Modeling and Animating Human Figures - Computer Animation: Algorithms and Techniques - page 307

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FIGURE 9.30
Telescoping joint with kinematically fit leg complex.

Incorporating more physics into the model, the kinematic control information for the figure can be
used to guide the motion (as opposed to constraining it). A simple inverse dynamics computation is then
used to try to match the behavior of the systemwith the kinematic control values. Desired joint angles are
computed based on high-level animator-supplied parameters such as speed and the number of steps per
unit distance. Joint torques are computed based on proportional-derivative servos (Eq. 9.1 ) . The differ-
ence between the desired angle, denoted by the underbar, and the current angle at each joint is used to
compute the torque to be applied at the next time step. The angular velocities are treated similarly. These
torque values are smoothed to prevent abrupt changes in the computed motion. However, choosing good
values for the gains ( k s , k v ) can be difficult and usually requires a trial-and-error approach.

y i y i

t ¼ k s y i y i ð Þ k v (9.1)

9.3.4 Forward dynamic control
In some cases, forward dynamic control instead of kinematic control can be effectively used. Kinemat-
ics still plays a role. Certain kinematic states, such as maximum forward extension of a leg, trigger
activation of forces and torques. These forces and torques move the legs to a new kinematic state, such
as maximum backward extension of a leg, which triggers a different sequence of forces and torques
[ 47 ]. The difficulty with this approach is in designing the forces and torques necessary to produce a
reasonable walk cycle (or other movement, for that matter). In some cases it may be possible to use
empirical data found in the biomechanics literature as the appropriate force and torque sequence.

9.3.5 Summary
Implementations of algorithms for procedural animation of walking are widely available in commercial
graphics packages. However, none of these could be considered to completely solve the locomotion
problem, and many issues remain for ongoing or future research. Walking over uneven terrain and
walking around arbitrarily complex obstacles are difficult problems to solve in the most general case.
The coordinated movement required for climbing is especially difficult. A recurring theme of this chap-
ter is that developing general, robust computational models of human motion is difficult, to say
the least.