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It's still that. You just take the position only, don't worry about the orientation.

How do we find xi from the (x(t), y(t)) given?

What is xi?

I thought we would calculate alphadot = (psuedo invese) * (xi)

Yes but what do you think is xi?

I would imagine it is some sort of velocity. Would we take the derivative of the (x(t),y(t))?

Yes

I have a 3x1 vector for my psuedo inverse. How do I multiply that by xi = (.5sin(t), .49cos(t) )?

You pseudoinverse should not be 3x1. What formula are you using?

I have to go