In this article, we propose an algorithm for computing a smoothed version of the distance between two objects. As opposed to the traditional Euclidean distance between two objects, which may not be differentiable, this smoothed distance is guaranteed to be differentiable. Differentiability is an important property in many applications, in particular in robotics, in which obstacle-avoidance schemes often rely on the derivative/Jacobian of the distance between two objects. We prove mathematical properties of this smoothed distance and of the algorithm for computing it, and show its applicability in robotics by applying it to a second-order kinematic control framework, also proposed in this article. The control framework using smooth distances was successfully implemented on a 7 DOF manipulator.

中文翻译：

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二阶运动机器人控制的平滑距离


在本文中，我们提出了一种用于计算两个对象之间距离的平滑版本的算法。与两个对象之间可能不可微的传统欧几里得距离相反，这种平滑距离保证是可微的。可微性是许多应用中的一个重要属性，特别是在机器人技术中，其中避障方案通常依赖于两个物体之间距离的导数/雅可比矩阵。我们证明了这种平滑距离及其计算算法的数学特性，并通过将其应用于本文中提出的二阶运动控制框架来展示其在机器人技术中的适用性。使用平滑距离的控制框架已在 7 DOF 机械臂上成功实现。