On the stability of nonholonomic multi-vehicle formation

The focus of the paper is to solve the stability problem of a multi-agent system composed of nonholonomic vehicles. The multi-vehicle formation is achieved following a first step where targets are identified and attractive sets circumscribing this are constructed. In a second step, the initial position and orientation of each agent is specified. In a last stage, a decentralized controller integrating a regulation control law, ensures obstacles avoidance, is elaborated. The formation’s stability is achieved if a group of agents reaches their common target with the right direction and without any motion planning. The LaSalle’s invariance principle is the mathematical tool used to prove the invariance of the elaborated set with respect to the nonholonomic multi-vehicle transient behaviors. The simulations illustrate the effectiveness of our strategy and it can be exploited in swarm navigation case.