Abstarct: Unlike most common robots today, a robot with a tensegrity structure which is a combination of rigid and soft components, can be light and flexible and can move well in unrestricted environments. In this thesis, a planar tensegrity robot is investigated. First, by studing various available structures according to the desired expectations, an appropriate structure for the robot is proposed. Then, the bondgraph model of this robot is extracted and by extracting its Lagrangian dynamic model, the accuracy of the obtained bondgraph model is evaluated. Finally, optimization is done to find the appropriate path for the robot’s moving; Due to the importance of structural stability in this robot, the resulting path has the least potential energy and therefore the most stability during movement.