From Configuration-Space Clearance to Feature-Space Margin: Sample Complexity in Learning-Based Collision Detection

TL;DR

This paper analyzes the sample complexity of SVM-based collision detection in robot motion planning, providing theoretical bounds and a statistically guaranteed algorithm for classifying collision-free configurations.

Contribution

It introduces a theoretical framework for the sample complexity of SVMs in collision detection, linking it to robot system clearance and motion planning parameters.

Findings

Bound on the number of samples needed for desired accuracy

Algorithm with statistical error guarantees

Theoretical link between clearance and sample complexity

Abstract

Motion planning is a central challenge in robotics, with learning-based approaches gaining significant attention in recent years. Our work focuses on a specific aspect of these approaches: using machine-learning techniques, particularly Support Vector Machines (SVM), to evaluate whether robot configurations are collision free, an operation termed ``collision detection''. Despite the growing popularity of these methods, there is a lack of theory supporting their efficiency and prediction accuracy. This is in stark contrast to the rich theoretical results of machine-learning methods in general and of SVMs in particular. Our work bridges this gap by analyzing the sample complexity of an SVM classifier for learning-based collision detection in motion planning. We bound the number of samples needed to achieve a specified accuracy at a given confidence level. This result is stated in terms relevant to robot motion-planning such as the system's clearance. Building on these theoretical results, we propose a collision-detection algorithm that can also provide statistical guarantees on the algorithm's error in classifying robot configurations as collision-free or not.