Posture Prediction and Optimization - Human Motion Simulation: Predictive Dynamics - page 63

Finally, the objective function for the unconstrained optimization problem

becomes:

f ð q ; q ; q Þ 5 w 1 f discomfort 1 w 2 f inconsistnacy 1 w 3 f nonsmoothness

0 X

nTIME

(3.29)

end - eff path 2

1000 : jj x ð q ð t j ÞÞ 2 x ð t j Þjj

1

j 5 1

Mi (2004) describes the objective terms in Equations (3.25) and (3.28) in
greater detail.
The limits for the generalized coordinates q i are determined based on rough
estimates and observation. However, these joint limits are input parameters to the
optimization and can correspond to any anthropometric specifications. The values
for the weights in Equation (3.29) are determined based on trial-and-error
experiments.

3.13 Motion prediction of a 15-DOF model
Applying the current motion prediction algorithm to the 15-DOF model results in
the motion shown in Figures 3.11 and 3.12 . The motion was generated using an
initial posture with zero rotation and an approximate target point of (41, 55,

32). Since the minimum jerk model is well accepted for point-to-point motion
(Flash and Hogan, 1985), the end-effector follows a minimum jerk Cartesian path
for this example. The optimization used 43 discretized Cartesian points along the
path to constrain the end-effector. The five screenshots show the instantaneous
postures at t

2

0.0, 0.25, 0.5, 0.75, and 1.0 seconds. The calculation took about
17 seconds on a 1.8-GHz Pentium4 CPU with 512-MB RAM.
Figure 3.13 provides the some of the joint trajectories from the motion predic-
tion. By inspecting the curve, it is apparent that the joint movements are smooth
and continuous; they are devoid of abrupt changes in velocity or acceleration.
However, note that the initial and final velocities are not necessarily zero. For an
isolated point-to-point movement, restricting the initial and final velocities is intu-
itively desirable.
Furthermore, this motion is slightly unnatural, with excessive torso movement.
As discussed earlier, it was necessary to combine the distance constraint with the

5

FIGURE 3.11
Motion prediction on 15-DOF model at five time instants.