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discrete system is quite linear, the precise location of the sample points is not critical. There are,

however, a few potential pitfalls to be avoided in choosing them:

1. Since we cannot necessarily predict the sign of the required perturbations from one

operating point, K=0, rather than at the nominal point itself.

such a case.

Figure 3.24 (a) shows

2. Samples should span a sufficiently large range in order to avoid local distortions in

h(K). A typical failure due to this problem can be seen in Figure 3.24 (b).

3. Sample points should not consist of excessively large control perturbations.

When the

current state is far from the limit cycle, large control perturbations can result in the

biped falling over.

Including a fall as a sample can lead to a poor model.

This

Sample scaling factors of k_fwd= ±5 degrees for hip pitch and k_lat= ±1 degree for hip roll give

acceptable linear models for our biped models over a wide variety of gaits.