Trajectory tracking of nonholonomic mobile robots by geometric control on special Euclidean group

Abstract

AbstractThis article studies the trajectory tracking of nonholonomic mobile robots by using geometric control methods, with extension to consensus tracking and formation tracking. Different from the system model given in the Euclidean space, we establish the dynamics of mobile robots on the tangent bundle of the Lie group, which is a global and unique description independent of local coordinates. Firstly, the tracking control of one leader with one follower is considered, which is converted to the stabilization of two relative subsystems by designing an adjoint system. Then, the controller is extended to consensus tracking of multiple robots connected by a directed acyclic graph, where the convex combination on nonlinear manifolds is introduced to construct a virtual leader for each follower. Next, the relation between consensus control and formation control is established, and a new transformed system is constructed so as to derive the formation tracking controller from the consensus result. Finally, simulation examples are presented to verify the effectiveness of the proposed controllers.