Topological Online Learning for Displacement-based Formation Control

2026-06-22

AI Summary

This study addresses formation distortion in multi-robot systems under disturbances caused by fixed communication topologies. To this end, the authors propose TOLD, a real-time edge-level adaptive framework that introduces online topology learning into displacement-based formation control for the first time. By employing Online Gradient Flow (OGF) and Online Exponential Gradient Flow (OExpGF), the method dynamically optimizes interaction weights over directed graphs, guaranteeing bounded distortion and asymptotic consensus, respectively, in single-integrator models. These edge-level adaptations operate in concert with node-level controllers to enhance overall robustness. Simulations demonstrate a median cumulative mean squared distortion reduction of 1.2%–33.14%, while hardware experiments on Crazyflie 2.0 platforms show median formation distortion reductions exceeding 62% with OGF and 31.4% with OExpGF.

Abstract

This paper addresses the problem of robust formation control by introducing Topological Online Learning for Displacement-based (TOLD) formation control, a real-time edge-level adaptation framework. Unlike conventional node-level robust controllers that regulate individual robot inputs without modifying the interaction topology, TOLD updates the interaction topology weights online to directly minimize formation distortion. Two strategies are proposed under the TOLD formation control framework: Online Gradient Flow (OGF) with unconstrained weights and Online Exponential Gradient Flow (OExpGF) with non-negative convex weights. Theoretical analysis establishes that, for single-integrator agents over directed graphs, OExpGF guarantees asymptotic consensus, while OGF ensures bounded formation distortion. Simulations with twelve robots under intermittent disturbances show 1.2%-33.14% median cumulative Root Mean Distortion Error reduction when augmenting TOLD with node-level controllers. Hardware experiments with Crazyflie 2.0 quadrotors demonstrate over 62% (OGF) and 31.4% (OExpGF) reduction in median formation distortion compared to fixed-weight consensus.

Problem

• formation control
• topology adaptation
• displacement-based
• multi-robot systems
• formation distortion

Innovation

• Topological Online Learning
• Displacement-based Formation Control
• Online Gradient Flow
• Interaction Topology Adaptation
• Formation Distortion Minimization