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arXiv 2604.09800cs.ROcs.SYeess.SY
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连续体平面抓取的运动学

Kinematics of continuum planar grasping

Department of Mechanical and Aerospace Engineering, University of South Florida(南佛罗里达大学机械与航空航天工程系)

Udit Halder, Nicolas Echeverria Zambrano, Xincheng Li

AI总结:

本文提出分析框架研究软连续体臂抓取平面物体时的几何特性,通过优化控制理论确定最优抓取配置,并提出连续体抓取质量度量标准。

摘要:

本文提出一个分析框架,用于研究当软连续体臂抓取平面物体时出现的几何特性。臂的中心线和物体边界均被建模为光滑曲线。抓取问题被公式化为一个运动学边界跟随问题,在此问题中,物体边界作为臂的'影子曲线'。这种公式化导致了一组以相对几何形状变量表示的简化运动学方程,其中臂的曲率作为控制输入。一个优化控制问题被提出以确定能够实现最优抓取配置的可行臂形状,并通过庞特里亚金极大值原理求解。基于所得到的最优抓取运动学,利用相关连续体抓取映射的代数性质提出了一类连续体抓取质量度量标准。还讨论了动态环境中的反馈控制方面。所提出的方法通过系统性的数值模拟进行了说明。

英文摘要:

This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as a kinematic boundary following problem, in which the object boundary acts as the arm's 'shadow curve'. This formulation leads to a set of reduced kinematic equations expressed in terms of relative geometric shape variables, with the arm curvature serving as the control input. An optimal control problem is formulated to determine feasible arm shapes that achieve optimal grasping configurations, and its solution is obtained using Pontryagin's Maximum Principle. Based on the resulting optimal grasp kinematics, a class of continuum grasp quality metrics is proposed using the algebraic properties of the associated continuum grasp map. Feedback control aspects in the dynamic setting are also discussed. The proposed methodology is illustrated through systematic numerical simulations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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