Adaptive formation control in absence of leader´s velocity information

In the leader-following approach, it has been commonly assumed that the leader robot´s velocity information may be either measured or telecommunicated. However, in some circumstances, it is difficult to satisfy it because the follower robots may not have the sensor or the communication device to obtain accurate enough leader robot´s velocity. Therefore this study proposes an adaptive formation control approach for multiple mobile robots in the absence of the velocity information of the leader robot. The proposed control system only requires a knowledge of the leader´follower relative distance and the bearing angle. The smooth projection algorithm is employed to estimate time-invariant or time-varying velocities of the leader robot. Using Lyapunov stability theory, it is shown that the formation errors are uniformly ultimately bounded and converge to an adjustable neighbourhood of the origin. Simulation and experiment results are provided to demonstrate the performance and stability of the proposed formation scheme.