Formation Adaptive Control for Nonholonomic Dynamic Agents: Regulation and Tracking

In this paper, a solution for the formation control of a group of nonholonomic uncertain agents is proposed. The configuration pattern is generated from a given potential function, which may also incorporate a strategy for collision avoidance. The system parametric uncertainties are compensated by a robust adaptive control algorithm named binary adaptive control which combines the good transient properties and robustness of Sliding Mode Control with the desirable steady-state properties of parameter adaptive systems delivering continuous control signals, thus avoiding chattering. First, a static formation (regulation) scenario is considered. Conditions for semi-global stability of the multi-agent system are established using Lyapunov theory for decentralized control schemes. Then, the control scheme is extended for trajectory tracking to be performed by the group of agents while maintaining a desired geometric pattern. In the case of regulation, only the relative position information with respect to neighboring agents and individual velocity are available for the control implementation for each agent. In the case of tracking, also the velocities of the neighbors are needed. Simulations are presented to validate the theoretical results.