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

Abstract

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 θ * II , and the inter-leg angle ϕ 0 . We examine the energy efficiency and walking speed to demonstrate that Virtual Slope Walking is effective in generating high speed and energyefficient 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. Keywords Biped locomotion · High speed · Energy efficiency · Virtual Slope WalkingAbbreviations m the mass of the body; r the length of the stance leg; r s , r e the length of the stance leg before and after leg extension; θ the clockwise angle of the stance leg with respect to the vertical line; ω the angular velocity of the stance leg; ϕ the inter-leg angle; g gravitational acceleration; E c the complementary energy in one step; E d the dissipated energy in one step; E T the total mechanical energy; T step period; T s , T e the start and end time of stance leg extension, respectively.

Balanced Walking with Capture Steps

“…al. [16] suggested an elegant open-loop gait generation technique inspired by passive walking down a shallow slope. This approach creates a virtual downwards slope by shortening the swing leg before support exchange and recharging energy by extending the leg again during the support phase.…”

Analysis of a biped powered walking model based on potential energy compensation

“…In table 1 [15], we list the energy efficiency of some other models both passive and active, and also that of human being. We can see that the energy efficiency of Passive Dynamic Walking is almost equal to that of human being.…”

Biped walking by elastic potential energy and control strategy

“…Collins and Ruina built the 'Cornell biped' by using ankle push-off to provide power [9]. Asano [10], Dong Hao [11] and Xiaoyue Zhang [12] powered the robots by increasing their gravity potential energy in each step. The 'Stepper 2D' based on the 'virtual slope walking' method achieved the maximum relative speed of 4.48 leg/s [11].…”