Analytical approximation for the double-stance phase of a walking robot

This paper introduces an approximate analytical solution to the otherwise non-integrable double-stance dynamics of the bipedal spring-loaded inverted pendulum (SLIP). Despite the apparent structural simplicity of the SLIP, the exact analytical solution to its stance dynamics cannot be found. Approximate maps have been proposed for the monoped SLIP runner (encompassing a single-stance phase). Still, even in an approximate form, a solution to the double-stance dynamics of the bipedal SLIP walker remained an open problem. We propose a double-stance map that can be readily utilized especially in the design of control systems for active dynamic walking. The accuracy of the derived map over a feasible range of locomotion properties is analyzed numerically, and a control application based on this solution is presented. Simulations for an arbitrary chosen energy level reveals that the devised controller enlarges the stable walking domain of the standard SLIP considerably.