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

2025-02-06

AI Summary

This paper addresses the lack of theoretical foundations for sample complexity in learning-based robot collision detection using SVM classifiers. It introduces the geometric clearance in configuration space into statistical learning analysis for the first time, establishing a quantitative relationship between clearance and the margin in feature space. By integrating computational geometry, statistical learning theory, and robot modeling, the authors derive an upper bound on the minimum sample size required to achieve a given accuracy ε and confidence 1−δ. Furthermore, they propose a practical SVM-based collision detection algorithm with provable error bounds. The key contributions are: (1) the first theoretical framework for SVM sample complexity tailored to robot collision detection; (2) a clearance-driven generalization error analysis method; and (3) a learning-based collision detector that simultaneously ensures theoretical guarantees and engineering feasibility.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Analyzes SVM sample complexity in collision detection.
• Binds samples for accuracy in robot motion planning.
• Proposes algorithm with error guarantees for collision detection.

Innovation

• SVM for collision detection
• Sample complexity analysis
• Statistical error guarantees