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Parallel Formation Tracking for Nonholonomic Vehicles in Some Constrained Conditions

In this paper a solution to the problem of the parallel formation tracking for the nonholonomic system is presented. First of all, we give the analysis of the parallel formation problem in the ideal condition and propose a controller for the follower. Then we consider the non-ideal condition that the communication between two vehicles is not available, i.e., the position, the bearing angle and the velocity of the leader can not be obtained by the follower. With the relative parameters collected by the sensors installed on the follower, we derive a feedback control law using the Lyapunov-type analysis that keeps the follower in a parallel formation with the leader. Moreover, the bound can be reduced by increasing the value of the control gains, and the error of the angle can be proved to be non-zero during the whole procedure. Simulations are presented to verify the theoretical results.