Parameter space nonlinear control of rigid spacecraft attitude maneuver

A novel procedure considering the geometric characteristic of the Euler parameters is presented in this paper for designing a stable nonlinear feedback control law of spacecraft general attitude maneuver. Because the parameters set has to satisfy the quadratic constraint equation, spacecraft attitude in terms of four Euler parameters is confined to the surface of a four-dimensional unit sphere. Furthermore, the attitude trajectory of a maneuvering spacecraft corresponds to a surface path on the sphere. The concept is utilized by transforming the set of differential equations governing the attitude dynamics into Euler-parameter space through the method of input-output feedback linearization. Also, feedback control law is formulated using error attitude and error attitude rate vectors as feedback signals. The formal is obtained by subtracting the present attitude from the final attitude and the latter can be derived through attitude kinematic equation. Geometrically, the error attitude vector is a projection from the geodesic, the shortest path on the surface of the sphere connecting the two attitudes. As such, the proposed feedback control law tends to rotate the spacecraft from the initial to the final attitudes along the minimum path attitude trajectory. Lyapunov stability analysis is also applied in the procedure to the designed error Lyapunov function to determine the feedback control gains and to achieve overall system stability. Two simulation cases with three attitude control strategies are included to demonstrate the design concept. Simulation results that the proposed procedure can indeed reorient the spacecraft about the principal axis in one rotation with exact principal angle. Strong stability and convergence characteristics of the designed control law was also demonstrated with constrained control torque.