用支持向量机分析机器人避障学习的样本需求，给出可验证的准确率保证。
From Configuration-Space Clearance to Feature-Space Margin: Sample Complexity in Learning-Based Collision Detection
- 基于支持向量机建模避障判断，以机器人配置间隙为理论依据
- 首次给出达到指定精度所需样本数的数学上界
- 适合需要安全保证的机器人路径规划应用
运动规划是机器人领域的核心挑战，近年来基于学习的方法受到广泛关注。本文聚焦于其中一种关键环节：利用机器学习技术（特别是支持向量机，SVM）判断机器人配置是否发生碰撞，这一过程称为‘碰撞检测’。尽管此类方法日益流行，但缺乏对其效率和预测准确性的理论支撑，与通用机器学习及SVM的丰富理论形成鲜明对比。本文通过分析用于运动规划中学习型碰撞检测的SVM分类器的样本复杂度，填补了这一空白。我们给出了在给定置信度下实现特定精度所需样本数的上界，结果以机器人系统间隙等运动规划相关量表示。基于这些理论成果，我们提出了一种可提供分类误差统计保证的碰撞检测算法。
原文摘要 · Abstract (English)
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.
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