On the Convergence of Multi-robot Constrained Navigation: A Parametric Control Lyapunov Function Approach

This paper studies the distributed multi-robot constrained navigation problem. While the multi-robot collision avoidance has been extensively studied in the literature with safety being the primary focus, the individual robot's destination convergence is not necessarily guaranteed. In particular, robots may get stuck in the local equilibria or periodic orbits of the multi-robot system, some of which are practically known as the deadlock and the livelock behaviors. Inspired by the combination of Control Lyapunov Function (CLF) and Control Barrier Function (CBF) for the nonlinear system's constrained stabilization, the authors present a guaranteed safe feedback control policy with improved convergence performance. The proposed Parametric CLF (PCLF) scheme adaptively determines the appropriate CLF parameterization within the in-stantaneous feasible action space. The algorithm also induces a conditional global asymptotic convergence guarantee for multi-robot system of single-integrator dynamics, and is empirically effective for nonlinear nonholonomic vehicle model. Empiri-cally, the proposed PCLF-CBF framework exhibits superior performance than state-of-the-art methods, including its de-generated counterpart of various CLF-CBF solutions.