31

2. the RV projection function, g.

3. the fixed control perturbations, [!]U.
4. the desired (target) values for the RVs, ^Q_i^d
   +1^{, for each cycle, i.}

The parameters of the discrete system model (Q^nomand J) and the required perturbation scalings,

K^*
i^{, are calculated automatically.}

These computations will be discussed in Section 3.7 after the

various elements of the bipedal control system have been described.

3. 3

Application to Bipedal Locomotion

In attempting to generate balanced locomotion for a biped, we must first select the numberof

control dimensions to be used. For successful balance, the base of support must, on average,

remain under the centre of mass and the torso should remain generally upright.

Only two control

dimensions are required to achieve this, one in each dimension of the horizontal plane.

Thus to

balance each step, our bipedal control system will use two RV dimensions and require two LPPs

which span the RV space.

Since we use pose control exclusively with our biped we will use B

and [!]Pto represent the pose control equivalents of U^nomand [!]Urespectively.

The base PCG, B, describes one complete cycle of motion, or in the case of bipedal walking, two

steps. For bipedal walking we choose to split the cycle into two symmetric halves and apply our

control

formulation

to

each

step.

The

PCG

control

perturbations,

[!]P,

affect

the

motion

throughout the cycle, rather than at a single point in the cycle.

Figure 3.6illustrates the overall pose control structure used for our bipedal systems.

The

structure is an expansion of Eq. 3.4, for N=2, with the left step and right step perturbations

specified explicitly. In summary, each step is balanced by the choice of two scalar parameters, for

example, k₁₀and k₂₀for step 0. These parameters are calculated automatically using the discrete

system model.