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Evidence supporting the use of a linear discrete system model for bipedal control and the details of

model construction are presented later in the thesis (Section 3.6), after the particular choices of

RVs and LPPs have been described.

The key to using the linear predictive model for determining the correct control action is the

following.

Once the linear discrete system model has been constructed, the control perturbation

scalings required to drive Q_i+1to a desired value, can be computed using the inverse model:

K_i=J^-1DQ_i^d
+1

(3.11)

where [!]Q_i^d
+1^{= Qnom- Q}
cycle.^id
+1^{, the desired change in the RVs with respect to Qnomfor the current}

Figure 3.5 shows the limit cycle viewed as state trajectory with respect to time. Three consecutive

controlled cycles of a 1D discrete system are shown in this diagram, Tis the cycle period, k_iis the

perturbation scaling for cycle i, and V_iis the resulting state trajectory for cycle i. In this example,

Q_i^d
+1^{, the desired RV value for each cycle, is held constant for all three cycles.}

t

Our control formulation assumes the following apriori information, supplied by the user:

1. the open-loop control, U^nom.