Topological Online Learning for Displacement-based Formation Control
For multi-robot formation control, this work provides a real-time edge-level adaptation method that improves robustness to disturbances, offering a practical improvement over fixed-weight approaches.
This paper introduces Topological Online Learning for Displacement-based (TOLD) formation control, which adapts interaction topology weights online to minimize formation distortion. Simulations show 1.2%-33.14% reduction in median cumulative distortion, and hardware experiments with Crazyflie quadrotors demonstrate over 62% (OGF) and 31.4% (OExpGF) reduction in median formation distortion compared to fixed-weight consensus.
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.