Self-oscillation when controlling the movement of a hopping vehicle

The planar problem of controlling the vertical and horizontal motion of a one-legged hopping vehicle with due regard for the weight of the leg is analytically investigated. The design of the telescopic leg uses an elastic element, which basically ensures the movement of the vehicle and carries out energy recuperation. The servomotor in the telescopic leg link is used only to compensate for irreversible energy losses for overcome friction and collisions at the moments of landing and detachment from the supporting surface. It is shown that there are stable periodic solutions (self-oscillations) that allow the use of an open control system for vertical movement of the vehicle (maintaining a given height of jumps). Control of the horizontal movement of the device is carried out only by working out during the phase of the flight the required value of the forward carrying of the leg at the moment of landing. To control the movement of the vehicle, it is enough positional servomotors that provide an output to a given end position.