Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle contours if a check collides with an obstacle. The algorithms outperform conventional free-space planners such as A* especially when the queried points are far apart. The thesis presents novel search methods to speed up vector-based algorithms in non-convex obstacles by delaying line-of-sight checks. The "best hull" is a notable method that allows for monotonically increasing path cost estimates even without verifying line-of-sight, utilizing "phantom points" placed on non-convex corners to mimic future turning points. Building upon the methods, the algorithms R2 and R2+ are formulated, which outperform other vector-based algorithms when the optimal path solution is expected to have few turning points. Other novel methods include a novel and versatile multi-dimensional ray tracer for occupancy grids, and a description of the three-dimensional angular sector for future works.

翻译：基于向量的算法是最优任意角度路径规划中的新型算法，其设计灵感来源于Bug算法。该算法通过直接对查询点间进行视线检测来绕过自由空间，若检测到与障碍物碰撞则沿障碍物轮廓进行搜索。相较于A*等传统自由空间规划器，该算法在查询点相距较远时表现尤为优异。本论文提出了新颖的搜索方法，通过延迟视线检测来加速基于向量的算法在非凸障碍物环境中的运行。其中"最佳外壳"方法具有显著优势，即使未验证视线也能实现路径成本估计的单调递增，该方法通过在非凸角点设置"幻象点"来模拟未来的转向点。基于这些方法，本文构建了R2和R2+算法，当最优路径解预期具有较少转向点时，其性能优于其他基于向量的算法。其他创新方法包括：适用于占据栅格的新型通用多维光线追踪器，以及为未来研究构建的三维角扇区描述框架。