Spring Loaded Inverted Pendulum embedding: Extensions toward the control of compliant running robots

This paper explores systematic control strategies for the stabilization of running on compliant robots with nontrivial torso pitch dynamics. The Spring Loaded Inverted Pendulum (SLIP) embedding controller is revisited and its pertinence to more general legged robot models is investigated. It is first deduced that - in the context of an asymmetric hopper - the existence of a SLIP embedding control law requires nominal running motions in which the torso is kept at a constant angle. To remove this overly restrictive condition, a new method is proposed here that retains the advantage of generating control inputs acting in concert with the compliant dynamics of the plant without explicit reliance on the SLIP. To illustrate the enhanced control authority afforded by the proposed method, a minimalist setting is considered, in which a three-degree-of-freedom asymmetric hopper is controlled by a single actuator located at the hip.