tryss

[MiladShafiee]

In this issue we suggest a controller for early contact detection and stabilization of locomotion that can be used in push recovery controller (for avoiding impact with the ground) or walking on the ground with uncertainty.

[MiladShafiee]

The other paper that also is similar to the Kajita method is as following: \begin{equation} f-f_d=m \ddot q +d (\dot q -\dot q_d) \end{equation}

Here, m and d are the inertia and damping coefficients of the component, respectively, and by following approximations we have:

\begin{equation} \dot q_d (t)=\frac{q_d (t) -q_d (t-\Delta t)}{\Delta t}=\frac{\Delta q_d (t)}{\Delta t} \end{equation}

\begin{equation} \dot q_d (t)=\frac{q (t) -q (t-\Delta t)}{\Delta t} \end{equation}

\begin{equation} \ddot q(t)=\frac{q(t)-2q(t-\Delta t)+q(t-2\Delta t)}{\Delta t^2} \end{equation}

By substituting the first equation into the above equation we will have:

\begin{equation} q(t)= \left( f(t)-f_d(t)+\frac{d \Delta q_d (t)}{\Delta t}+(\frac{2m}{\Delta t^2}+\frac{d}{\Delta t}) q(t-\Delta t) q(t- \Delta t)- \frac{m}{\Delta t^2} q(t-2\Delta t) \right) /(\frac{m}{\Delta t^2}+\frac{d}{\Delta t}) \end{equation}