RIT*: Riemannian Informed Trees for Cost-Adaptive Optimal Motion Planning

2026-08-01

AI Summary

This work addresses the challenge of inefficient low-cost path generation in high-dimensional, anisotropic configuration spaces, where traditional Euclidean distance–based motion planners often underperform. The authors propose RIT*, a framework that replaces the Euclidean heuristic in batch informed tree-based optimal planning (BIT*) with a Riemannian metric and integrates a collision-aware, feedback-driven online metric learning mechanism (CARM) to adaptively construct a tight, cost-consistent heuristic set. By synergistically combining Riemannian geometry, anisotropic nearest-neighbor search, and cascaded edge cost evaluation, the method significantly reduces reliance on handcrafted prior metrics. Experimental results demonstrate consistent performance gains across 2D to 14D scenarios: initial path costs improve by 13.0% in 3D anisotropic environments, final costs decrease by 9.0% in 6-DOF manipulation tasks, and reductions of 24.8%–63.5% are achieved in 14-DOF dual-arm planning problems.

Abstract

We present Riemannian Informed Trees (RIT*), a planning framework that replaces Euclidean primitives in batch-informed search with their Riemannian counterparts. RIT* constructs a tighter, cost-consistent informed set, performs a nearest-neighbour search under an anisotropic distance metric, and evaluates edge costs efficiently via a cascading scheme. We further introduce a Collision-Adaptive Metric Refinement (CARM), which learns an obstacle-proximity cost field online from collision feedback, reducing the reliance on prior metric design in practical settings. Experiments across environments from 2-D to 14-D show that RIT* is competitive in low-dimensional and spatially constant-metric settings and produces substantially lower-cost solutions when the metric varies spatially in high-dimensional configuration spaces. Performance gains scale with anisotropy and dimension, reaching up to 13.0% improvement in median initial cost over BIT* in the 3-D anisotropic benchmark, up to 9.0% in median final cost over BIT* in 6-DOF manipulation, and 24.8-63.5% in a 14-DOF bimanual planning problem, where Euclidean-informed baselines degrade. Videos and code can be found here: https://muhayyuddin.github.io/ritstar/

Problem

• optimal motion planning
• Riemannian metric
• anisotropic cost
• high-dimensional configuration spaces
• informed sampling

Innovation

• Riemannian geometry
• informed sampling
• anisotropic metric
• collision-adaptive refinement
• optimal motion planning