Trajectory tracking and formation control of a platoon of mobile robots

This thesis is concerned with controlling a platoon of wheeled mobile robots (WMR), where the robots are aimed to follow a trajectory while they maintain their formation intact. The control design is carried out by considering unicycle kinematics for each robot, and the leader-follower structure for the formation. It is assumed that every robot except the one located at the end of each platoon can potentially be the leader to the one behind it. It is also assumed that each follower is capable of sensing its relative distance and relative velocity with respect to its preceding robot. The stability of the proposed control law is investigated in the case of perfect sensing and in the presence of input saturation. The impact of measurement noise on the followers is then studied assuming that a known upper bound exists on the measurement error, and a linear matrix inequality (LMI) methodology is proposed to design a control law which minimizes the upper bound on the steady-state error. The problem is then investigated in a more practical setting, where the control input is subject to delay, and that the tracking trajectory can be different in distinct time intervals. It is to be noted that delay often exists in this type of cooperative control system due to data transmission and signal processing, and if neglected in the control design, can lead to poor closed-loop performance or even instability. Furthermore, switching in tracking trajectory can be used as a collision avoidance strategy in the formation control problem. Delay dependent stability conditions are derived in the form of LMIs, and the free-weighting matrix approach is used to obtain less conservative results. Simulations are presented to demonstrate the efficacy of the results obtained in this thesis