Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation

This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain dynamics while still providing guarantees of transient tracking performance throughout the learning phase. Within the proposed approach, a disturbance estimation law is adopted to estimate the pointwise value of the uncertainty, with pre-computable estimation error bounds (EEBs). The learned dynamics, the estimated disturbances, and the EEBs are then incorporated in a robust Riemann energy condition to compute the control law that guarantees exponential convergence of actual trajectories to desired ones throughout the learning phase, even when the learned model is poor. On the other hand, with improved accuracy, the learned model can help improve the robustness of the tracking controller, e.g., against input delays, and can be incorporated to plan better trajectories with improved performance, e.g., lower energy consumption and shorter travel time.The proposed framework is validated on a planar quadrotor example.