Minimalistic models of an energy efficient vertical hopping robot

The use of free vibration in elastic structure can lead to energy efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, this paper explores three minimalistic models of free vibration that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three one-dimensional models are examined that contain different configurations of simple spring-damper-mass components. The self-stability of these models are also investigated in simulation. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the control parameters are analyzed for the energy efficient hopping.