基于分组一致性的刚体集群姿态协同控制

Cooperative attitude control in rigid body swarms based on group consensus

姿态协同控制是刚体集群相关应用的重要问题,而控制集群内刚体保持不同姿态的研究仍然较少.针对这一问题,引入了分组一致性理论,提出了基于分组一致性的刚体集群姿态协同控制.采用修正型罗德里格斯参数(modified Rodrigues parameters)描述刚体集群的姿态,并将集群中的刚体分为两个分组.对于刚体集群的无向通信拓扑结构,在入度平衡假设的基础上,运用Ostrowski圆盘定理,给出了集群包含两个分组的情况下Laplacian矩阵特征值的分布,为稳定性分析提供了确切的依据.设计了分布式的控制器,采用Lyapunov稳定性理论,理论上证明了该控制器的有效性,并通过计算机仿真对本文所提控制方法进行了验证.

Cooperative attitude control is a key problem in the application of rigid body swarms, yet, there is little research into maintaining different attitudes within rigid body swarms. To solve this problem, group consensus theory is introduced, and attitude control based on group consensus is proposed. Modified Rodrigues parameters are used to describe the attitude of rigid bodies, and these rigid bodies are separated into two subgroups. Based on the in-degree balance and application of Ostrowski’s theorem, the distribution of eigenvalues of a Laplacian matrix is shown for the undirected communication topology of the rigid body swarms when the swarms consists of two subgroups, providing an accurate basis for stability analysis. A distributed controller is designed, and utilizing Lyapunov stability theory, the effectiveness of the controller is theoretically demonstrated and the proposed algorithm is verified using computer simulation.