TY - GEN

T1 - Bounded and Linear Quadratic Optimal Low-Thrust Collision Avoidance in Circular Orbits

AU - Itzhaki, Tom

AU - Shaferman, Vitaly

N1 - Publisher Copyright:
© 2024 by the authors.

PY - 2024

Y1 - 2024

N2 - This paper proposes two optimal-control-based algorithms for low-thrust collision avoidance. The maneuvering object’s nominal orbit is assumed to be circular, and only the position of the passive object relative to the nominal orbit at the conjunction is used. Therefore, the Clohessy-Wiltshire equations are used to model the relative dynamics. The first algorithm maximizes the weighted miss distance with a bounded thrust, whereas the second also minimizes the propellant consumption via a quadratic cost function on the weighted miss distance and the control effort. The two guidance laws are given in closed form and have only minor numerical components. The bounded guidance law only requires a numerical gradient-based optimization of two parameters, and the linear quadratic guidance law only requires solving for the roots of a 6-th-order polynomial. The two guidance laws require very low computational effort, making them suitable for the onboard implementation of small satellites. The guidance laws were evaluated in simulation and showed excellent evasion performance. Comparison between the two proposed guidance laws shows that for the same miss distance and maximum thrust, the minimum propellant law saves a significant amount of propellant, compensating for a slightly longer maneuver duration. Therefore, choosing which algorithm to use in a specific scenario depends on time and propellant considerations.

AB - This paper proposes two optimal-control-based algorithms for low-thrust collision avoidance. The maneuvering object’s nominal orbit is assumed to be circular, and only the position of the passive object relative to the nominal orbit at the conjunction is used. Therefore, the Clohessy-Wiltshire equations are used to model the relative dynamics. The first algorithm maximizes the weighted miss distance with a bounded thrust, whereas the second also minimizes the propellant consumption via a quadratic cost function on the weighted miss distance and the control effort. The two guidance laws are given in closed form and have only minor numerical components. The bounded guidance law only requires a numerical gradient-based optimization of two parameters, and the linear quadratic guidance law only requires solving for the roots of a 6-th-order polynomial. The two guidance laws require very low computational effort, making them suitable for the onboard implementation of small satellites. The guidance laws were evaluated in simulation and showed excellent evasion performance. Comparison between the two proposed guidance laws shows that for the same miss distance and maximum thrust, the minimum propellant law saves a significant amount of propellant, compensating for a slightly longer maneuver duration. Therefore, choosing which algorithm to use in a specific scenario depends on time and propellant considerations.

UR - http://www.scopus.com/inward/record.url?scp=85191322627&partnerID=8YFLogxK

U2 - 10.2514/6.2024-0094

DO - 10.2514/6.2024-0094

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AN - SCOPUS:85191322627

SN - 9781624107115

T3 - AIAA SciTech Forum and Exposition, 2024

BT - AIAA SciTech Forum and Exposition, 2024

T2 - AIAA SciTech Forum and Exposition, 2024

Y2 - 8 January 2024 through 12 January 2024

ER -