Synthesis of Adaptive Controllers for Spacecraft Rendezvous Maneuvers using Nonlinear Models of Relative Motion

This work is concerned with the design of adaptive learning controllers for rendezvous maneuvers of two spacecraft. Unlike earlier efforts using linearized dynamics, the current work considers the nonlinear equations of relative motion. The main idea behind the Lyapunov-based controller design is to allow a flexibility in the time-varying gains to adapt in proportion to the relative distance of the two spacecraft. By augmenting an adaptive controller, one opts to improve controller performance. The adaptation schemes of the controller gains are derived via Lyapunov redesign methods. In order to gain some insights on the choice of the optimal gains, a scheme that penalizes a combination of the relative position error and of the relative velocity error is considered. Extensive numerical studies are provided to further support the theoretical predictions on the choice of controller gains.