Bernstein's approximation of non holonomic motion equation

Non-holonomic equation = ydot(t) = xdot(t) tan(theta(t))

The approximation involves the following steps

• Approximate x(t) and tan(theta(t)) with beizer curves

• Differentiate the Bernstein's approximation

• Find the weights of the bernstein polynomial for constraints

• Get the y(t) and x(t)

The code doesn't require mathematica and order can be varied

Bernstein's approximation is uniform even over higher derivatives

![alt text][logo] [logo]: www.github.com/tvsrr/bernstein_approximation_non_holonomic_trajectory/Bernstein_path.jpg