Attitude Trajectory Optimization and Momentum Conservation with Control Moment Gyroscopes

Abstract

In this work, we formulate a specialized trajectory optimization problem and adapt a computationally tractable numerical solver for rest-to-rest attitude transfers with CMG-driven spacecraft. First, we adapt a momentum conserving dynamical model which avoids many of the numerical challenges (singularities) introduced by common dynamical approximations. To formulate and solve our trajectory optimization problem, we design a locally stabilizing Linear Quadratic (LQ) regulator on the system's configuration manifold, then lift it into the ambient state space to produce suitable terminal and running LQ cost functionals. Examining the performance benefits of solutions to this optimization problem, we find significant improvements in maneuver time, terminal state accuracy, and total control effort. Finally, this analysis highlights an acute shortcoming in cost functions which use the control input (rather than accurately modelled power usage) to penalize maneuver energy cost.