切换拓扑下多刚体系统分组姿态协同控制

Group attitude cooperative control of multiple rigid bodies system with switching topologies

针对切换拓扑条件下的多刚体系统分组姿态协同控制问题进行了研究.采用修正型罗德里格斯参数(modified Rodrigues parameters)描述刚体姿态.构造的多刚体系统包含若干个分组,并通过分块的邻接矩阵和Laplacian矩阵来描述切换拓扑.给定了分组姿态协同的定义,设计了分布式的控制输入.证明了多刚体系统达到分组姿态协同的充要条件是系统拓扑为连通图.并且每个拓扑的驻留时间不影响系统达到分组姿态协同.理论分析过程中应用了 Lyapunov稳定性理论.计算机仿真表明了所设计的控制输入的有效性;并且仿真结果说明,如果切换拓扑不连通,那么多刚体系统无法达到分组姿态协同.

Group attitude cooperative control of multiple rigid bodies system is investigated in this paper.The attitude of rigid bodies is described by modified Rodrigues parameters.The multiple rigid bodies system is constructed with several subgroups in it,and the switching topologies are denoted by block adjacency matrix and block Laplacian matrix.The definition of group attitude cooperation is provided,and distributed control input is designed.It is proved that the topologies being connected is the sufficient and necessary condition for multiple rigid bodies system to achieve group attitude cooperation.And the system reaching group attitude cooperation is not influenced by the dwelling time of each topology.Lyapunov stability theory is applied in the theoretical analysis.Computer simulation shows the correctness and effectiveness of the method proposed,and the simulation results show that if the switching topologies are not connected,the system cannot reach group attitude cooperation.