Biomedical Engineering Reference
In-Depth Information
parameters from Chapter 2 and cost functions as human performance measures,
this presents a very robust method for creating and inducing different behavior
while calculating naturalistic motions.
The optimization formulation contains three main ingredients:
1. A cost function: A cost function is a human performance measure to be
minimized or maximized. In our case, there are many cost functions, forming
a multi-objective optimization problem.
2. Design variables: The variables are individual DOF joint displacements that
will be calculated from the algorithm. In our case, these are the joint variables
that define the position and orientation of each segmental link.
3. Constraints: Constraints are mathematical expressions that bound the
problem. A constraint that makes the distance between the end-effector
and the target point be within a specified tolerance is imposed. Joint
ranges of motion are necessary constraints, but additional constraints are
added as appropriate.
Many cost functions exist, and others are being developed by many research-
ers and in many fields. We will demonstrate the use of a number of such func-
tions for posture prediction, which will
then be used in the formulation for
predictive dynamics in a later chapter.
This chapter focuses on introducing a general optimization-based formulation
for predicting postures. These postures compare well with those assumed by real
humans.
The optimum posture (set of q-values) is determined by solving the following
optimization problem:
R DOF
Minimize: Discomfort
Find:
q A
(3.1)
;
Effort
;
etc
:
Subject to: x ð q Þ
targetpoint
end - effector
2
2 x
# ε
(3.2)
q i #
q i
and
q i #
;
i
1
;
2
; ...;
DOF
5
target point is the point in
space that will be touched. The feasible space for a problem such as the one in
Equation (3.2) is defined as the set of all points x for which all of the constraints
are satisfied.
where q is the vector of generalized joint variables and x
3.5.1 Design variables
As suggested earlier, the design variables are the generalized coordinates q i ,orin
vector form, q 5 ½ q 1
T . Since all joints are rotational, q i have units of
radians. Many optimization algorithms require an initial guess, which entails
determining initial values for the design variables. The initial guess can be some-
what arbitrary, although it is helpful to use a feasible point. In this study, an
:::
q DOF
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