High-speed and energy-efficient biped locomotion based on Virtual Slope Walking

In our previous work, we have presented results on Virtual Slope Walking, that is when a robot walks on level ground down a virtual slope by leg length modulation, based on the potential energy restoration in Passive Dynamic Walking. In this paper, we introduce the model of Virtual Slope Walking with Trajectory Leg Extension (TLE) and equivalent Instantaneous Leg Extension (ILE) under the Equivalent Definition. The analytic solution of the model’s fixed point is obtained to analyze the essence of Virtual Slope Walking. We systematically investigate the characteristics and illustrate the effect of model parameters: the length-shortening ratio β, the equivalent extension angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta^{*}_{\mathrm{II}}$\end{document}, and the inter-leg angle ϕ0. We examine the energy efficiency and walking speed to demonstrate that Virtual Slope Walking is effective in generating high speed and energy-efficient walking. The high energy efficiency of the proposed model is theoretically confirmed. And the fast walking is validated by the experiments of a planar biped robot Stepper-2D, which achieves a sufficiently fast relative speed of 4.48 leg/s.