Cooperative control of nonholonomic multi-robot system using control barrier functions

DOI编号  10.7641/CTA.2021.10085
2022,39(4):663-670

 作者 单位 E-mail 娜茜泰 内蒙古大学 naxitai@163.com 高飞 内蒙古大学 翁智 内蒙古大学 夏元清 北京理工大学

本文设计了一种基于屏障控制函数(CBF)的分布式协同控制算法, 实现了领航–跟随者框架下非完整约束 多智能体系统的连通性与编队控制. 首先, 通过将连通性保持问题建模为系统约束, 定义了该约束的调零屏障函 数(ZBF). 其次, 在此基础上, 构建李雅普诺夫函数与角速度输入之间的关系, 对跟随者智能体设计了基于调零屏障 函数的协同控制算法, 其中线速度控制器保证跟随者的速度的跟踪与队形的跟踪, 而梯度型角速度控制器实现跟随 者角度的矫正. 然后, 利用调零屏障函数不变集相关引理证明了连通性约束集为正不变集, 若初始时刻连通, 则跟随 者智能体始终与领航者保持连通性. 同时, 本文提出的算法实现编队误差的渐近收敛. 本文中的队形适用常见的固 定队形编队需求, 也适用于领航者是动态(有线速度和角速度)的情况. 最后, 通过数值仿真进一步验证了该算法在 不同队形需求下的有效性.

In this paper, a distributed cooperative control algorithm based on the control barrier function (CBF) is designed to realize the connectivity and formation control of nonholonomic constrained multi-agent systems under the leader-follower framework. The connectivity maintenance objective is modeled as a system constraint, and the corresponding zeroing barrier function (ZBF) is defined. By constructing the relationship between the Lyapunov function and the input angular velocity, the linear velocity controller ensures speed tracking and formation tracking, and angular velocity controller realizes the correction of motion angle. The connectivity constraint ZBF is proved to be positive invariant, which shows that the follower agent always maintains connectivity with the leader when they are initially connected, meanwhile the formation error is asymptotically convergent. The formation in this paper is appropriate for not only the common fixed formation requirements, but also the situation where the leader is dynamic (with linear speed and angular speed). At the end of this paper, the effectiveness of the proposed algorithm under different formation is verified by numerical simulation.