Abstarct: For any mobile device, the ability to navigate in its environment is important. Avoiding dangerous situations such as collisions and unsafe conditions provide a trajectory optimization problem which is the process of designing a trajectory that minimizes or maximizes some measure of performance within prescribed constraint boundaries. In particular, a procedure for computing optimal trajectories in presence of obstacles is proposed. This thesis addresses the problem of planning collision free paths for mobile robots and different evolutionary techniques are used to solve optimization problems. Moreover including obstacle avoidance, a gradient of a potential field centered on the obstacle is considered baxsed on potential field algorithm. This optimization problem can accommodate such effects as s terrain, robot dynamics. In order to investigating energy efficiency, the new problem is developed. An energy object function is minimized in order to extend run-time of battery-powered on trajectory. The energy is dissipated mostly in the motors, which strongly depends on the velocity profile. The algorithms are presented for wheeled mobile robot trajectory generation that achieves a high degree of generality and efficiency. Experimental tests have been also carried out in order to validate the effectiveness of the proposed procedure. The reporting results are obtained by gathering movement data from an empirical study of iRobot’s Roomba™. The efforts are focused on improvements to a research robotic system by the sensors available on the Roomba. Graphical simulator is designed for the detail necessary in the algorithms. Simulation and experiments are performed, and compared to the results presented. They show good performance and ability to avoid the local minimum problem in most of the cases.