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.

翻译：运动规划是机器人学中的核心挑战，近年来基于学习的方法获得了广泛关注。我们的工作聚焦于这类方法的一个特定方面：利用机器学习技术，特别是支持向量机（SVM），来评估机器人构型是否无碰撞，这一操作被称为“碰撞检测”。尽管这些方法日益流行，但缺乏支持其效率和预测准确性的理论支撑。这与机器学习方法（尤其是SVM）丰富的理论成果形成鲜明对比。我们的工作通过分析运动规划中基于学习的碰撞检测所用SVM分类器的样本复杂度，弥合了这一差距。我们界定了在给定置信水平下达到指定准确率所需的样本数量。该结果以机器人运动规划相关的术语（如系统间隙）进行表述。基于这些理论成果，我们提出了一种碰撞检测算法，该算法还能为机器人构型是否无碰撞的分类错误提供统计保证。