I am stuck at computing the translation and rotation of a robot moving onto an ellipse given by:
$$ p(t) =(m) + \cos(t)∗a + \sin(t)*b $$
where m = center of ellipse and the two axes a (horizontal) and b (vertical).
At the moment I am using derivation $p'(t)$ for calculating the translation, like
$$ p'(t)_x = -\sin(t)*a \\ p'(t)_y = \cos(t)*b $$
$$ p'(t) = \sqrt{p'(t)_x^2 + p'(t)_y^2} $$
and rotation velocity, with
$$ p''(t)_x = -\cos(t)*a \\ p''(t)_y = -\sin(t)*b $$
$$ p''(t) = \frac{p'(t)_x p''(t)_y - p''(t)_x p'(t)_y}{ (p'(t)_x)^2 + (p'(t)_y)^2} $$
(see formula)
However, the robot is just moving in strange curls instead of an ellipse. If anyone needs the full code just say so.
$$ \omega = \dot{\phi} = \frac{\dot{d_x}\ddot{d_y} - \ddot{d_x}\dot{d_y}}{\dot{d_x}^2+\dot{d_y}^2} $$