47

Two separate problems must be solved in order to achieve the motions we seek:

1. We must choose an RV target value, Q^d, on the cycle, which is likely to drive the

2. We must construct the discrete system model of Eq. 3.9 and then use it to compute the

final control perturbation for each step.

This involves calculating the discrete system

Jacobian, J, and the nominal operating point, Q^nomfor each step.

Desired RV Values

3. 7. 1

The desired (target) values for the RVs should be chosen each step to keep the system near a limit

cycle.

We choose to use a constant target value for all steps. The idea is that by forcing the RVs

to the same desired value at the same point in each cycle, a limit cycle will be generated.

This

approach is sufficient both to drive the system into a stable limit cycle initially and to maintain it.

Allowing the RV targets to vary from one step to the next can be useful, but requires a way to

select them.

This possibility is further explored in Chapter 5 where variation in Q^dis used to

provide control over the biped's walking speed.

Once the choice is made to use constant RV targets, the particular values must be chosen.

This is

essentially a trial-and-error process. However, common sense and the behaviour of the open-loop

system can provide valuable clues. For example, if a straight forward walking motion is desired,

the lateral RV target can be quickly estimated using the final pose in one PCG step as shown in

Figure 3.19.

Similarly, the first few steps of the open loop motion (such as that in Figure 3.8)

can provide a reasonable estimate for the forward component targets.

Finally, performing a

number of trials with different forward Q^dvalues provides a solution, if one exists, as well as

information on the useful range of target values. In this case, a "trial" is an attempt to balance the

biped's motion by applying our proposed control technique with some particular trial value of Q^d
.