无需初始猜测，即可在动态障碍物中生成最优无碰撞轨迹。
Systematic Constraint Formulation and Collision-Free Trajectory Planning Using Space-Time Graphs of Convex Sets
- 用凸集时空图构建约束，自动满足复杂时空条件。
- 静态环境与动态环境均能生成全局最优轨迹。
- 适合机器人路径规划、自动驾驶等实时避障场景。
本文提出在杂乱动态环境中生成最优、无碰撞且随时间变化的轨迹。由于存在大量空间和时间约束，传统数值求解器难以获得有效初始猜测。通过图的凸集（GCS）及近期发展的凸集时空图（ST-GCS）框架，可无需提供初始猜测即生成最小距离无碰撞轨迹。我们还推导了通用的GCS兼容约束，并提出一种直观策略将一般约束适配至该框架。实验表明，当环境静态时，ST-GCS与标准GCS结果一致；在复杂动态环境中，可生成全局最优轨迹。
原文摘要 · Abstract (English)
In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex Sets (GCS) and the recently developed Space-Time Graphs of Convex Sets (ST-GCS) enable us to generate minimum distance collision-free trajectories without providing an initial guess to the solver. We also explore the derivation of general GCS-compatible constraints and document an intuitive strategy for adapting general constraints to the framework. We show that ST-GCS produces equivalent trajectories to the standard GCS formulation when the environment is static, as well as globally optimal trajectories in cluttered dynamic environments.
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。