Coordinated tracking for multiple nonholonomic vehicles on SE(2)

This paper addresses the problem of consensus and formation control for nonholonomic multivehicle systems. The problem is formulated using the definition of the convex combination on SE(2) which simultaneously preserves the nonholonomic constraint in its left-invariant kinematics. The formation tracking follows by asymptotically tracking of the virtual references precisely defined based on the convex combination of the states of the neighboring vehicles. The methodology is applied to a group of seven unicycle-type vehicles connected with each other through a directed acyclic graph. The conditions on which nonholonomic vehicles can be in a coordination are developed by the notion of the nonholonomic adjoint orbit. For trajectory tracking, we develop the error dynamics in polar terms which provides a suitable setting for designing a simple and efficient control law. Finally, a backstepping technique is used to shift the kinematic control to the dynamic system. The theoretical results are supported by numerical simulation of the trajectory tracking as well as the formation tracking.