Safe Decentralized Density Control of Multi-Robot Systems using PDE-Constrained Optimization with State Constraints

Abstract: In this paper, we introduce a decentralized optimization-based density controller designed to enforce set invariance constraints in multi-robot systems. By designing a decentralized control barrier function, we derived sufficient conditions under which local safety constraints guarantee global safety. We account for localization and motion noise explicitly by modeling robots as spatial probability density functions governed by the Fokker-Planck equation. Compared to traditional centralized approaches, our controller requires less computational and communication power, making it more suitable for deployment in situations where perfect communication and localization are impractical. The controller is validated through simulations and experiments with four quadcopters.