  This paper studies the tracking control problem for nonholonomic mobile
robots based on second order dynamics, with application to consensus tracking
and formation tracking. The greatest novelty in this paper is that the
reference trajectory can be arbitrarily chosen, in the sense that the condition
of persistency excitation and any other requirements are not imposed on the
leader. In this paper, at first, the tracking control of one leader with single
follower is taken into consideration, which is converted to the stabilization
of two relative subsystems by the design of an adjoint system. Then, the single
follower tracking controller is extended to the consensus tracking of multiple
nonholonomic mobile robots connected by a directed acyclic graph, in which the
convex combination in nonlinear manifolds is introduced to construct a virtual
leader for each follower. Next, the relationship between consensus control and
formation control is established for multiple nonholonomic mobile robots, with
the result that a new transformed system is constructed so as to obtain the
formation tracking control strategy from the consensus tracking result.
Finally, simulations are presented to verify the effectiveness of the control
laws.
