Loewner Order Heuristic Boosts Robot Motion Planning Efficiency

Informed sampling techniques are critical for accelerating motion planners by focusing search on promising regions, but existing methods rely on Euclidean heuristics that become inadmissible under configuration-dependent Riemannian metrics. Scalar eigenvalue bounds restore admissibility but discard directional structure, producing overly conservative sets. Now, Phone Thiha Kyaw and Jonathan Kelly from the University of Toronto (presumably) introduce a matrix-valued admissible heuristic that leverages the Loewner order on symmetric positive definite matrices to compute the tightest constant lower bound on the metric tensor while preserving its full directional geometry. Their approach maps the Riemannian informed set to an isotropic Euclidean space via Cholesky factorization, enabling direct, rejection-free sampling using standard prolate hyperspheroid algorithms.

Experiments on three robotic platforms—a 6-DoF UR5, 7-DoF Franka, and 14-DoF PR2—under three distinct Riemannian metrics demonstrate that the proposed heuristic consistently produces tighter informed sets than both the Euclidean baseline and scalar eigenvalue bounds. This leads to faster convergence across multiple state-of-the-art asymptotically optimal planners. The work, submitted to IEEE Robotics and Automation Letters (RA-L), promises more efficient motion planning in complex, high-dimensional configuration spaces, with direct applications to industrial manipulation and autonomous systems.