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The Dijkstra algorithm is a classic path planning method, which in a discretegraph space, can start from a specified source node and find the shortest pathbetween the source node and all other nodes in the graph. However, to the bestof our knowledge, there is no effective method that achieves a function similarto that of the Dijkstra's algorithm in a continuous space. In this study, anoptimal path planning algorithm called convex dissection topology(CDT)-Dijkstra is developed, which can quickly compute the global optimal pathfrom one point to all other points in a 2D continuous space. CDT-Dijkstra ismainly divided into two stages: SetInit and GetGoal. In SetInit, the algorithmcan quickly obtain the optimal CDT encoding set of all the cut lines based onthe initial point x_{init}. In GetGoal, the algorithm can return the globaloptimal path of any goal point at an extremely high speed. In this study, wepropose and prove the planning principle of considering only the points on thecutlines, thus reducing the state space of the distance optimal path planningtask from 2D to 1D. In addition, we propose a fast method to find the optimalpath in a homogeneous class and theoretically prove the correctness of themethod. Finally, by testing in a series of environments, the experimentalresults demonstrate that CDT-Dijkstra not only plans the optimal path from allpoints at once, but also has a significant advantage over advanced algorithmsconsidering certain complex tasks.

CDT-Dijkstra: Fast Planning of Globally Optimal Paths for All Points in 2D Continuous Space