Mobile robots are used in a variety of applications ranging from domestic robotics to autonomous vehicles. In several applications, it is important to conduct motion planning for robots to find optimal paths with respect to parameters such as space and time. Classical search methods in the literature can be adapted to guide robotic paths and plan the motion of mobile robots. In this work, we explore three methods, namely the deterministic depth-first search and breadth-first search, and the heuristic A* search. We adapt these to the context of mobile robots navigating a maze and accordingly present the deployed algorithms and corresponding experiments with comparisons. These findings are useful in applications where mobile robots are utilized since the optimization of their paths is beneficial in motion planning. We explain applications of this study in areas such as human-robot collaboration (HRC) and unmanned aerial vehicles (UAVs) for motion planning in robotic paths.