Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds

[2606.02879] Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds

[Submitted on 1 Jun 2026]

Title:Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds

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Abstract:Informed sampling techniques accelerate sampling-based motion planners by focusing the search on promising regions of the state space, yet most existing methods rely on Euclidean heuristics that become inadmissible under configuration-dependent Riemannian metrics. While scalar eigenvalue bounds restore admissibility by uniformly scaling the Euclidean distance, they discard the directional structure of the metric, producing overly conservative informed sets. We propose a matrix-valued admissible heuristic that exploits the Loewner order on symmetric positive definite matrices to compute the tightest constant lower bound on the metric tensor while preserving its full directional structure. The Cholesky factorization of this bound defines a linear map to an isotropic Euclidean space in which the Riemannian informed set reduces to a standard prolate hyperspheroid, enabling direct, rejection-free sampling using existing algorithms. Experiments on manipulation tasks with a 6-DoF UR5, 7-DoF Franka, and 14-DoF PR2 under three distinct Riemannian metrics show that our heuristic produces consistently tighter informed sets than both the Euclidean and scalar eigenvalue bounds, accelerating convergence across multiple state-of-the-art asymptotically optimal planners.

Comments: Submitted to IEEE Robotics and Automation Letters (RA-L)

Subjects:

Robotics (cs.RO)

Cite as: arXiv:2606.02879 [cs.RO]

(or arXiv:2606.02879v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2606.02879

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Phone Thiha Kyaw [view email] [v1] Mon, 1 Jun 2026 20:51:01 UTC (1,386 KB)

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