Continuous Robust Formation Tracking Controllers for Underactuated Planar Agents

This article proposes adaptive control schemes for formation tracking of underactuated planar vehicles in the presence of unknown disturbances and constant velocity leaders, with the leaders' velocity vectors being unknown to other vehicles. The target formation is specified by either the relative positions or bearings between certain control points of the planar agents and the motion of the leaders. Uniform asymptotic convergence to the target formation of the vessels under the presented tracking controllers and a certain assumption on the interaction graph is established by using Lyapunov stability theory and Barbalat's lemma. The uniform ultimate boundedness, thus the internal stability, of the non‐actuated lateral dynamics of the agents is proven rigorously by input‐to‐state stability of the obtained cascade control system and by utilizing the square‐integrability of the velocity tracking error of the control points. Provided that the interaction graph of the system is undirected, an adaptive formation tracking control law is then proposed for the underactuated vehicles without the relative velocities between the agents. Simulation results are provided to show the effectiveness of the proposed control protocols.