This paper presents a deep analysis of a novel method entitled Dhouib-Matrix-SPP-24 (DM-SPP-24) and its application to rapidly generate the shortest trajectory for an autonomous mobile robot. For this problem, the environment is represented by a grid map where several obstacles are exposed with static positions and the main objective is to plan the shortest trajectory for an autonomous mobile robot from the current to the target positions with obstacles free-collisions. This study introduces an in-depth exploration of the twenty-four movement directions of the DM-SPP-24 method, an application on six grid maps and a comparison to several recent metaheuristics taken from the literature (such as the Improved Ant Colony Algorithm, the enhanced Ant Colony Optimization with Gaussian Sampling, the Particle Swarm Optimization, the Genetic Algorithm and other methods). Indeed, a new method namely DM-SPP-24 is introduced and this study notes an improvement in the quality and the rapidity of the generated solution by DM-SPP-24 versus the solution produced by the recent published metaheuristics in the literature. This work serves as a valuable resource for robotics and path planning viewing that it introduces a very fast and accurate method (DM-SPP-24) to plan the trajectory of an autonomous mobile robot.