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# Optimal trajectory generation

## Optimal trajectory generation

(OP)
Hello all,
I have a two dimensional trajectory y=f(x), defined by a dense vector of 10.000 or so points. Given the maximum acceleration and speed of y(t) and x(t), I need to calculate the optimal x(t), to minimize the overall time. How can do it? Is there some C or C++ routine around in the network?
Thank you.

### RE: Optimal trajectory generation

I would make two cubic splines. One for y(u) and one for x(u) where u is the index for both the x and y spline. you know the desired velocity you want it v(t)=sqrt(y'(u)^2+x'(u))^2) so solve for u. Since you probably just have a set of points for x and y you will need to be able find the derivative at each point u to compute the next point. Hopefully your spine function has this capability.

Better motion controllers have functions to make this easier. Writing your own from scratch will take some time.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

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