Collision-Aware Density-Driven Control of Multi-Agent Systems via Control Barrier Functions

Abstract: This paper tackles the problem of safe and efficient area coverage using a multi-agent system operating in environments with obstacles. Applications such as environmental monitoring and search and rescue require robot swarms to cover large domains under resource constraints, making both coverage efficiency and safety essential. To address the efficiency aspect, we adopt the Density-Driven Control (D$^2$C) framework, which uses optimal transport theory to steer agents according to a reference distribution that encodes spatial coverage priorities. To ensure safety, we incorporate Control Barrier Functions (CBFs) into the framework. While CBFs are commonly used for collision avoidance, we extend their applicability by introducing obstacle-specific formulations for both circular and rectangular shapes. In particular, we analytically derive a unit normal vector based on the agent's position relative to the nearest face of a rectangular obstacle, improving safety enforcement in environments with non-smooth boundaries. Additionally, a velocity-dependent term is incorporated into the CBF to enhance collision avoidance. Simulation results validate the proposed method by demonstrating smoother navigation near obstacles and more efficient area coverage than the existing method, while still ensuring collision-free operation.