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.
This work was done by Behçet Açıkmeşe and Shui Motaghedi of Caltech for NASA's Jet Propulsion Laboratory. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Mechanics/Machinery category.
The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-42301.
This Brief includes a Technical Support Package (TSP).

Algorithm Optimally Allocates Actuation of a Spacecraft
(reference NPO-42301) is currently available for download from the TSP library.
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Overview
The document presents a technical disclosure of an innovative algorithm developed by NASA's Jet Propulsion Laboratory (JPL) aimed at optimizing the actuation allocation for spacecraft. This technology, identified by NTR Number 42301 and detailed in NASA Tech Brief NPO-42301, addresses a critical challenge in spacecraft control: efficiently distributing control forces and torques among available actuators, such as thrusters and reaction wheels.
The motivation behind this development stems from the need to enhance the performance of spacecraft by ensuring that the control logic can effectively allocate the required forces and torques to the actuators. The algorithm formulates the allocation problem as a sequence of quadratic and linear programming tasks, which are then solved using a highly efficient primal-dual optimization method. This approach not only provides an optimal allocation solution but also minimizes the error between the required and provided forces and torques, ensuring precise control.
A significant advantage of this algorithm is its ability to deliver the instantaneous minimum fuel solution, which is crucial for maximizing the efficiency and longevity of spacecraft operations. By optimizing fuel usage, the algorithm contributes to better overall mission performance, making it a valuable tool for various aerospace applications.
The document emphasizes the novelty of this work, highlighting how it differs from prior art in the field. The efficiency of the solution algorithm is guaranteed, which is a critical factor for real-time applications in spacecraft maneuvering. The technical support package also indicates that the results of this research are part of NASA's Commercial Technology Program, aimed at making aerospace-related developments accessible for broader technological, scientific, or commercial applications.
For further inquiries or additional information, the document provides contact details for JPL's Innovative Technology Assets Management, encouraging interested parties to reach out for collaboration or support.
In summary, this document outlines a significant advancement in spacecraft control technology through the development of an optimal actuation allocation algorithm, showcasing NASA's commitment to innovation in aerospace engineering and its potential impact on future space missions.

