Optimal waypoint scheduling of an imaging satellite

A new result in optimal control is applied to the scheduling of high-resolution imaging of successive ground targets from an orbiting satellite. In the envisioned low-cost satellite application, attitude control is accomplished solely through reaction wheels; there is no thrusting capability. Reaction wheels are particularly suited to pointing applications in which the spacecraft rotates slowly or not at all. To quickly change the pointing direction to a new target, either the reaction wheels must be powerful or the satellite moment of inertia must be small. Design tradeoffs dictate that slew time between targets is not insignificant, reducing the economic value per orbit of the mission. Solving for the optimal solution is complicated by the fact that attitude control dynamics are nonlinear (unit quaternions for attitude and Euler equations for attitude rate), there is limited torque magnitude available to the reaction wheels, and there is the need to periodically dump momentum. The objective of this study is to determine time optimal control policies to slew between scheduled waypoint views. The multiple-interval generalization of Pontryagin's Maximum Principle, established in a soon-to-be-complete PhD dissertation, is proposed to find the optimal attitude policy. The generalization addresses the total scheduling problem over a given orbit, not just time minimization from waypoint to waypoint. An example based on design characteristics of a small imaging satellite is set up, and solution methods are explored.