In this paper, the combination of the attitude synchronization and rigid formation problem of multiple moving rigid bodies are considered. The moving rigid bodies communicate with each other via a distance-dependent interaction network, yielding the dynamical neighbor relations and the coupling relationship between positions and attitudes of all rigid bodies. The finite-time control and potential function techniques are combined in the design of distributed control laws for the torques and forces of rigid bodies. We construct the admissible set on the initial states, in which the theoretical results on the attitude synchronization, rigidity maintenance and collision avoidance are established simultaneously without relying on the dynamical connectivity of the neighbor graphs. Furthermore, by transforming the stability of rigid formations into the stability of the parameterized systems, we show that the local asymptotic stability of rigid formations can be achieved. A simulation example is given to illustrate the theoretical results.

本文考虑了多个移动刚体的姿态同步和刚体形成问题的结合。运动的刚体通过距离相关的交互网络相互通信，从而产生动态的邻居关系以及所有刚体的位置和姿态之间的耦合关系。在刚体的转矩和力的分布式控制定律的设计中，结合了有限时间控制和势函数技术。我们在初始状态下构造了可允许集合，其中在不依赖于相邻图的动态连通性的情况下，同时建立了关于姿态同步，刚度保持和避免碰撞的理论结果。此外，通过将刚性地层的稳定性转换为参数化系统的稳定性，我们表明可以实现刚性地层的局部渐近稳定性。仿真例子说明了理论结果。