  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.
