Consensus control for vehicles with nonholonomic constraints on special euclidean group SE(2)

This paper studies the consensus control for multiple nonholonomic vehicles, whose kinematics evolve on Special Euclidean group SE(2). Since the purpose of researching consensus control is to design formation control strategies, a consensus-based formation controller is proposed in the text as well. At first, the paper gives the preliminaries and a general formulation of the problem. Then, a global and asymptotical consensus control law is introduced for two nonholonomic vehicles on SE(2). From any initial configuration, the vehicles can be driven to the same position and orientation asymptotically under the presented controller. Next, with the aid of the geometric convex combination on SE(2), the consensus control law for multi-vehicle systems is addressed, on the basis of the result of two vehicles consensus. Then, the paper presents the consensus-based formation controller for vehicles with parallel desired formations, where all the vehicles are parallel to each other in a straight line along the side of vehicles. For verification of the theoretical results, numerical simulations are given at the end.