Quadratic programming controls multi-robot motion safely and efficiently
Safe Ergodic Control for Multi-Robot Systems via Quadratic Programming
Robotics
Summary
Robots often need to explore certain areas more carefully than others, like when monitoring the environment. The authors created a new method that helps multiple robots move so they spend time in each area according to a specific plan, while making sure they don’t collide or leave safe zones. They designed a control technique that combines these goals into a single mathematical problem that robots can solve quickly in real time. Their approach was tested in both simulations and real drone flights with three robots working together.
What this means in practice
- •For environmental monitoring teams: Coordinate multiple robots to safely sample spatial regions according to time-varying interest distributions without collisions in real time.
- •For drone fleet operators: Enable real-time planning and control of multiple aerial robots to inspect and cover diverse areas while guaranteeing safety constraints.
Authors
Yo Toyomoto, Mohamed Elobaid, Bryce L. Ferguson, Alberto Quattrini Li, Shinkyu Park
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.