In this paper, a mobile robot (tricycle robot) and its kinematic and dynamic model are presented. Moreover, its simulation and model control are derived. For a mobile robot to be autonomous, it must perform command tasks and perceive the environment. In this context, navigation plays an important role in the interaction of the robot with its environment. It consists in the determination of possible trajectories by the robot to follow a predefined trajectory. To accomplish this task, our approach relies on the dynamic motion of the robot to generate admissible trajectories. The reference trajectory is first constructed based on a predefined trajectory. To eliminate the navigation problem, an optimization problem with constraints, it is necessary to reduce the difference between the predicted trajectory of the robot and the desired trajectory. Moreover, it is possible to control the behaviour of the robot by using a trajectory parameterized with the dynamic model and its control. Finally, the display of experimental results up to the implementation of the object detection.