作者：Kooktae Lee, Ruchika Singh
来源：arXiv cs.RO（机器人）
正文
Mathematics > Optimization and Control
arXiv:2609.22678v1 (math)
[Submitted on 19 Sep 2026]
Title:Riemannian Density-Driven Optimal Control: Tangent-Space LQR for Second-Order Multi-Agent Systems on Curved Manifolds
Authors:Kooktae Lee, Ruchika Singh
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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.
Subjects:
Optimization and Control (math.OC); Multiagent Systems (cs.MA); Robotics (cs.RO); Systems and Control (eess.SY)
Cite as:
arXiv:2609.22678 [math.OC]
(or
arXiv:2609.22678v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2609.22678
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arXiv-issued DOI via DataCite
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优化与控制 · 多智能体 · 机器人 · eess.SY
由「前沿雷达」于 2026-09-19 采集。正文取自原文页面，已保留出处链接。标题与正文版权归原作者所有。
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