提出连续体抓取的静力学分析框架，优化接触力分布以实现稳定抓握。
Statics of continuum planar grasping
- 将连续体抓取建模为线性控制问题，接触力作为控制输入。
- 通过最优控制最小化所需接触力，提升抓取效率。
- 可评估抓握质量并找到最佳抓取配置，适合柔性机器人研究者。
受八爪鱼触手、象鼻等生物附肢启发，连续体机器人抓取提供了一种灵活且自适应的对象操作方法。与传统刚体抓取不同，连续体机器人利用分布式柔性和整体接触实现鲁棒且灵巧的抓握。本文提出一个控制理论框架，用于分析与平面物体的连续接触静力学。物体的静平衡方程被建模为线性控制系统，其中分布接触力作为控制输入。为优化抓握性能，构建了一个约束最优控制问题，以最小化维持静止抓握所需的接触力，解法基于庞特里亚金最大值原理。此外，引入两个优化问题：(i) 定义连续体抓握质量度量，推广刚体抓握质量指标；(ii) 寻找最大化连续体抓握质量的最佳抓取构型。文中还提供了多个数值结果以阐明方法有效性。
原文摘要 · Abstract (English)
Continuum robotic grasping, inspired by biological appendages such as octopus arms and elephant trunks, provides a versatile and adaptive approach to object manipulation. Unlike conventional rigid-body grasping, continuum robots leverage distributed compliance and whole-body contact to achieve robust and dexterous grasping. This paper presents a control-theoretic framework for analyzing the statics of continuous contact with a planar object. The governing equations of static equilibrium of the object are formulated as a linear control system, where the distributed contact forces act as control inputs. To optimize the grasping performance, a constrained optimal control problem is posed to minimize contact forces required to achieve a static grasp, with solutions derived using the Pontryagin Maximum Principle. Furthermore, two optimization problems are introduced: (i) for assigning a measure to the quality of a particular grasp, which generalizes a (rigid-body) grasp quality metric in the continuum case, and (ii) for finding the best grasping configuration that maximizes the continuum grasp quality. Several numerical results are also provided to elucidate our methods.
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