为杜宾车辆设计可任意延长的平滑轨迹，最少仅需两次曲率转折。
Trajectory elongation strategies with minimum curvature discontinuities for a Dubins vehicle
- 用三个半径可变的圆弧拼接生成曲率受限轨迹。
- 覆盖所有可达长度，且曲率转折点不超过两个。
- 提出八类圆弧组合路径，适用于复杂导航场景。
本文提出在任意给定方向点之间设计任意长度、曲率受限的轨迹策略。所提轨迹由三个半径可变的圆弧拼接而成，确保在所有情况下最大覆盖可达长度集合，且曲率变化点最多仅两个。通过引入内切圆概念，将圆-圆-圆轨迹扩展为八种类型：{LLL, LLR, LRR, LRL, RRL, RLL, RLR, RRR}。论文给出了轨迹的数学表达式，并分析了各类轨迹的存在条件与分类标准。进一步研究了不同延长策略下轨迹长度的变化规律，推导出所有方向点对的可达长度集合。最后通过数值仿真验证了方法的有效性。
原文摘要 · Abstract (English)
In this paper, we present strategies for designing curvature-bounded trajectories of any desired length between any two given oriented points. The proposed trajectory is constructed by the concatenation of three circular arcs of varying radii. Such a trajectory guarantees a complete coverage of the maximum set of reachable lengths while minimising the number of changeover points in the trajectory to a maximum of two under all scenarios. Additionally, by using the notion of internally tangent circles, we expand the set of Circle-Circle-Circle trajectories to eight kinds, consisting of {LLL, LLR, LRR, LRL, RRL, RLL, RLR, RRR} paths. The paper presents a mathematical formulation of the proposed trajectory and the conditions for the existence and classification of each kind of trajectory. We also analyse the variation of the length of the trajectory using suitable elongation strategies and derive the set of reachable lengths for all pairs of oriented points. Finally, the results of this paper are illustrated using numerical simulations.
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。