摘要
Aiming for the coordinated motion and cooperative control of multi-agents in a non-rectangular bounded space, a velocity consensus algorithm for the agents with double- integrator dynamics is presented. The traditional consensus algorithm for bounded space is only applicable to rectangular bouncing boundaries, not suitable for non-rectangular space. In order to extend the previous consensus algorithm to the non- rectangular space, the concept of mirrored velocity is introduced, which can convert the discontinuous real velocity to continuous mirrored velocity, and expand a bounded space into an infinite space. Using the consensus algorithm, it is found that the mirrored velocities of multi-agents asymptotically converge to the same values. Because each mirrored velocity points to a unique velocity in real space, it can be concluded that the real velocities of multi-agents also asymptotically converge. Finally, the effectiveness of the proposed consensus algorithm is examined by theoretical proof and numerical simulations. Moreover, an experiment is performed with the algorithm in a real multi-robot system successfully.
针对多智能体在非矩形有界空间的运动,提出了二阶动态系统的速度一致性算法.传统的有界空间一致性算法只适合矩形有界空间,对于非矩形有界空间不再适用.为了将已有的一致性算法扩展到非矩形空间,引入镜像速度矩阵的概念,它不仅可将不连续的实际速度转化成连续的镜像速度,而且可将有界空间扩展成无限大虚拟空间.运用此算法,发现多智能体在虚拟空间中镜像速度渐近一致.由于每个镜像速度对应唯一的实际空间速度,多智能体实际速度也达到渐近一致.最后,通过理论证明和数值仿真验证了算法的可行性,并且成功地将算法运用到一组实际多机器人系统上.
基金
The National Natural Science Foundation of China(No.61273110)
the Specialized Fund for the Doctoral Program of Higher Education(No.20130092130002)
