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Riemannian Density-Driven Optimal Control: Tangent-Space LQR for Second-Order Multi-Agent Systems on Curved Manifolds

arXiv · AI, language, vision and robotics · article · Sep 19, 2026 · UTC

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 res

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