Lyapunov and Sliding Mode Based Leader-follower Formation Control for Multiple Mobile Robots with an Augmented Distance-angle Strategy

Abstract

In this paper, a new two-layer control strategy which combines Kinematic Controller based on Lyapunov Theory (KCLT) with Dynamic Controller based on Sliding Mode (DCSM) is proposed to solve the problem of leader-follower formation control for multiple wheeled mobile robots (M-WMR). An augmented distance-angle leader-follower formation kinematic is constructed to describe the formation states, and a 2D LiDAR sensor is utilized to measure the states instead of using camera and image processing on each follower. Instead of transferring the measured formation states into reference position command for each follower, KCLT is designed to generate follower’s velocity command. By taking the velocity command of followers as reference signals, DCSM is implemented to realize formation control. Lyapunov stability theory verifies that with the designed controller all the error signals can converge to 0 theoretically, which implies formation control of M-WMR under the proposed method can be realized. Real experiments with one leader and two followers are carried out to demonstrate the effectiveness of the proposed control schema. In order to verify the robustness of the proposed method, the reference rotational velocity of the leader robot is designed to change between +0:2 rad/s and -0:2 rad/s at some specified position. And the experimental results are compared with that of traditional proportional-integral-derivative (PID) method.