# Algorithm Optimally Allocates Actuation of a Spacecraft

## TBMG-2038

## 07/01/2007

- Content
A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix⋅vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as subalgorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.

- Citation
- "Algorithm Optimally Allocates Actuation of a Spacecraft," Mobility Engineering, July 1, 2007.