通过去扭曲参数化空间，让机器人规划出更短路径。
Planning Shorter Paths in Graphs of Convex Sets by Undistorting Parametrized Configuration Spaces
- 用非凸目标优化时，通过去扭曲参数化空间恢复真实距离
- 在3个机器人场景中路径长度和时间显著缩短，计算开销微增
- 适合需精准路径的复杂运动规划，如双臂协作或旋转控制
基于优化的运动规划提供灵活建模能力。图式凸集（GCS）通过将配置空间表示为有限个凸集的并集，实现轨迹优化的可行性与最优性保证。非线性参数化可扩展该方法处理运动学闭环等问题，但会扭曲距离，导致以凸目标求解时获得的路径在原始空间中次优。本文提出一种扩展GCS的方法，支持非凸目标，可在保持可行性保障的同时“去扭曲”优化空间。我们在三个机器人规划场景中验证该方法：双臂协同搬运物体、使用欧拉角表示的三维旋转集合，以及一种有理参数化解析运动学以认证无碰撞区域。结果表明，该方法显著缩短路径长度与轨迹时长，仅带来轻微运行时间增加。
原文摘要 · Abstract (English)
Optimization based motion planning provides a useful modeling framework through various costs and constraints. Using Graph of Convex Sets (GCS) for trajectory optimization gives guarantees of feasibility and optimality by representing configuration space as the finite union of convex sets. Nonlinear parametrizations can be used to extend this technique to handle cases such as kinematic loops, but this distorts distances, such that solving with convex objectives will yield paths that are suboptimal in the original space. We present a method to extend GCS to nonconvex objectives, allowing us to "undistort" the optimization landscape while maintaining feasibility guarantees. We demonstrate our method's efficacy on three different robotic planning domains: a bimanual robot moving an object with both arms, the set of 3D rotations using Euler angles, and a rational parametrization of kinematics that enables certifying regions as collision free. Across the board, our method significantly improves path length and trajectory duration with only a minimal increase in runtime. Website: https://shrutigarg914.github.io/pgd-gcs-results/
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