Running with constant energy

The dynamics of Raibert's planar one legged hopper have been studied quite extensively in the particular case of vertical hopping and no translational velocity. These studies have pointed out the possibility of complicated behaviors. The forward motion of the one legged hopper has also been investigated in recent literature, with the restriction of low velocities. It appears from these references that the control of the energy of the hopper is a difficult problem due to the necessity of integrating the hopper's dynamical equations during the stance phases. In this paper, the authors consider the problem of controlling the leg's forward motion under the assumption that the energy of the hopper is constant. The authors unveil results that do not depend on the spring of the leg and analyse a few simple control schemes