Robust Bearing-Based Formation Tracking Control of Underactuated Surface Vessels: An Output Regulation Approach

Abstract

This article is concerned with the robust formation tracking control of a group of underactuated surface vessels whose formation is characterized by the relative bearings between the vessels. Control protocols are proposed to asymptotically steer certain points on the vessels, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hand points</i> , which lie ahead of their centers of mass along the longitudinal axes, to track the desired moving formation; such a control method is called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">an output regulation approach</i> . The moving formation is guided by the motions of two or more agents, which are referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">leaders</i> , and the other <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">follower</i> agents track the leaders by maintaining bearing constraints to neighbors. The proposed control schemes are designed based on a backstepping technique and sliding mode control. The latter is employed to attenuate known bounded disturbances present in the vessels' dynamics. When the bounds of the disturbances are unknown, an adaptive control protocol is subsequently investigated, under which the system is shown to converge to a small neighborhood of the target formation. Further, sufficient conditions on the upper bound of the hand points' desired velocities are provided for the uniform ultimate boundedness of the vessels' internal sway-yaw dynamics. Simulation results are provided to support the theoretical analysis.