[Help-gsl] How to Fit an intracable formula

[Alex Brussee]

Hi All,

I have a problem which i cannot solve. I used the GSL library (BFGS) to 
generate a Minimum Jerk Optimal solution in the form of a fifth order bezier 
curve going from a starting point to a via point to an end point. This 
generates a Data Set (x,y positions) on which i would like to fit a 
differential steering path.

The differential steering path is generated using a formula that describes 
left and right wheel speeds seperately. This causes the Path generated to be 
intracable. Thus so are the partial derivatives of the distance (x,y) 
travelled.

BFGS can estimate the partial derivatives, but in the gsl-library it seems 
that the partial derivatives must be supplied by the user (mf.df = &func). 
This works great in the case of the tracable polynomials, but how can i get 
the BFGS optimizer to work without these derivatives. (Or can someone give 
me the integration of my formula, beceause mathematica cannot)

The speed functions attached to the differential steering:
x(t)=Amp1*((1/(tau1-tau2))*exp(t/tau1)-(1/(tau1-tau2))*exp(t/tau2))
y(t)=Amp2*((1/(tau3-tau4))*exp(t/tau3)-(1/(tau3-tau4))*exp(t/tau4))
(just to make clear that the resulting formula is indeed intracable, see 
also http://rossum.sourceforge.net/papers/DiffSteer/DiffSteer.html )

My question:
1. Is there another (better) way in gsl to fit the generated path using 
Amp1,tau1,tau2,Amp2,tau3,tau4 to the data set ?
2. Is there a way to obtain the partial derivatives by anther procedure, or 
did i overlook something ?

thnx for helping me out

Alex Brussee
:)

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