用偏微分方程实现多机器人安全节能的实时密度控制
Safe and Energy-Aware Multi-Robot Density Control via PDE-Constrained Optimization for Long-Duration Autonomy
- 通过福克-普朗克方程建模机器人密度分布
- 确保避障、持续充电和目标密度跟踪
- 适合长时自主任务的多机器人系统
本文提出一种新型多机器人密度控制框架，可在空间安全和能量可持续性保障下运行。机器人随机运动通过福克-普朗克偏微分方程（Fokker-Planck PDE）在密度层面进行建模。将控制李雅普诺夫函数与控制屏障函数结合于PDE中，以实现目标密度跟踪、障碍物区域规避以及多充电周期下的能量充足性。由此产生的二次规划求解器支持快速在线实施，可实时调整控制指令。通过多机器人实验与大量仿真验证了该控制器在定位与运动不确定性下的有效性。
原文摘要 · Abstract (English)
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.
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