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Such parameterizations can equivalently be thought of as a linear parametric perturbationwhich

modifies the open-loop behaviour of a base PCG.

The perturbations are identical in form to the

balance control LPPs of Chapter 3, but differ in function.

Instead of providing step-to-step

variations for balance, the perturbations presented in this chapter are applied over a number of

steps and are used to vary the overall behaviour of a balanced base PCG in order to achieve a

different motion from the original.

By recasting the interpolation described above as an LPP, it

can then be applied directly to other base PCGs to hopefully effect a similar qualitative change in

the motion. For example, if b( B1 )walks straight forward and b( B2 )turns to the right, then

[!]P = B2 - B1

might be called a turning LPP and could be applied to various other basic gaits to allow them to

turn.

This is the interpretation we shall build on in the rest of this chapter.

5. 3

Turning Perturbations

One important parameterized perturbation can be used to achieve turning motions.

When applied

to the base PCG of Section 3.4 and subsequently controlled

for

balance,

this

perturbation

provides a means to smoothly vary the curvature of the biped's path.

Furthermore, by applying a

simple proportional control law to determine a suitable turning rate, the biped can be made to

follow an arbitrary direction and thus the path of the biped can be controlled.

Figure 5.5 (a) and (c) show the PCG perturbation for a right turn for the human model.

The

perturbation affects only the left and right hip yaw DOFs (3:2 and 6:2).

The conceptual operation

of the perturbation is straightforward. In order to cause the biped to turn, the foot is placed on the

ground at an angle which points toward the new direction of travel.

During the stance phase, the

hip realigns the body with the foot, which remains fixed relative to the ground.