87

of

tighter.

The

16

degree

turning

perturbations

fail,

resulting

in

a

turning

limit

cycle

approximately 0.75 meters in radius, a more useful lower limit in terms of the motion that can be

animated.

The walks still suffer from the biped facing too much toward the centre of the turn.

For tight turns, the biped's outside swing leg interpenetrates the stance leg in a noticeable fashion.

Nonetheless, the perturbations provide a good basis for higher level control of the biped's path.

5. 3. 1

Point and Path Following

By applying simple feedback control, the biped can be made to walk in a desired direction.

Proportional control of the angle of the current facing direction and the desired direction as given

by a target point is used to generate an appropriate turning rate.

The pose control applied each step including balance control is the same form as Equation 5.1.a:

( B + k_turn[!]P_turn) + k₁[!]P₁+ k₂[!]P₂

In the case of separate left and right turning control perturbations,

kturn> 0 applies to the right turning perturbation and [!]Pturn= [!]Pturnright kturn< 0 applies to the left turning perturbation and [!]Pturn= [!]Pturnleft

and k_turnis computed according to the proportional control law:

k_turn= k_qq

where qis the angle between the biped's current facing direction and a vector to the target point,

as illustrated in Figure 5.10.

k_qis a gain constant which determines how tightly the biped turns

for a given error in direction.

avoid large, unstable turn rates.

k_turnis bounded to a predetermined maximum value in order to