Posture Prediction and Optimization - Human Motion Simulation: Predictive Dynamics - page 51

relative to a position that is deemed most comfortable, and the posture with the
minimum discomfort gravitates towards the neutral position, effort is measured
relative to a starting position, regardless of the starting position's comfort level.
Consequently, effort depends greatly on the initial configuration of the limbs prior
to motion and is most significant when a series of target points are selected with
the posture changing from point to point. For an initial set of joint variables
q initial
i

, a simple measure of effort is expressed as follows:

X

n
i 5 1 γ i ð q i 2

2

q initial
i

f Effort ð q Þ 5 Þ (3.9)

where γ i is a weight assigned to each joint and is comparable to w i .

3.7.3 Delta potential energy
Potential energy is a well-understood basic concept and has been used success-
fully as an objective with robotic movements. However, implementing an energy
function as a human performance measure requires special considerations. This
proposed performance measure stems from difficulties with the above-mentioned
joint displacement function and from deficiencies in an existing performance
measure that depends on the potential energy of an arm (Abdel-Malek et al.,
2001a d; Mi et al., 2002b; Mi, 2004 ).
With joint displacement, the weights are set based on intuition and experimen-
tation, and although the postures obtained by minimizing joint displacement are
acceptable, the question arises as to whether or not there are more practical, less
ad hoc approaches to setting the weights. The idea of potential energy provides
one such alternative. With potential energy, the weights are essentially based on
the mass of different segments of the body, and in a sense, an individual objective
function is developed for each segment.
Whereas the previous potential-energy function incorporates only the potential
energy of an arm, we consider the complete upper body. We represent the primary
segments of the upper body with six lumped masses: three for the lower, middle,
and upper torso, respectively; one for the upper arm; one for the forearm; and one
for the hand. We then determine the potential energy for each mass. The actual
masses for the segments are determined based on data from Chaffin and Anderson
(1991). The heights of the masses, rather than the joint displacements, provide the
components of the human performance measure. Mathematically, the weight (force
of gravity) of a segment of the upper body provides a multiplier for movement of
the segment in the vertical direction. The height of each segment is a function of
the joint angles, so, in a sense, the weights of the lumped masses replace the scalar
multipliers w i , which are used in the joint displacement function.
If potential energy is used directly, as is the case with the previous potential-
energy function, there is always a tendency for the avatar to simply bend over,
thus reducing potential energy. All of the lumped masses gravitate towards the