Design of a LQR controller of reduced inputs for multiple spacecraft formation flying

Starin, Scott R.; Yedavalli, Rama K.; Sparks, Andrew G.

doi:10.1109/acc.2001.945908

Cited by 42 publications

(10 citation statements)

References 7 publications

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“…Having a large number of spacecraft in close formation requires to execute complex maneuvers with minimal fuel consumption and reliable collision avoidance systems. To account for these tasks, several control strategies have been studied; the Linear Quadratic Regulator (LQR) applied to the control of spacecraft in formation using the ClohessyWiltshire (CW) (Clohessy & Wiltshire, 1960) model for circular reference orbits, was used by Starin (Starin, 2001) where an infinite time cost function was minimized by the algebraic Riccati equation. Bainum et al (Bainum et al, 2005) presented further studies where the LQR was used along with the Tschauner and Hempel (TH) (Tschauner & Hempel, 1965) model for elliptic reference orbits.…”

Section: Introductionmentioning

confidence: 99%

Close proximity formation flying via linear quadratic tracking controller and artificial potential function

Palacios

Ceriotti

Radice

2015

Advances in Space Research

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A Riccati-based tracking controller with collision avoidance capabilities is presented for proximity operations of spacecraft formation flying near elliptic reference orbits. The proposed dynamical model incorporates nonlinear accelerations from an artificial potential field, in order to perform evasive maneuvers during proximity operations. In order to validate the design of the controller, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) will be implemented, extending it to scenarios with multiple spacecraft performing reconfigurations and on-orbit position switching. The results show that the tracking controller is effective, even when nonlinear repelling accelerations are present in the dynamics to avoid collisions, and that the potential-based collision avoidance scheme is convenient for reducing collision threat.

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Section: Introductionmentioning

confidence: 99%

Close proximity formation flying via linear quadratic tracking controller and artificial potential function

Palacios

Ceriotti

Radice

2015

Advances in Space Research

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“…The following approaches are typical control methods that are employed within this structure, namely: (1) proportional/derivative (PD) control; 2 (2) feedback linearization design approach; 3 (3) Sliding mode control; 7 and (4) LQR and H ∞ control. 8 In the VS approach, the SC behave as rigid bodies embedded in a larger, virtual rigid body. The overall motion of the virtual structure as specified by positions and orientations of the SC within it are used to generate reference trajectories for each individual SC to track using its own controllers.…”

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confidence: 99%

Coordinated Attitude Control of Spacecraft Formation Without Angular Velocity Feedback: A Decentralized Approach

Mehrabian¹,

Tafazoli²,

Khorasani³

2009

AIAA Guidance, Navigation, and Control Conference

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In this paper, motivated by recent developments of velocity-free spacecraft (SC) attitude control techniques and behavioral-based SC formation control a decentralized control algorithm for attitude coordination of SC formation without angular velocity feedback is presented. Asymptotic stability of the SC formation is guaranteed by using Lyapunov analysis and LaSalle's theorem. The advantage of our proposed algorithm is that it requires limited information exchange among the SC in the formation (only attitude information exchange is necessary). Additionally, the proposed algorithm can be extremely useful when angular velocity information of the SC in the formation in not available due to sensor failures or communication constraints. Unlike other popular methods in the robotics area which tend to assume simple dynamics such as linear systems and single or double integrator dynamic models, in this paper, the full nonlinear attitude dynamics of the SC is considered to track fast time-varying reference trajectories. Nomenclature e Euler vector θ Euler angle, rad q The unit-quaternion q Vector part of the quaternion q 4 Scalar part of the quaternion R Rotation matrix [] × Cross product matrix Q(q) Quaternion product matrix ω Spacecraft angular velocity vector, rad/sec E(q) Matrix based on quaternion u External torque (control effort), N-m F B Body frame F I Inertial frame J Spacecraft moments of inertial matrix, kg-m 2 δq Quaternion error δω Angular velocity error, rad/sec q jn Quaternion error between jth and nth spacecraft ω jn Angular velocity error between jth and nth spacecraft, rad/sec A Constant matrix B Constant matrix * This research is supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) Strategic Projects.

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“…At present, most of the studies for spacecraft formation flying are focused on circular orbits. [5][6][7][8] Therefore, the linear Hill equation can be used to obtain the algebraic solution of relative motion. Characteristics of relative motion of each spacecraft relative to the master spacecraft can be presented for formation design and control.…”

Section: Introductionmentioning

confidence: 99%

Fixed Thrust Optimal-Fuzzy Combined Control for Spacecraft Formation Flying

Pengji¹,

Zhao²,

Yang³

2004

Trans. Japan Soc. Aero. S Sci.

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The fixed thrust optimal-fuzzy combined formation control method is mainly studied for spacecraft formation flying in circular orbits based on two-body relative dynamics. The linear Hill's equation is used in relative dynamics, and the circular formation in three dimensions is designed. In fuzzy control, relative position, velocity and acceleration errors are selected as fuzzy variables and the multiplication and weighted average principle are introduced into fuzzy inference so as to maximize the reduction of the coupling effect. And since J2 perturbation is known, it will be taken into account effectively in fuzzy control method. In time-fuel optimal control, the simplified relative error model is used and an optimal controller is provided through the minimum principle. Thus, this paper combines both controls above to form the optimal-fuzzy formation control. Optimal control is adopted when relative position errors reach a certain threshold, while fuzzy control works for the small errors lower than that threshold. Finally, to take circular formation as an example, the simulation results demonstrate that not only does the optimal-fuzzy combined control system have a good response performance, but also excels in fuel consumption.

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Design of a LQR controller of reduced inputs for multiple spacecraft formation flying

Cited by 42 publications

References 7 publications

Close proximity formation flying via linear quadratic tracking controller and artificial potential function

Close proximity formation flying via linear quadratic tracking controller and artificial potential function

Coordinated Attitude Control of Spacecraft Formation Without Angular Velocity Feedback: A Decentralized Approach

Fixed Thrust Optimal-Fuzzy Combined Control for Spacecraft Formation Flying

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