm is effective, that is, the proposed algorithm can make the end effectors of the multi-manipulator systems reach the corresponding Voronoi region centroids with the minimum cost function value, and the speed gradually converges to zero, forming the optimal coverage of the target region. In particular, the algorithm takes the manipulator as the research object, which enriches the existing research on the coverage control agent model. In addition, based on the nonlinear structural characteristics of the manipulator, the coverage control law of the task space designed in the algorithm can also be applied to the coverage control research of the second order system agent, expanding the existing coverage control research based on the first order system.
- Multi-manipulator Systems /
- Coverage control /
- Voronoi tessellation /
- Euler-Lagrange system

HTML全文

图 1 二连杆机械臂结构示意图

Figure 1. Structure diagram of two link manipulator

下载: 全尺寸图片幻灯片

图 2 Voronoi区域及其质心示意图

Figure 2. Diagram of Voronoi regions and their centroids

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图 3 机械臂末端轨迹图

Figure 3. Trajectory diagram of manipulator end effectors

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图 4 机械臂区域覆盖过程图

Figure 4. Trajectory diagram of manipulator end effectors

下载: 全尺寸图片幻灯片

图 5 机械臂关节速度及末端位置变化图

Figure 5. Variation diagram of joint speed and end position of manipulators

下载: 全尺寸图片幻灯片

多机械臂系统最优覆盖控制算法总体框架
Input：多机械臂系统初始关节角$q=[q_{1}, \cdots, q_{n}]^{{\rm{T}}}$；末端执行器初始位置$P=[p_{1}, \cdots, p_{n}]^{{\rm{T}}}$;目标区域的敏感度函数$ \phi({e}) $；任务执行时间$ t $.
Output：多机械臂系统的末端移动轨迹、末端位置变化、关节速度变化及多机械臂最优分布；
1. 初始化：机械臂的关节角速度$d q=\left[\dot{q}_1, \cdots, \dot{q}_n\right]^{\rm{T}}$,末端速度$d P=\left[\dot{p}_1, \dot{p}_2, \cdots, \dot{p}_n\right]^{\rm{T}}$,末端加速度$d d P=\left[\ddot{p}_1, \ddot{p}_2, \cdots, \ddot{p}_n\right]^{\rm{T}}$；
2. 根据当前每个机械臂末端执行器的位置对目标区域进行Voronoi划分,并获得每个Voronoi区域的质心和质量信息；
3. 计算末端执行器位置与相应区域质心的距离$d=[\\|p_1-C_{V_1}\\|, \cdots,\\|p_n- C_{V_v}\\|]^{\rm{T}}$；
4. 若$ d>0$或$ d P \neq 0$,进入步骤5；
若$ d=0$且$ d P=0$,进入步骤6；
5. 由控制器（10）计算机械臂的动力输入$\tau=\left[\tau_1, \tau_2, \cdots, \tau_n\right]^{\rm{T}}$,得到下一时刻的机械臂的关节角位移$q=\left[q_1, \cdots, q_n\right]^{\rm{T}}$、关节角速度$d q=\left[\dot{q}_1, \cdots, \dot{q}_n\right]^{\rm{T }}$、多机械臂系统末端的位置$P=[p_1, \cdots, p_n]^{\rm{T}}$和速度${d P}=\left[\dot{p}_1, \dot{p}_2, \cdots, \dot{p}_n\right]^{\rm{T}}$,重复步骤2到4,
6. 算法执行时间结束,多机械臂系统实现了对目标区域的最优覆盖.

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表 1 多机械臂系统初始参数设定

Table 1. Initial parameter setting of multi-manipulator systems

初始参数	机械臂底端初始坐标	关节角$ q_{1} $	关节角$ q_{2} $
机械臂1	(0,0)	$ \dfrac{1}{3} \pi $	$ -\dfrac{1}{6} \pi $
机械臂2	(1,1)	$ -\dfrac{2}{3} \pi $	$ -\dfrac{1}{6} \pi $
机械臂3	(1,0)	$ \dfrac{2}{3} \pi $	$ \dfrac{1}{3} \pi $
机械臂4	(0,1)	$ -\dfrac{1}{4} \pi $	$ \dfrac{1}{6} \pi $

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