  This paper presents Learning-based Autonomous Guidance with RObustness and
Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear
motion planners with formal robustness and stability guarantees, by designing a
differential Lyapunov function using contraction theory. LAG-ROS utilizes a
neural network to model a robust tracking controller independently of a target
trajectory, for which we show that the Euclidean distance between the target
and controlled trajectories is exponentially bounded linearly in the learning
error, even under the existence of bounded external disturbances. We also
present a convex optimization approach that minimizes the steady-state bound of
the tracking error to construct the robust control law for neural network
training. In numerical simulations, it is demonstrated that the proposed method
indeed possesses superior properties of robustness and nonlinear stability
resulting from contraction theory, whilst retaining the computational
efficiency of existing learning-based motion planners.
