Conventional local planners frequently become trapped in a locally optimal trajectory, primarily due to their inability to traverse obstacles. Having a larger number of topologically distinctive paths increases the likelihood of finding the optimal trajectory. It is crucial to generate a substantial number of topologically distinctive paths in real-time. Accordingly, we propose an efficient path planning approach based on tangent graphs to yield multiple topologically distinctive paths. Diverging from existing algorithms, our method eliminates the necessity of distinguishing whether two paths belong to the same topology; instead, it generates multiple topologically distinctive paths based on the locally shortest property of tangents. Additionally, we introduce a priority constraint for the queue during graph search, thereby averting the exponential expansion of queue size. To illustrate the advantages of our method, we conducted a comparative analysis with various typical algorithms using a widely recognized public dataset\footnote{https://movingai.com/benchmarks/grids.html}. The results indicate that, on average, our method generates 320 topologically distinctive paths within a mere 100 milliseconds. This outcome underscores a significant enhancement in efficiency when compared to existing methods. To foster further research within the community, we have made the source code of our proposed algorithm publicly accessible\footnote{https://joeyao-bit.github.io/posts/2023/09/07/}. We anticipate that this framework will significantly contribute to the development of more efficient topologically distinctive path planning, along with related trajectory optimization and motion planning endeavors.

翻译：传统的局部规划器常因无法穿越障碍物而陷入局部最优轨迹。生成更多拓扑不同路径可提高最优轨迹的搜寻概率，因此实时生成大量拓扑不同路径至关重要。为此，我们提出一种基于切线图的高效路径规划方法，以生成多条拓扑不同路径。与现有算法不同，本方法无需判别两条路径是否属于同一拓扑结构，而是基于切线的局部最短特性直接生成多条拓扑不同路径。同时，我们在图搜索过程中引入队列优先级约束，避免队列规模指数级增长。为验证方法优势，我们利用广泛采用的公开数据集\footnote{https://movingai.com/benchmarks/grids.html}与多种典型算法进行对比分析。结果表明，本方法在100毫秒内平均可生成320条拓扑不同路径，相较于现有方法实现了显著的效率提升。为促进社区后续研究，我们已将所提算法的源代码公开\footnote{https://joeyao-bit.github.io/posts/2023/09/07/}。我们预期该框架将有力推动更高效的拓扑不同路径规划、相关轨迹优化及运动规划研究的发展。