# Objective Function

The objective function is stated as a function of a zeroth order term,
first order term (with an epsilon_1 coefficient), and second order
term (with an epsilon_2 coefficient). Can you explain to me the
purpose of each term? I know that the first term gives the maximum
cooperation between muscles (if epsilon 1 and 2 are neglected), and
that the second term (epsilon 1) determines which muscles have the
largest input into the system (when epsilon 1 is made large), but what
does the third term (the second order, epsilon 2 coefficient term) do?
What role does it play in the optimality criterion?

Sarah

Hi Sarah,

I think you can find the answers you are looking for in the tutorial
on inverse dynamic analysis: http://www.anybodytech.com/76.0.html.
Please notice that the system uses either epsilon_1 or epsilon_2, and
that the latter requires that you use the quadratic optimizer.

I should also frankly admit that the current version of our system
has problems with the robustness of the quadratic optimizer. This is
something we are aware of and are looking at. It is actually a bit
strange because it has previously been quite stable. But my guess is
that you will have problems using the QP solver for your shoulder
models before we get a more robust version released. We apologize for
this.

On a longer term, we are planning solvers that can solve recruitment
objective functions of user-defined powers. As you may be aware, the
choice of objective function is a bit of a religious issue in inverse
dynamics, and we really would perfer no to make the choice for our
users.

Please do ask again if you have questions after having studied the
tutorial.

Best regards,
John,
AnyBody Support

— In anyscript@yahoogroups.com, “Sarah R. Sullivan” <sarsulli@e…>
wrote:
> The objective function is stated as a function of a zeroth order
term,
> first order term (with an epsilon_1 coefficient), and second order
> term (with an epsilon_2 coefficient). Can you explain to me the
> purpose of each term? I know that the first term gives the maximum
> cooperation between muscles (if epsilon 1 and 2 are neglected), and
> that the second term (epsilon 1) determines which muscles have the
> largest input into the system (when epsilon 1 is made large), but
what
> does the third term (the second order, epsilon 2 coefficient term)
do?
> What role does it play in the optimality criterion?
>