Safe Ergodic Control for Multi-Robot Systems via Quadratic Programming

2026-10-04

AI Summary

This work addresses the limitation of existing safe ergodic control methods, which rely on offline optimization and decouple ergodic objectives from safety constraints, thereby hindering real-time deployment. We propose a quadratic programming (QP)-based real-time cooperative monitoring controller for multi-robot systems. A key innovation is the introduction of a time-differentiable Gaussian kernel ergodic metric, whose exponential decay property is reformulated as a time-varying control barrier function constraint to enable the joint optimization of ergodicity and safety. The feasibility of the QP formulation and the exponential convergence of the metric are rigorously proven in theory. Simulation results demonstrate superior performance compared to baseline methods, and the effectiveness of the proposed approach is further validated through hardware experiments on a three-UAV platform.

Abstract

Ergodic control drives robots to spend time in each region in proportion to a spatial distribution of interest, making it well suited for dense spatiotemporal environmental monitoring. Existing safe ergodic controllers rely on offline trajectory optimization or hierarchical architectures, which limit real-time applicability and decouple the ergodicity objective from the safety constraint. This paper presents a quadratic programming (QP)-based controller that treats ergodicity and safety jointly. We first introduce a Gaussian-kernel ergodic metric that, unlike the classical indicator-based metric, is time differentiable. This allows the exponential decay of the metric to be imposed as a time-varying control barrier function (CBF) constraint, relaxed by a slack variable, alongside hard CBF constraints for region containment and inter-robot collision avoidance. We establish that the resulting QP remains feasible from any safe initial configuration and that, up to the slack term, the ergodic metric decays exponentially. Simulations show improved performance over baseline methods, and experiments with three aerial vehicles validate the work on real hardware.

Problem

• Ergodic control
• Multi-robot systems
• Safety constraints
• Real-time control

Innovation

• Ergodic Control
• Quadratic Programming
• Control Barrier Function
• Gaussian-Kernel Metric
• Multi-Robot Systems