Abstract
Implementing virtual fixtures in guiding tasks constrains the movement of the robot's end effector to specific curves within its workspace. However, incorporating guiding frameworks may encounter discontinuities when optimizing the reference target position to the nearest point relative to the current robot position. This article aims to give a geometric interpretation of such discontinuities, with specific reference to the commonly adopted Gauss-Newton algorithm. The effect of such discontinuities, defined as Euclidean Distance Singularities, is experimentally proved. We then propose a solution that is based on a Linear Quadratic Tracking problem with minimum jerk command, then compare and validate the performances of the proposed framework in two different human-robot interaction scenarios.
Abstract (translated)
在引导任务中实现虚拟 fixtures 限制了机器人末端执行器的运动，使其在工作空间内沿着特定的曲线运动。然而，在将引导框架集成到机器人中时，在优化参考目标位置与当前机器人位置的最近点之间时，可能会遇到平滑曲线。本文旨在给出这种不连续性的几何解释，并特别针对通常采用的高斯-牛顿算法进行说明。这种不连续性，定义为欧氏距离奇点，已通过实验得到了证明。然后我们提出了一个基于线性二次规划问题最小加速度命令的解决方案，并比较和验证了在两种不同的人机交互场景中，所提出的框架的性能。
URL
https://arxiv.org/abs/2405.03473
