Safe Coverage Control via Optimal Transport and Control Barrier Functions

Abstract

This paper addresses multi-agent coverage control with safety requirements in environments with obstacles. The nominal Optimal Transport Coverage Control (OTCC) law derives from the Kantorovich dual of the optimal transport problem and follows the prior formulation for workload balancing through auxiliary potentials. A Lyapunov function based on the primal-dual gap establishes local exponential stability of the nominal dynamics when a gain ratio condition holds. To enforce collision avoidance, we incorporate Control Barrier Functions (CBF) through a quadratic program that modifies the nominal control. The CBF implementation uses soft constraints with slack variables to preserve feasibility when safety constraints conflict with velocity limits. For comparison, we also implement Artificial Potential Fields (APF) in simulation. We conduct ten simulation runs with random initial positions for agents and obstacles. Both methods achieve nearly identical coverage performance. OTCC with CBF keeps the minimum agent-obstacle distance at the safety threshold of 0.300 across all runs and the Lyapunov derivative negative at every time step. OTCC with APF allows the distance to drop to 0.289 and produces occasional positive Lyapunov steps. In narrow passages, OTCC with APF becomes trapped in local minima while OTCC with CBF navigates through and reaches the centroids. The CBF method requires $8.6 \times 10^{6}$ operations per step compared to $4.0 \times 10^{5}$ for APF, but provides smoother control, stronger stability guarantees, and more reliable safety enforcement. These advantages make CBF the preferred choice for safety-critical multi-agent coverage tasks when computational resources permit.