提出可微距离度量，解决机器人避障中梯度计算难题
A Differentiable Distance Metric for Robotics Through Generalized Alternating Projection
- 基于广义交替投影，推导凸多面体的光滑投影公式
- 确保物体重叠时距离为零，且在所有条件下可微
- 已在仿真平台UAIBot开源，适用于控制与规划任务
在众多机器人应用中，不仅需要计算机器人与环境间的距离，还需其导数（如使用控制屏障函数时）。然而传统欧氏距离不可微，亟需替代方案。近期有研究提出保证可微性的度量方法[1]，但存在重要缺陷。本文给出更简洁实用的凸多面体光滑投影表达式，并确保物体重叠时距离严格为零。实验验证了该方法的有效性。所提距离度量已通过基于Python的仿真工具包UAIBot公开。
原文摘要 · Abstract (English)
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean distance is not differentiable, there is a need for alternative distance metrics that possess this property. Recently, a metric with guaranteed differentiability was proposed [1]. This approach has some important drawbacks, which we address in this paper. We provide much simpler and practical expressions for the smooth projection for general convex polytopes. Additionally, as opposed to [1], we ensure that the distance vanishes as the objects overlap. We show the efficacy of the approach in experimental results. Our proposed distance metric is publicly available through the Python-based simulation package UAIBot.
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