Relationships Between Maneuver Time and Energy for Reaction Wheel Attitude Control

Abstract

The dichotomy between minimum time and minimum effort is well known. Minimum-time solutions are synonymous with large effort, whereas minimum effort solutions imply large time horizons. Shortest-time attitude maneuvers are minimum-time slews for agile reorientation of space vehicles. Intuition and experience would suggest that such maneuvers are expensive in terms of effort. This paper will show that this is not the case: Agile maneuvers exist within the energy budget associated with conventional attitude control systems. Moreover, even for conventional slew strategies (such as eigenaxis), energy requirements can be reduced. The energy savings are realized via a reallocation of the control effort by exploiting null motions within the control space, over the maneuver trajectory. A cost functional for minimum-energy slews is developed that is in line with true energy cost associated with reaction wheel-based attitude control systems. This energy metric is incorporated into a family of constrained nonlinear optimal control formulations whose solutions present a relationship between transfer time and energy. Both agile (off-eigenaxis) slews and conventional (eigenaxis) slews are studied. A trade space between transfer time and energy is identified, which can be exploited for mission operations, planning, and design.