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How can I find the instantaneous directional vector of 3D dubins vehicle?

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http://www.et.byu.edu/~beard/papers/preprints/BeardMcLain__.pdf

 

I've figured out how to find out the instantaneous position of the vehicle.

But Will the direction be the delta of the current position and next position?

I am not sure, is there a reliable way to do it?

Of course, I already have the start direction and some ending directions

in the spirals and straight lines.

For example, when the vehicle starts at radian 4.7, with a left turn

can I assume at time 0, it is at 4.7 and at time 1, it will be at 4.6.....(left-handed system)

The elevation isn't taken into account anyways....

Thanks

Jack

Edited by lucky6969b

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As a first approximation, take the positions at times t+0.001 and t, subtract them and multiply the resulting vector by 1000. This is an inelegant approximation, but it's really easy to implement and to get right. If you end up using a fancier method, you can still use the inelegant method to verify that your fancier code is correct.

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