Biomedical Engineering Reference
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are unknown and must be determined simultaneously. It will be seen that an
optimization-based formulation is ideally suited to solve such problems. Recent
results have shown that this method is applicable to gait prediction, lifting move-
ments, pushing and pulling movements, climbing, and many other tasks. Indeed,
an entire task made up of multiple sub-tasks can be created whereby a true
physics-based predictive human simulator is created.
The objective of this topic is to clearly demonstrate the basic formulation
needed to develop a PD task.
1.2 How does predictive dynamics work?
Predictive dynamics is an optimization-based method for predicting human
motion, while taking into consideration the biomechanics, physics of the motion,
and human behavior.
Consider a general optimization problem, for which there are three main
ingredients ( Arora, 2012 ):
1. A set of design variables, which in our case are the joint profiles (i.e., joint
angles as functions of time) and the torque profiles at each joint
2. Multiple cost functions to be optimized, which are human performance
measures that represent functions that are important to accomplishing the
motion (e.g., energy, speed, joint torque, etc.), and
3. Constraints on the motion (e.g., collision avoidance, joint ranges of motion, etc.).
This general optimization problem is readily solved using existing optimiza-
tion algorithms and codes. The field of optimization is mature and many such
codes exist that have been verified and validated, and tested with many different
complex problems.
Solving the above optimization problem predicts human motion as illustrated
in Figure 1.1 . It has been shown that for static postures (i.e., predicting final
human postures to reach an object), this method is very successful; it produces
human-like results ( Abdel-Malek et al., 2001a
d; Abdel-Malek et al., 2004a
c;
Abdel-Malek et al., 2006 ).
Now we add the issue of dynamics. We are interested in seeing how human
motion is predicted for scenarios that involve dynamic influences including but
not limited to external loads, obstacles, and running. The general concept is the
addition of the laws of physics, i.e., equations of motion, as constraints. Instead
of calculating specific static postures, we now calculate time-varying angles for
each joint in the body, which are also called motion profiles. Instead of a simple
displacement cost function, we implement an energy and effort driving perfor-
mance measures, which drive the motion to minimize these two measures. This is
indeed the essence of our theoretical framework ... we believe that humans act
and move because humans want to minimize or maximize certain objectives. This
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