Obtaining the optimal shortest path between two points on a quasi-developable Bézier-type surface using the Geodesic-based Q-learning algorithm

One of the most important problems is the computation of the shortest path between two points, because the search for the shortest path is very important in various fields, such as path planning of autonomous mobile robots. With this goal in mind, this study presents a novel method for determining the most efficient route connecting two locations on a surface. This approach relies on the geodesic properties of the surface points, the surface's ability to be unfolded without distortion, and the utilization of the Q -learning algorithm. The first part of the proposed method constructs a quasi -developable B & eacute;zier-type surface from two boundary cubic trigonometric B & eacute;zier-type curves using the computed optimal four shape parameters. The subsequent stage of the introduced technique identifies the best and most direct route between two designated points on the derived quasi -developable B & eacute;zier-style surface. This is achieved through the utilization of the Geodesic -based Improved Epsilon Greedy Q -Learning (IEGQL) algorithm. Additionally, we have used the proposed algorithm in a mobile application developed for the elderly. This application involves offering a mobile game designed to ascertain the shortest path, with the goal of enhancing cognitive engagement among the elderly population as a preventive measure against Alzheimer's disease. Moreover, the proposed method is compared with Dijkstra's algorithm and A -Star algorithm, which are the best known algorithms for the shortest path problem.