  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.
