11

principles along with various forms of additional control can be applied to running for a fully-

dynamic, complex human model.

The ground model for the runner uses a 1 DOF constraint

which allows motion only in the body's pitch DOF.

Legged locomotion has also received significant attention

in

the

robotics

and

biomechanics

literature.

Research in the biomechanics literature is directed primarily toward gait analysis.

Of

particular interest is the efficiency of natural motion in humans and animals [McM84] [Ale84] and

the identification of various determinants of gaitand their role in normal and pathological gaits

[TT76] [SCD80] [MM80] [IRT81] [SSH82] [PB89].

To

this

end,

a

number

of

dynamic

locomotion models have been proposed [VJ69] [MM80] [McM84] [Tow85] [PB89].

approaches generally make assumptions which limit their usefulness for animation.

These

Typical

assumptions include a simplified biped model and/or motion only in a plane [VJ69] [TT76]

[Tow85] [McM84] [PB89].

[TT76] [McM84] [PB89].

Some only consider the open-loop motion over one or two steps

The

robotics

literature

has

more

in

common

with

the

goals

of

physically-based

computer

animation than biomechanics does.

It has as an objective the synthesis of legged locomotion,

rather than analysis. While some works present only simulation results and others implement real

robots, all systems, of necessity, incorporate some form of forward dynamics.

Many approaches

propose

various

reduced-order

models

for

the

equations

of

motion

and

rely

on

reference

[MS84]

trajectories, typically based either on the motion of

an

inverted

pendulum

[FM84]

[KKI90] [KT91] or on measured human data [VS72] [HF77].

As with biomechanics, the

complexity of the locomotion problem is often reduced through the use of simplified biped

models.

Constraining motion to the sagittal plane, is perhaps the most common simplification

[HF77] [FM87] [KKI90] [KT91] [CHP92].

A number of approaches deal only with statically

stable walking motions in which the biped is balanced at all points in the walk cycle [HF77]

[ZS90] [SZ92]. While such motions may be quite useful for a robot due to their inherent stability,