用几何方法分析软体机械臂抓取平面物体的运动规律。
Kinematics of continuum planar grasping
- 将抓取问题转化为曲线跟随的运动学问题，用曲率控制臂形。
- 通过最优控制求解理想抓取姿态，实现稳定抓握。
- 适合研究软体机器人抓取与控制的学者参考。
本文提出一种解析框架，研究软体连续体机械臂抓取平面物体时的几何特性。机械臂中心线和物体边界均建模为光滑曲线，抓取问题被表述为一个运动学边界跟随问题，其中物体边界作为机械臂的‘影子曲线’。该形式导出一组基于相对几何形状变量的简化运动学方程，以机械臂曲率为控制输入。构建了一个最优控制问题以确定实现最优抓取配置的可行臂形，并利用庞特里亚金最大值原理求解。基于所得最优抓取运动学，提出一类基于连续体抓取映射代数性质的抓取质量度量。同时讨论了动态设置下的反馈控制问题。所提方法通过系统的数值仿真进行验证。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。