Distributed Adaptive Global Stabilization of a Class of Rigid Formation Systems

Abstract

Accurate distance-based formation control is frequently compromised by the presence of multiple equilibria. A standard gradient law can direct a multiagent system to the zero-gradient set; however, it may fail to attain the unique desired configuration, thereby jeopardizing the overall mission reliability. To overcome this limitation while maintaining collision safety, we put forward a fully distributed, globally stabilizing control framework. First, a scalable graph-decomposition algorithm is employed to verify whether a formation graph exhibits the requisite cascade structure and automatically extract its interconnections. Subsequently, based on the cascade structure derived from the algorithm, a distributed perturbed gradient control law is implemented to facilitate the multiagent system in achieving the desired globally stable formation. Furthermore, the distributed adaptive velocity estimation law is introduced, relying solely on the relative positions of the agents, thus eliminating the necessity to ascertain the velocities of neighboring agents. This method effectively addresses the challenge of simultaneously ensuring collision avoidance and maintaining the desired formation shape. Finally, the global convergence and stability properties are obtained using the cascade system stability theory and adaptive control theory. Simulations are included to validate the effectiveness of the globally asymptotically stable formation control strategy.