发表机构
University of Toronto Institute for Aerospace Studies (UTIAS); Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory (MIT CSAIL)（多伦多大学航空航天研究所; 麻省理工学院计算机科学与人工智能实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对约束运动规划，提出使用子流形从构型空间继承的诱导度量来测量路径长度，使隐式与显式表示产生相同几何，并将黎曼度量规划扩展到约束子流形，实验验证于双臂操作。
AI 中文摘要
在约束运动规划问题中，任务约束和闭环约束将机器人的运动限制在其构型空间的一个弯曲的、低维子流形上。规划器使用度量来衡量路径长度，该度量设定了在每个方向上移动的代价。在欧几里得度量下，该代价处处相同，而在一般黎曼度量（如动能度量）下，代价可能随方向和构型而变化。现有方法通常隐式地将子流形描述为约束水平集，或通过参数化显式地描述。隐式表示通常与构型空间的欧几里得度量结合，显式表示则与参数域结合，因此规划器最小化的路径长度取决于表示方式。相反，我们使用诱导度量来衡量路径长度，该度量是子流形从构型空间上的黎曼度量继承而来的。隐式和显式表示产生相同的诱导度量，只是用不同坐标表达，因此具有相同的几何性质。该结果对构型空间上的任何黎曼度量都成立，而不仅仅是欧几里得度量。因此，度量的选择独立于表示的选择。利用这一结果，我们将黎曼度量下的规划从无约束空间扩展到约束子流形，通过在基于采样的规划器和轨迹优化器中应用诱导度量。对于显式表示，诱导度量还考虑了参数化引入的畸变。在双臂操作设置（两个Franka机械臂在末端执行器任务约束下）的实验中，我们比较了欧几里得度量和动能度量。
英文摘要
In constrained motion planning problems, task and loop-closure constraints restrict a robot's motion to a curved, lower-dimensional submanifold of its configuration space. Planners measure path length with a metric, which sets the cost of moving in each direction. Under the Euclidean metric, this cost is the same everywhere, whereas under a general Riemannian metric, such as the kinetic-energy metric, the cost can vary with direction and configuration. Existing methods often describe the submanifold either implicitly, as a constraint level set, or explicitly, through a parameterization. The implicit representation is typically combined with the Euclidean metric of the configuration space, and the explicit representation with the parameter domain, so the path length that a planner minimizes depends on the representation. Instead, we measure path length with the induced metric, which the submanifold inherits from a Riemannian metric on the configuration space. The implicit and explicit representations yield the same induced metric, expressed in different coordinates, and hence the same geometry. This result holds for any Riemannian metric on the configuration space, not only the Euclidean one. The choice of metric is therefore independent of the choice of representation. Using this result, we extend planning under a Riemannian metric from unconstrained spaces to constraint submanifolds by applying the induced metric in both a sampling-based planner and a trajectory optimizer. For an explicit representation, the induced metric also accounts for the distortion that the parameterization introduces. In experiments on a bimanual manipulation setup with two Franka arms under end-effector task constraints, we compare the Euclidean and kinetic-energy metrics.
Comments9 pages, 2 figures, 4 tables
