A Coupled Control Barrier Function Approach to Deadlock-Free Multi-Robot Conflict Resolution

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Article Summary

Many robotic applications involve scenarios where multiple robots interact and the decisions of one robot influence the behavior of others. This paper presents a quadratic programming (QP)-based feedback controller for multi-robot conflict resolution with input constraints. Safety is enforced using coupled Control Barrier Function (CBF), while a yielding matrix encodes how robots influence each other. Unlike existing methods with fixed or hard priorities, the proposed framework enables yielding preferences while guaranteeing deadlock-free operation by design. Sufficient conditions are established for the controller to be locally Lipschitz. The optimal CBF sign- indefinite slack is shown to admit a finite uniform bound, which is compensated through an enlarged CBF safety margin to obtain a forward invariant set contained within the desired safe set. The analysis also identifies an irreducible slack component due to finite maximum deceleration that cannot be eliminated by increasing the slack penalty. Finally, sufficient conditions on the yielding matrix and nominal controller are derived to exclude deadlock states. Simulations demonstrate adaptive coordination across yielding preferences and robustness to robot failures.

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