I have a random trajectory (x and y locations) with many sharp turns. I want to remove all such sharp turns and want to make the trajectory smooth. Can anyone suggest a way for that?
Filter it, so that if a turn is too sharp, it is ignored.
If you want better advice than that you will need to tell us more about the way you are steering your trajectory.
I choose a random point and a random unit vector and updates the x and y based on the direction of that unit vector. (The angle of the unit vector is limited to a range). But when it reaches the boundaries it produces sharp turns to make sure it does not cross it. How can I avoid such sharp turns without crossing the boundaries?
To smooth it out the effective boundary needs to be smoothed out: it can't remain sharp, but a procedure should be defined, that, when the base point is within some distance to the boundary, then the update varies appropriately. But what does this have to do with neural networks?
Cubic spline interpolation will produce a C2 trajectory, which you can interprete as a realization of a function valued random process. Obviously, doing this assumes implicitly that the input data are error free. If the input data is to be considered noisy, it should be filtered as suggested in previous comments
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