Design and Optimization of a Nonlinear Lyapunov based Attitude Control Law for Rigid Spacecraft

In this paper, a nonlinear Lyapunov-based attitude control law is proposed to perform onorbit slewing maneuvers and stabilization for spacecraft. A new class of Lyapunov function candidate, which includes a quadratic term and a nonlinear kinematic term based on direction cosine matrix has been proposed. The structure of the Lyapunov function candidate allows for the design of a control algorithm, which includes a linear combination of three unit vectors multiplied by three scalar coefficient functions. The coefficient functions are explicitly present in the Lyapunov function description. The coefficient functions can be easily replaced by other families of Lebesgue integrable functions. In this paper a specific coefficient function based on a geometric feature is represented. The functions involve the use of three inertial spheroids, which have their 2nd focuses on the spacecraft center of gravity. The values of the coefficient functions are evaluated based on the distance of some specific points on these spheroids. Moreover, a nonlinear global optimization of the controller is done, which aims to reduce the settling time and total effort of the attitude maneuver. In particular, Particle Swarm Optimization method is used in order to minimize the objective function. The nonlinear optimization will evaluate the gains and also the optimum shape of the spheroids to be used in the Lyapunov function. The results of the numerical simulation for this control law have been compared with two conventional PD attitude controllers, and has shown a superior performance in terms of settling time and total effort for slew maneuvers. Furthermore, the sensitivity of the controller to uncertainties in inertia matrix and control input is evaluated, and compared to other controllers.