Safe and Energy-Aware Multi-Robot Density Control via PDE-Constrained Optimization for Long-Duration Autonomy

2026-04-16

AI Summary

This work addresses the coupled challenge of spatial safety and energy sustainability in long-term operation of multi-robot systems. The authors propose a density evolution model based on the Fokker–Planck partial differential equation, which uniquely integrates PDE-constrained optimization with control Lyapunov functions and control barrier functions. This integration simultaneously ensures collision avoidance, accurate tracking of desired spatial densities, and satisfaction of energy sufficiency constraints across multiple charging cycles. An efficient online control strategy is realized through real-time quadratic programming. The approach is validated through both physical experiments and large-scale simulations, demonstrating its effectiveness under localization and motion uncertainties. The method enables provably safe, energy-sustainable, and stable long-term autonomous operation of multi-robot systems.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• multi-robot density control
• spatial safety
• energy sustainability
• long-duration autonomy
• PDE-constrained optimization

Innovation

• PDE-constrained optimization
• density control
• multi-robot systems
• energy-aware control
• control barrier functions