Distributed Observer-Based Adaptive Trajectory Tracking and Formation Control for the Swarm of Nonholonomic Mobile Robots with Unknown Wheel Slippage

Nonholonomoic mobile robots (NMRs) are widely used in logistics transportation and industrial production, with motion control remaining a key focus in current WMR research. However, most previously developed controllers assume ideal conditions without considering motion slippage. Neglecting slippage factors often leads to reduced control performance, causing instability and deviation from the robot’s path. To address such a challenge, this paper proposes an intelligent method for estimating the longitudinal wheel slip, enabling effective compensation for the adverse effects of slippage. The proposed algorithm relies on the development of an adaptive trajectory tracking controller for the leader robot. This controller enables the leader robot to accurately follow a virtual reference trajectory while estimating the actual slipping ratio with precision. By employing this approach, the mobile robot can effectively address the challenge of wheel slipping and enhance its overall performance. Next, a distributed observer is developed for each NMR that uses both its own and adjacent robot’s information to determine the leader’s state. To solve this difficulty for the follower robot to receive the states of the leader in a large group of robots, distributed formation controllers are designed. Further, Lyapunov stability theory is utilized to analyze the convergence of tracking errors that guarantees multi-robot formation. At last, numerical simulations on a group of NMR are provided to illustrate the performance of the designed controller. The leader robot achieved a low RMSE of 1.7571, indicating accurate trajectory tracking. Follower robots showed RMSEs of 2.7405 (Robot 2), 3.0789 (Robot 4), and 4.3065 (Robot 3), reflecting minor variations due to the distributed control strategy and local disturbances.