Optimal Torque Assignment for Redundant Wheels

Paper number

IAC-05-C1.3.08

Author

Dr. Takehiro Nishiyama, Mitsubishi Electric Corporation, Japan

Coauthor

Dr. Katsuhiko Yamada, Mitsubishi Electric Corporation, Japan

Year

2005

Abstract

Reaction wheels are generally used for attitude control of spacecraft. When the number of wheels is four or more, the assignment of the attitude control torques to the wheels is not unique because of the redundancy. Usually, the wheel torque assignment is given by multiplying a constant matrix by the attitude control torques, but more efficient assignment using the redundancy is desired for more effective control. The wheel torque assignment problem is formulated as a simple minimax problem in which the maximum of wheel torques is minimized, but it is not practical to solve the problem directly on spacecraft onboard computers because of the computational cost.
In this paper, the minimax problem is transformed to a linear programming problem (LP), and the dual problem of the LP is considered. Then using some geometrical characteristics of the problem, an effective and robust algorithm is derived. The proposed algorithm can be applied to any configuration of wheels. Only simple algebraic calculations are needed to give torque assignment, and the optimality is guaranteed theoretically.
This paper shows the detailed derivation of the algorithm using the LP theory. It is also shown that the wheel torque assignment for the given attitude control torques is unique and the torque assignment is continuous with respect to the change in the attitude control torques. Numerical studies are also carried out to verify these analytical results and the performance of the algorithm. As a result, the magnitude of the maximum attitude control torque is increased on average by more than 20 percent in comparison with a general assignment method using a constant matrix.

Abstract document

IAC-05-C1.3.08.pdf

Manuscript document

IAC-05-C1.3.08.pdf (🔒 authorized access only).

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