Deadlock-Resistant Safety-Critical Mobile Robot Navigation Using Guiding Vector Fields and Model Predictive Control

This paper investigates the safe navigation of mobile robots in complex-static-obstacle environments and proposes a deadlock-resistant navigation control method. First, convex polygonal obstacles are modeled using the Log-Sum-Exp (LSE) function. Goal and obstacle avoidance guiding vector fields (GVFs) are then constructed, and an obstacle-bypassing method is developed using the goal direction and local obstacle geometry. The goal and obstacle avoidance GVFs are further blended to construct a navigation GVF, for which a regional sufficient condition excluding complete cancellation is established. On this basis, a safe robot navigation controller is designed by combining the navigation GVF with a model predictive control (MPC) framework incorporating discrete-time control barrier function (DCBF) constraints. We also give conditions for obstacle avoidance throughout each sampling interval under bounded one-step position prediction errors. Numerical simulations show that, in the tested scenarios, wherethe tested artificial potential field (APF) and conventional MPC-DCBF configurations fail to complete the navigation task, the proposed methodcan bypass obstacles and reach the goal. Hardware experiments further validate the effectiveness of the proposed method on a physical robot platform in a preconfigured environment.