用黎曼几何优化运动规划，让机器人在复杂空间中走更省力的路。
RIT*: Riemannian Informed Trees for Cost-Adaptive Optimal Motion Planning
- 用黎曼度量替代欧氏距离，构建更精确的搜索空间
- 在14维双臂任务中，相比基线方法降低24.8%~63.5%路径成本
- 可在线学习障碍物邻近代价场，减少对预设度量依赖
我们提出黎曼信息树（RIT*），将批量信息搜索中的欧氏原语替换为黎曼对应形式。RIT* 构建更紧致、成本一致的信息集，在各向异性度量下执行最近邻搜索，并通过级联方案高效评估边成本。我们进一步引入碰撞自适应度量精化（CARM），从碰撞反馈中在线学习障碍物邻近代价场，降低对先验度量设计的依赖。在2维到14维环境中的实验表明，RIT* 在低维且度量恒定场景中表现竞争力，而在高维配置空间中度量随空间变化时，能生成显著更低代价的路径。性能提升随各向异性和维度增加，在3维各向异性基准上初始成本中位数比BIT*降低13.0%，6自由度操作任务中最终成本降低9.0%，14自由度双臂规划问题中成本降低24.8%-63.5%，而欧氏信息基线则明显退化。视频与代码见：https://muhayyuddin.github.io/ritstar/
原文摘要 · Abstract (English)
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/
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