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This research introduces a PDE-constrained optimization framework that integrates stochastic motion modeling with control barrier functions to ensure spatial safety and energy sustainability for multi-robot fleets. By solving a quadratic program in real-time, the method effectively handles localization uncertainties and manages energy constraints across multiple charging cycles. The approach represents a significant step toward long-duration autonomy for dense robot deployments without relying on centralized planning bottlenecks.
Safe and Energy-Aware Multi-Robot Density Control via PDE-Constrained Optimization for Long-Duration Autonomy
arXiv:2604.15524v3 Announce Type: replace-cross Abstract: This paper presents a novel density control framework for multi-robot systems with spatial safety and energy sustainability guarantees. Stochastic robot motion is encoded through the Fokker-Planck Partial Differential Equation (PDE) at the density level. Control Lyapunov and control barrier functions are integrated with PDEs to enforce target density tracking, obstacle region avoidance, and energy sufficiency over multiple charging cycles. The resulting quadratic program enables fast in-the-loop implementation that adjusts commands in real-time. Multi-robot experiment and extensive simulations were conducted to demonstrate the effectiveness of the controller under localization and motion uncertainties.
Abstract:This paper presents a novel density control framework for multi-robot systems with spatial safety and energy sustainability guarantees. Stochastic robot motion is encoded through the Fokker-Planck Partial Differential Equation (PDE) at the density level. Control Lyapunov and control barrier functions are integrated with PDEs to enforce target density tracking, obstacle region avoidance, and energy sufficiency over multiple charging cycles. The resulting quadratic program enables fast in-the-loop implementation that adjusts commands in real-time. Multi-robot experiment and extensive simulations were conducted to demonstrate the effectiveness of the controller under localization and motion uncertainties.
Systems and Control (eess.SY); Robotics (cs.RO)
arXiv:2604.15524 [eess.SY]
(or arXiv:2604.15524v3 [eess.SY] for this version)
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