The manipulation of flexible objects such as cables, wires and fresh food items by robot hands forms a special challenge in robot grasp mechanics. This paper considers the steering of flexible linear objects in planar environments by two robot hands. The flexible linear object, modeled as an elastic non-stretchable rod, is manipulated by varying the gripping endpoint positions while keeping equal endpoint tangents. The flexible linear object shape has a closed form solution in terms of the grasp endpoint positions and tangents, called Euler's elastica. This paper obtains the elastica solutions under the optimal control framework, then uses the elastica solutions to obtain closed-form criteria for non self-intersection, stability and obstacle avoidance of the flexible linear object. The new tools are incorporated into a planning scheme for steering flexible linear objects in planar environments populated by sparsely spaced obstacles. The scheme is fully implemented and demonstrated with detailed examples.

翻译：机器人手对电缆、导线及生鲜食品等柔性物体的操作构成了机器人抓取力学中的特殊挑战。本文研究平面环境下双机器人手对柔性线性物体的导引问题。该柔性线性物体被建模为不可拉伸的弹性杆，通过改变夹持端点位置并保持端点切线方向一致的方式进行操控。柔性线性物体的形状存在关于抓取端点位置与切线的闭合形式解，称为欧拉弹性曲线。本文首先在最优控制框架下推导弹性曲线解，进而利用该解获得柔性线性物体无自交、稳定性及避障的闭合形式判据。这些新工具被整合到稀疏障碍物分布的平面环境柔性线性物体导引规划方案中。该方案已完整实现，并通过详细算例进行演示。