Adaptive A* RRT* for Robot Navigation in Maze

Autonomous navigation relies on path planning algorithms that must balance computational efficiency, optimality, and flexibility in challenging environments. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{A}^{\ast}$</tex> performs poorly in unstructured surroundings, though it is excellent in gridbased applications with little computing time. Conversely, RRT* handles high-dimensional spaces but has slow convergence and suboptimal paths. The hybrid algorithm (Hybrid A*-RRT*) presented in this paper addresses these limitations by combining the heuristic-driven accuracy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A^{\ast}$</tex> with the random exploration of RRT*. First, the algorithm generates an optimal path using A* then directionally biases RRT* sampling regions of interest, thereby reducing unnecessary node expansion and accelerating convergence. Experiments demonstrate the algorithm's effectiveness across dynamically generated maze environments with varying complexity levels determined by grid cell size. Key performance metrics include path length, the nodes inspected, the number of iterations, and the computational time. In complex environments, the hybrid method reduces computation time by 80 % compared to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A^{\ast}$</tex> and by 59 % compared to RRT*, while maintaining Path lengths within 9 % of A* optimality and exploring 48 % fewer nodes than RRT*. The hybrid approach achieves 100 % success across all study environments, thereby illustrating its value in finding a middle path between solution speed and quality. In 3D or multi-agent circumstances, later studies might use this approach.