Practical Distance-Based Formation Stabilization and Tracking of Nonholonomic Multi-agent Systems

This paper investigates practical distance-based formation stabilization and tracking issues for nonholonomic multi-agent systems (MASs). Firstly, the agent’s nonholonomic kinematics is represented as a left invariant system on a Lie group. Through the introduction of an auxiliary state and a virtual control guided by the transverse function method, the original system is effectively converted into a fully actuated one. Secondly, under the assumption of infinitesimal and minimal rigidity in the graph, a gradient-descent-based virtual controller is devised for the transformed MASs, facilitating practical rigid formation stabilization. Thirdly, a discontinuous distributed velocity estimator is designed for formation tracking. The nonholonomic MASs achieve the desired formation shape while effectively tracking the reference trajectory. Finally, the effectiveness of the proposed method is verified by numerical examples.