This paper presents a new solution to the motion planning problem for nonlinear underactuated vehicles. The approach solves the problem by generating a polynomial curve connecting the desired initial and final positions for the vehicle and then using the curve to estimate the vehicle's complete configuration along the trajectory. The solution to the basic motion planning problem can be coupled with randomized path planning algorithms to solve the obstacle avoidance and multiple vehicle versions of the problem.
Numerical simulations illustrate the algorithm's performance on an underactuated planar vehicle.