提出可微碰撞检测方法，让轨迹优化更高效安全
Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization
- 用解析表达式构建可微碰撞条件，支持优化求解
- 将多面体近似为光滑代数集合，实现非光滑体碰撞检测
- 适合需要高精度路径规划的机器人控制场景
基于优化的方法广泛应用于复杂任务的快速、多样化求解，如无碰撞运动或存在接触时的规划。然而，这些方法通常需强制执行物体间的非穿透约束，导致问题非平凡且计算成本高昂，使优化方法在规划与控制中的应用面临挑战。本文提出一种高效施加集合间非穿透约束的方法，适用于碰撞感知轨迹优化等场景。引入新的可微条件，具有解析表达式，从而实现配置空间优化中对非碰撞的精确建模。为在非光滑体之间使用这些条件，提出将多面体近似为光滑半代数集合的方法。通过多个数值实验验证所提方法性能，并与近期文献中提出的基线方法进行对比。
原文摘要 · Abstract (English)
Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。