A method and apparatus are disclosed for determining a trajectory for a vehicle, wherein the method includes: identifying a starting position (p0) for the vehicle; identifying a desired terminal position (P) for the vehicle; linearly approximating dynamics of the vehicle; and using the starting position (p0), the desired terminal position (P), and the linear approximation, determining the trajectory for the vehicle. The linear approximation can be constrained by a requirement (e.g., specification) that a magnitude of a velocity of the vehicle is greater than or equal to a threshold value for the velocity. The vehicle may have a curvature limit.