通过深度生成模型逼近高维自运动流形
Approximating High Dimensional Self-Motion Manifolds via Deep Generative Models
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中文总结 AI 辅助
本文提出一种基于深度生成模型的概率方法，通过采样与聚类逼近任意维度的自运动流形，无需改变架构，首次实现7R机械臂四维SMM的高效逼近。
中文摘要 AI 辅助
自运动流形（SMM）刻画了冗余机械臂在固定末端执行器位姿下无限逆运动学解集的几何结构，其高效恢复是可行且全局最优运动规划的基础。现有方法如零空间连续法和基于学习的方法均基于SMM是曲线的假设构建，无法扩展到更高冗余度的情况。我们转而采用概率视角：SMM是给定目标位姿下配置的条件后验分布的支撑集，因此恢复SMM可归结为从学习到的分布中采样，并通过聚类分离其不相交的分量。该公式与流形维度无关，且随着冗余度增加无需改变网络架构。在本工作中，我们证明了我们的方法能够以与最新零空间连续法和基于学习方法相当的性能逼近一维SMM，并且是首个能够在7R机械臂位置任务中逼近高冗余四维SMM的方法。项目网站：此https URL。
英文摘要
Self-motion manifold (SMM) characterizes the geometric structure of the infinite inverse kinematic solutions set of a redundant manipulator at a fixed end-effector pose, and its efficient recovery underpins feasible and global optimal motion planning. Existing methods such as null-space continuation and learning-based methods are formulated around the assumption that an SMM is a curve, and do not extend to higher redundancy orders. We instead adopt a probabilistic view: SMMs are the support of the conditional posterior over configurations given a target pose, so that recovering it reduces to sampling from a learned distribution and separating its disjoint components by clustering. The formulation is independent of the manifold dimension and requires no architectural change as the redundancy order grows. In this work, we demonstrate that our method can approximate 1-D SMMs with performance comparable to the latest null-space continuation and learning-based approach, and that it is the first method capable of approximating highly redundant 4-D SMMs in a 7R manipulator for position tasks. Project website: \href{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}
发表机构
- University of New South Wales（新南威尔士大学）
机构由 AI 辅助整理，请以论文原文为准。
