Inertia-independent generalized dynamic inversion feedback control of spacecraft attitude maneuvers

Abstract

The generalized dynamic inversion control methodology is applied to the spacecraft attitude trajectory tracking problem. It is shown that the structure of the skew symmetric cross product matrix alleviates the need to include the inertia matrix in the control law. Accordingly, the proposed control law depends solely on attitude and angular velocity measurements, and it neither requires knowledge of the spacecraft's inertia parameters nor it works towards estimating these parameters. A linear time-varying attitude deviation dynamics in the multiplicative error quaternion is inverted for the control variables using the generalized inversion-based Greville formula. The resulting control law is composed of auxiliary and particular parts acting on two orthogonally complement subspaces of the three dimensional Euclidean space. The particular part drives the attitude variables to their desired trajectories. The auxiliary part is affine in a free null-control vector, and is designed by utilizing a semidefinite control Lyapunov function that exploits the geometric structure of the control law to provide closed loop stability. The generalized inversion singularity avoidance is made by augmenting the generalized inverse with an asymptotically stable fast mode that is driven by angular velocity error's norm from reference angular velocity. Asymptotic tracking is achieved for detumbling maneuvers as the stable augmented mode subdues singularity. If the steady state desired quaternion trajectories are time varying, then asymptotic tracking is lost in favor of close ultimately bounded tracking because the stable augmented mode continues to be excited during steady state phase of response. A rest-to-rest slew and a trajectory tracking maneuver examples are provided to illustrate the methodology.