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This research advances multi-robot coordination by integrating ergodicity objectives directly into real-time quadratic programming, eliminating the need for offline trajectory optimization or hierarchical systems. By formulating a time-differentiable Gaussian-kernel metric as a control barrier function, the method ensures safety constraints like collision avoidance are met while guaranteeing exponential decay of the monitoring error. The approach is validated through simulations and hardware experiments with aerial vehicles, offering a practical solution for dense spatiotemporal environmental monitoring tasks.
Safe Ergodic Control for Multi-Robot Systems via Quadratic Programming
arXiv:2610.05258v1 Announce Type: new 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.
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.
Robotics (cs.RO)
arXiv:2610.05258 [cs.RO]
(or arXiv:2610.05258v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2610.05258 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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