Trajectory tracking and obstacle avoidance in robot formations present significant challenges, especially in confined spaces. Traditional methods are constrained by offline optimization problems and are poorly suited for addressing these complexities in an online context. This paper presents a safety-critical model predictive control (MPC) strategy for tracking and obstacle avoidance of wheeled mobile robot (WMR) formations. Specifically, to improve the accuracy of obstacle avoidance in WMR formations, a novel discrete-time control barrier function (DCBF)-based polyhedral collision avoidance constraint is integrated into the MPC optimization framework. Then, by leveraging the Lagrangian dual function and strong duality of convex optimization, the implicit DCBF constraints are converted into equivalent explicit forms. This eliminates the nested optimization problem in the MPC framework and significantly reduces computation time. Theoretical analysis confirms that the new DCBF constraints maintain the feasible range of the original constraints. Finally, simulations and hardware experiments are performed on WMR formations to validate the effectiveness of the proposed method.
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