Decentralized Density Control of Multi-Robot Systems Using PDE-Constrained Optimization

In this letter, we propose a decentralized optimal density control strategy for multi-robot systems modeled as interacting Brownian particles. The robots' density dynamics are described by the Fokker-Planck equation, and an optimal control problem is formulated and solved accordingly. The stability of the decentralized controller is mathematically proven, and validated through simulations and experiments with a team of real brushbots. The results confirm the convergence of the proposed density-based decentralized optimal controller.