Low-energy control of a one-legged robot with 2 degrees of freedom

We consider the dynamics of forward motion for a one-legged hopping robot. We analyze the passive dynamics of the leg and find the necessary initial conditions which produce forward hopping. An approximate Poincare return map is derived using perturbation theory, and a control system designed to consume a small amount of energy is applied. Numerical simulations indicate that a moderate range of stable forward speeds may be achieved. The control strategy applied allows a steady-state hopping motion to be maintained using low-bandwidth sensory feedback while introducing little energy into the system