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.

翻译：本文介绍基于学习的自主指导,并附有强力和稳定性保障(LAG-ROS),通过使用收缩理论设计不同的Lyapunov功能,为基于机械的学习的非线性运动规划者提供正式的稳健性和稳定性保障。 LAG-ROS利用神经网络构建一个独立于目标轨迹的强力跟踪控制器模型,为此,我们表明,即使存在受约束的外部扰动,目标与受控轨迹之间的Eucliidean距离在学习错误中也呈指数性线性界限。 我们还提出了一个螺旋优化方法,最大限度地减少跟踪错误的稳态界限,以构建神经网络培训的强力控制法。 在数字模拟中,可以证明拟议方法确实具有由收缩理论产生的强力和非线性稳定性的超强性特性,同时保留现有基于学习的运动规划者的计算效率。