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More formally, to control walking speed, Q ^~
d_{, a new value for Qdis computed each step by}

adding a velocity feedback term to a nominal value of Q^das follows:

Q
~
d_=Qbiasd_+kp[!](vd-v)

( 5.1)

where

Q_bias^d

v_d

v

k_p

is a nominal bias value

is a desired speed

is a measure of the speed of the current step

is a proportional feedback gain

The bias value is required because the required Q^dfor a stationary walk (i.e. in-place) is not

necessarily 0. The feedback term adjusts Q ^~
d_{in the appropriate direction (more forward or more}

upright) by an amount proportional to the error in speed.

We choose to use the distance travelled

by the pelvis over the current step as a velocity measure for vandv_d.

The speed of the walk can be varied using either v_dor Q_bias^d, since both contribute a constant term

Fixing v_dand varying Q_bias^dis akin to choosing a nominal speed and

to the overall equation.

varying the actual speed about that point by leaning more forward or more upright.

To prevent excessively large accelerations that could cause a fall, the feedback term is limited in

magnitude:

DQ_max,

[!]

where DQ_maxis the maximum allowable change in Q
~
d_{from Qbias}d