Enhancing Path Planning Algorithms with CubicSearch: A Novel Structured Approach for Propagation and Obstacle Avoidance

Many path planning algorithms rely on generating random points that share specific attributes with the target, such as proximity. This approach can render algorithms ineffective in complex environments and increase execution time. Therefore, enhancing algorithms with classical logic and improving their speed is a promising avenue of research. CubicSearch is a new method that employs an organized and efficient way for propagation and obstacle avoidance, with minimized memory and time complexity to O(n/C), where $C$ is the accuracy. It integrates other algorithms, such as BFS (Breadth-First Search) for tree propagation, and Boolean array for obstacle checking and verifying visited points with a high level of memory management. Additionally, it allows for adjustable accuracy in propagation, which can control execution time. These features contribute to the method's effectiveness, producing near-optimal paths that can be refined to become fully optimal. Unlike random algorithms, CubicSearch reliably finds a path even when only one path exists between numerous obstacles. The results show that the CubicSearch algorithm effectively manages highly complex 3D environments space) with multiple obstacles (greater than 100,000), generating the shortest paths for large data inputs in under one second. For 2D environments, it provides real-time path finding, resolving any path in milliseconds.