A Differentiable Distance Metric for Robotics Through Generalized Alternating Projection
Abstract
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.
Cite
@article{arxiv.2507.01181,
title = {A Differentiable Distance Metric for Robotics Through Generalized Alternating Projection},
author = {Vinicius M. Gonçalves and Shiqing Wei and Eduardo Malacarne S. de Souza and Krishnamurthy Prashanth and Anthony Tzes and Farshad Khorrami},
journal= {arXiv preprint arXiv:2507.01181},
year = {2025}
}
Comments
This work has been submitted to the IEEE for possible publication