Point stabilization and trajectory tracking of underactuated surface vessels: A geometric control approach

Abstract

Abstract This paper studies the problem of point stabilization and trajectory tracking of underactuated surface vessels. Different from the models in the Euclidean space, the dynamics of the surface vessel is described on the tangent bundle of a matrix Lie group, and we utilize geometric control approaches to design the stabilization and tracking strategies. Firstly, a point stabilization controller is presented based on the logarithm map of the Lie group, which can stabilize the surface vessel to a desired configuration globally and asymptotically. Next, a relative system of the follower with respect to the leader is defined, so that the tracking problem is converted to the relative system’s stabilization. Then, we use a decomposition method to stabilize the relative system and derive the tracking controller by dint of the stabilization strategy for a single surface vessel. Finally, numerical simulations are provided to verify the effectiveness of the proposed controllers.