Displacement-based formation control with disturbance observer of multi-first-order systems

Abstract

This paper addresses the problem of displacement-based formation control for multi-agent systems with first-order integrator dynamics in the presence of external disturbances. Based on the proposed control law, a disturbance observer is developed to estimate the disturbances acting on each agent, and the estimated signals are incorporated into the control input for disturbance compensation. This approach enables the system to maintain the desired formation while enhancing its disturbance rejection capability. Lyapunov-based stability analysis shows that the formation error is uniformly ultimately bounded when the disturbance estimation error is bounded. Furthermore, if the estimation error converges to zero over time, the formation error asymptotically converges to zero. Simulation results on a five-agent system validate the effectiveness of the proposed method, demonstrating a significant reduction in formation error and improvement of system performance compared to the case without the disturbance observer.