Self-motion Robots and their static environments are the main topics for trajectory planning researchers, especially when the environments contain static and movable obstacles that make the robots' mission harder to reach their target. Therefore, accurate and comprehensive knowledge of autonomous robots' control strategies makes us take the basic steps to build our approach in mobile robot trajectory planning. Accordingly, in this research paper, we will provide an accurate detail of two path planning algorithms A star and 4_sector wavefront algorithms. Some modifications and improvements to its software structure for each algorithm will reduce the time it takes for the robot to reach the desired goal, taking into account the presence of obstacles in the map that is dealt with and how to avoid collision with it, especially dead-end obstacles, which cause the robot to enter into a state of making wrong decisions that can lead to a collision or a significant waste of time required to reach the specified goal. The simulation results of the A-star algorithm and 4_sector wavefront methods using MATLAB program are achieved in different ways using inputs via camera, then image processing is applied to determine the locations of obstacles, starting point, free space, and target point for the robot without any position error. The wavefront algorithm takes a shorter time than the A-star method to reach the final position.