Control method guides multi-robot teams on curved surfaces
Riemannian Density-Driven Optimal Control: Tangent-Space LQR for Second-Order Multi-Agent Systems on Curved Manifolds
Multiagent SystemsRobotics
Summary
Controlling many robots working together on curved surfaces is tricky because normal control methods assume flat ground. The authors create a new approach that lets these robots plan movements on curved spaces by translating their positions to flat tangent spaces, doing calculations there, and mapping results back onto the curved surface. Their method carefully accounts for the curved shape to keep robot distributions accurate over time. They tested this with simulations on shaped 3D surfaces and showed their approach helps groups of robots spread out as intended.
What this means in practice
- •For robotics engineers: Control robot teams operating on curved or non-flat terrains displaying coordinated spatial patterns using the proposed manifold-aware method.
- •For drone fleet operators: Manage aerial drone formations flying along curved surfaces like hills or domes by applying tangent-space optimal control calculations.
Authors
Kooktae Lee, Ruchika Singh
Abstract
Density-Driven Optimal Control (D2OC) provides an effective framework for steering multi-agent systems toward prescribed spatial distributions. However, existing D2OC formulations are primarily developed for Euclidean domains and do not directly account for intrinsic manifold geometry. This paper extends D2OC to second-order multi-agent systems evolving on Riemannian manifolds. The proposed Riemannian D2OC (R-D2OC) constructs a local distribution objective in the tangent space of each agent through logarithmic maps and uses its weighted center as the reference for a finite-horizon LQR. The resulting control is executed on the manifold through intrinsic second-order dynamics and parallel transport within a receding-horizon scheme. We establish local curvature-dependent bounds that quantify the approximation introduced by the tangent-space reduction and characterize the resulting target bias. Furthermore, we derive a conditional discrete-descent result showing that the closed-loop objective decreases when a local velocity-alignment condition is satisfied. Numerical simulations on a 3D ellipsoidal manifold demonstrate distribution-level control and empirically support the proposed approximation and descent results.