Attitude synchronization and rigid formation of multiple rigid bodies over proximity networks

Abstract

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.