46

These relationships allow us to attain final values for Qclose to the desired values for each step

using a simplified form of the Jacobian, discussed in the next section.

One interesting point to note is that the slope of the stance-COM curves in Figure 3.16 and Figure

3.17 are opposite in sign compared to the corresponding slopes for the up vector and swing-COM

RVs. This is due to the mechanism through which the stance-COM angle changes.

shows this effect exaggerated for clarity.

Figure 3.18

of M.

stance-C. of

Linear, Sampled "Balance" Control

3. 7

This section describes how the base PCG, perturbations and various RVs discussed in earlier

sections can be used to compute and apply the discrete system model parameters (Jand Q^nom) to

generate a balanced walk. The "balancing" is done by choosing appropriate RV target values for

each step and finding the scaling factors to apply to the PCG perturbations to reach them.

The

scaling factors are determined automatically using the inverse of the linear discrete system model

(Eq. 3.11). The balancing process is repeated, one step at a time, for as many steps as desired.

In some cases, the resulting walk is erratic and wanders.

reached.

In others,

a walking limit cycle is