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

TL;DR

This paper introduces a PDE-based density control framework for multi-robot systems that ensures safety and energy sustainability during long-term operations, validated through experiments and simulations.

Contribution

It develops a novel control approach integrating PDEs with Lyapunov and barrier functions for real-time, safe, and energy-aware multi-robot density management.

Findings

Effective in maintaining target density and obstacle avoidance.

Ensures energy sufficiency over multiple charging cycles.

Demonstrated robustness under uncertainties through experiments.

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.