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perturbations and, in part, to the fact that the motion is only constrained at a single point in the

cycle for each step.

One possible solution to this problem is to use the waist pitch degree-of-freedom of our human

model to continuously servo the torso to a desired angle from the vertical in the sagittal plane. The

torso servoing control is applied to the biped's waist pitch DOF.

example is calculated as

The applied torque for a planar

t=k_p[!](f-f_desired)-k_d[!]f ^·

where

tis the applied joint torque

f_desired

is the desired torso angle from vertical in the world frame (constant)

fis the torso angle with respect to world frame vertical

f ^· is the time derivative of f

k_pand k_dare the proportional and derivative gains

and

The parameters t, f_desired, and fare shown in Figure 3.25

Figure 3.25 -Torso servo parameters

With continuously-applied torso servoing, the torso motion becomes considerably smoother.

However, it also presents an additional problem when used with balance control.

The application

of a torso servo precludes the use of torso-based RVs since these will no longer vary with hip