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

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.

💡 Research Summary

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The paper presents a novel control framework that unifies Density‑Driven Control (D²C) with Control Barrier Functions (CBFs) to enable safe, efficient, non‑uniform area coverage by a swarm of mobile agents in environments containing both circular and rectangular obstacles. D²C, built on optimal transport theory, steers agents toward a reference density map that encodes spatial priorities (e.g., higher‑priority zones in disaster response or environmental monitoring). It operates in three decentralized stages: (A) optimal waypoint selection using locally sampled points, (B) weight update that transports importance weights to the agents’ new positions while minimizing the Wasserstein distance, and (C) local weight sharing among neighboring agents. While D²C excels at coverage efficiency, it lacks any collision‑avoidance mechanism.

To address safety, the authors develop CBFs tailored to the two obstacle shapes. For circular obstacles, the standard distance‑based CBF is retained. For rectangular obstacles, the paper analytically derives the distance to the nearest face and the unit outward normal vector based on the agent’s angle relative to the obstacle’s center. This yields a piecewise definition of the normal vector (aligned with the four axis directions) and a distance expression that depends on whether the agent is closer to a width or length side. Two CBFs are defined for each obstacle:

1. (h_{i,1}(x_k)=|y_k-p_{o,i}|^2-(r_{k,o,i}-1)^2), a pure geometric safety condition;
2. (h_{i,2}(x_k)), which augments (h_{i,1}) with a velocity‑dependent term (K_v\langle\hat n_{k-1,o,i},v_{k-1}\rangle). This term shrinks the admissible velocity component toward the obstacle as the agent approaches, thereby providing a buffer for realistic acceleration limits.

The combined controller is implemented as a quadratic program (QP) that minimizes the deviation from the D²C‑generated nominal control input while satisfying all CBF constraints:
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