The instantaneous leg extension model of Virtual Slope Walking

In our previous work, we have realized virtual slope walking that a robot can walk on level ground as it walks down a virtual slope by leg length modulation. In this paper, we present the instantaneous leg extension model of virtual slope walking to analyze the essentials of virtual slope walking. It has two straight massless legs and a point mass body at the hip. The stance leg is extended instantaneously while the swing leg is swung and shortened actively. We demonstrate that this model can exhibit stable walking cycles on level ground. We obtain the sufficient conditions for the existence of the fixed point. We then illustrate the effect of the model parameters on the fixed point to show how the fixed point can be determined by adjusting the parameters. Further, we theoretically proved that the fixed point is asymptotically stable, meaning that it is independent on the initial conditions. The validity of the proposed model has been examined by numerical simulations.