This paper presents Learning-based Autonomous Guidance with Robustness, Optimality, and Safety guarantees (LAG-ROS), a real-time robust motion planning algorithm for safety-critical nonlinear systems perturbed by bounded disturbances. The LAG-ROS method consists of three phases: 1) Control Lyapunov Function (CLF) construction via contraction theory; 2) imitation learning of the CLF-based robust feedback motion planner; and 3) its real-time and decentralized implementation with a learning-based model predictive safety filter. For the CLF, we exploit a neural-network-based method of Neural Contraction Metrics (NCMs), which provides a differential Lyapunov function to minimize an upper bound of the steady-state Euclidean distance between perturbed and unperturbed system trajectories. The NCM ensures the perturbed state to stay in bounded error tubes around given desired trajectories, where we sample training data for imitation learning of the NCM-CLF-based robust centralized motion planner. Using local observations in training also enables its decentralized implementation. Simulation results for perturbed nonlinear systems show that the LAG-ROS achieves higher control performance and task success rate with faster execution speed for real-time computation, when compared with the existing real-time robust MPC and learning-based feedforward motion planners.

中文翻译：

---

模仿学习的鲁棒和安全的实时运动计划：一种收缩理论方法

本文提出了一种具有鲁棒性，最优性和安全性保证的基于学习的自主制导（LAG-ROS），这是一种针对有界扰动的安全关键非线性系统的实时鲁棒运动规划算法。LAG-ROS方法包括三个阶段：1）通过收缩理论控制李雅普诺夫函数（CLF）的构建；2）基于CLF的鲁棒反馈运动计划器的模仿学习；3）通过基于学习的模型预测安全过滤器进行实时和分散实施。对于CLF，我们利用了基于神经网络的神经收缩度量（NCM）方法，该方法提供了差分Lyapunov函数，以最小化摄动和非摄动系统轨迹之间的稳态欧几里得距离的上限。NCM确保扰动状态保持在给定所需轨迹周围的有界误差管中，我们在其中采样训练数据以模仿基于NCM-CLF的鲁棒集中式运动计划器的学习。在培训中使用本地观察结果还可以使其分散实施。非线性系统的仿真结果表明，与现有的实时鲁棒MPC和基于学习的前馈运动规划器相比，LAG-ROS具有更高的控制性能和任务成功率，并具有更快的实时计算执行速度。