发表机构
Kyung Hee University; Advanced Institute of Convergence Technology (AICT)（庆熙大学; 先进融合技术研究院（AICT））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出RMRRT，一种在等距流形上统一处理等式与不等式约束的采样规划框架，通过障碍度量引导探索，实现100%成功率并减少规划时间。
AI 中文摘要
本文提出了一种运动规划框架，该框架在单一几何表述中统一了等式和不等式约束，用于高维机器人系统中的基于采样的规划。在传统的基于采样的规划器中，等式约束通常通过投影来强制执行，而不等式约束则通过诸如碰撞检测之类的二元有效性检查来单独处理，这常常导致探索效率低下。为了解决这一局限性，我们提出了黎曼障碍度量RRT（RMRRT），该算法在受等式约束的流形上构建统一的局部几何结构。RMRRT首先从对不等式敏感的障碍项构建环境障碍度量，然后通过与等式约束相关的(G)正交投影导出切空间度量。所得的切空间度量在引导和最近邻选择中一致使用，使探索偏离附近的不等式边界，同时保持一阶等式一致性。在这项工作中，该度量由基于符号距离的几何代理不等式实例化，以提供碰撞信息的切空间方向；硬可行性通过标准的有效性检查单独强制执行。实验结果表明，RMRRT在仿真和现实世界的各种受约束操作任务中均实现了100%的成功率，同时相对于代表性的受约束规划基线减少了规划时间。消融研究进一步表明，所提出的度量通过减少被拒绝的样本和缩短路径长度来提高探索质量。实验视频和源代码可在以下网址获取：此https URL
英文摘要
This paper presents a motion planning framework that unifies equality and inequality constraints within a single geometric formulation for sampling-based planning in high-dimensional robotic systems. In conventional sampling-based planners, equality constraints are typically enforced through projection, whereas inequality constraints are handled separately through binary validity checks such as collision testing, often leading to inefficient exploration. To address this limitation, we propose Riemannian Barrier Metric RRT (RMRRT), which constructs a unified local geometry for planning on equality-constrained manifolds. RMRRT first builds an ambient barrier metric from inequality-sensitive barrier terms and then induces a tangent-space metric via a (G)-orthogonal projection associated with the equality constraints. The resulting tangent-space metric is used consistently in both steering and nearest-neighbor selection, biasing exploration away from nearby inequality boundaries while preserving first-order equality consistency. In this work, the metric is instantiated from signed-distance-based geometric proxy inequalities to provide collision-informative tangent-space directions; hard feasibility is enforced separately through standard validity checks. Experimental results show that RMRRT achieves a 100% success rate across diverse constrained manipulation tasks in both simulation and real-world settings, while reducing planning time relative to representative constrained planning baselines. Ablation studies further demonstrate that the proposed metric improves exploration quality by reducing rejected samples and shortening path length. Experiment videos and source code are available at: https://rmrrt-anonymous.github.io
