将3D-CSC路径规划简化为二维搜索，提升计算效率。
Reparametrization of 3D CSC Dubins Paths Enabling 2D Search
- 通过新参数化方法将3D问题降维至2维变量搜索。
- 在多数测试场景中成功计算出符合曲率约束的路径。
- 适合需要高效轨迹规划的飞行器与水下机器人使用。
本文研究三维空间中车辆的杜宾路径规划问题，重点关注由圆弧-直线-圆弧（CSC）组成的路径，这类路径适用于固定翼飞机和水下潜航器等具有最小转弯半径限制的平台。本文提出一种新参数化方法，将3D CSC路径规划问题转化为仅需搜索两个变量的二维问题，显著降低搜索复杂度，并提供梯度信息辅助优化。结合数值求解器，我们在多种平面及三维场景中测试了路径解的数量与类型。结果表明，该方法在绝大多数测试案例中均成功生成有效路径，证明其在构建鲁棒、高效的曲率约束轨迹方面具有潜力。
原文摘要 · Abstract (English)
This paper addresses the Dubins path planning problem for vehicles in 3D space. In particular, we consider the problem of computing CSC paths -- paths that consist of a circular arc (C) followed by a straight segment (S) followed by a circular arc (C). These paths are useful for vehicles such as fixed-wing aircraft and underwater submersibles that are subject to lower bounds on turn radius. We present a new parameterization that reduces the 3D CSC planning problem to a search over 2 variables, thus lowering search complexity, while also providing gradients that assist that search. We use these equations with a numerical solver to explore numbers and types of solutions computed for a variety of planar and 3D scenarios. Our method successfully computes CSC paths for the large majority of test cases, indicating that it could be useful for future generation of robust, efficient curvature-constrained trajectories.
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