Koopman-Operator-Based Safe Learning Control for Spacecraft Attitude Reorientation with Angular Velocity Constraints

This article presents the design of a safe learning attitude controller, based on the Koopman operator (KO), for rest-to-rest spacecraft attitude reorientation under angular velocity constraints. Specifically, a higher-dimensional linear error attitude model is established based on the KO theory and then discretized. An explicit safe learning control strategy with safety-stabilization guarantee is then developed based on the transformed KO model. By performing a loop transformation and convexifying the safety-stabilization conditions, the safe learning controller design is further transformed into a constrained optimization problem, which is independent of the attitude states and thus can be solved offline. Finally, the trained higher-dimensional safe learning controller is mapped to the 3-D attitude controller of the original nonlinear system via the least-squares method for online implementation. In addition, the inner-approximation of the region of attraction (ROA) is provided. Comparison simulations are carried out to validate the effectiveness of the presented strategy.