Targeted jumping of compliantly actuated hoppers based on discrete planning and switching control

We address the operation of robotic legs with intrinsic elasticity in hopping cycles determined by the mechanical resonant properties of the system. This ensures energy efficiency and high jumping velocity and distance. Recently, we have shown in simulation that a simple, biologically inspired bang-bang controller operating in the local coordinate of the first resonant mode leads to limit cycles which are robust with respect to leg model uncertainties and ground properties. In this paper we address the velocity control of the hopping and the planning of the bang-bang control parameters for the case that the systems should not move at steady state velocity, but should have different step lengths and heights. We exploit the discrete structure and the small number of parameters of the controller to develop a fast optimization procedure for generating an arbitrary sequence of steps. This approach can provide high motion performance, robustness and substantial computational time saving compared to continuous trajectory and controller gain planning. The stationary and the aperiodic hopping is validated by experiments on a new planar elastic leg.