Abstract
In this paper, we explore the use of maximum hands-off control for attitude control of a spacecraft actuated by reaction wheels. The maximum hands-off, or L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -optimal, controller aims to find the sparsest control signal among all admissible control signals. L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -optimal problems are generally hard to solve as L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -cost functions are discontinuous and non-convex. Previous research have investigated methods to approximate the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -norm in the cost function, for instance by using an L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm. We propose an approach to the maximum hands-off control problem for spacecraft attitude control involving an L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> cost function relaxed through complementarity constraints. The controller is applied to the spacecraft attitude control problem, and the performance of the maximum hands-off controller is compared to that of the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -optimal controller. Simulations of a 6U CubeSat were conducted using CasADi as the primary optimization tool, and the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> - and L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -optimal control problems were discretized using direct multiple-shooting and solved using the IPOPT solver. In addition to these results, we propose a new control scheme, called moving maximum hands-off control, which lets the user specify in which time interval the control should occur, and then aims to find the sparsest control among all admissible controls based on this information. The moving maximum hands-off controller is demonstrated to be as sparse as the maximum hands-off controller for some spacecraft maneuvers.
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