u""" calc position

u""" calc yaw

u""" Calc first derivative if t is outside of the input x, return None

u""" search data segment index

u""" calc curvature

u""" Calc position if t is outside of the input x, return None

u""" Calc second derivative

u""" calc matrix A for spline coefficient c

u""" calc matrix B for spline coefficient c

return the t state based on QuinticPolynomial theory

check path above max speed, max a, does collision or not