A centralized optimal controller for formation flying spacecraft
Formation flying spacecraft is emerging as an enabling technology for the discovery of new type of science for the emerging NASA deep space and Earth science missions.
interferometers↗
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GVE-Based Dynamics and Control for Formation Flying Spacecraft
Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.
Breger, Louis↗
Parallel Estimation and Control Architectures for Deep-Space Formation Flying Spacecraft
The formation flying of precisely controlled spacecraft in deep space can be used to implement optical instruments capable of imaging planets in other solar systems. The distance of the formation from Earth necessitates a significant level of autonomy and each spacecraft must base its actions on its estimates of the location and velocity of the other spacecraft. Precise coordination and control is the key requirement in such missions and the flow of information between spacecraft must be carefully designed. Doing this in an efficient and optimal manner requires novel techniques for the design of the on-board estimators. The use of standard Kalman filter-based designs can lead to unanticipated dynamics--which we refer to as disagreement dynamics--in the estimators' errors. We show how communication amongst the spacecraft can be designed in order to control all of the dynamics within the formation. We present several results relating the topology of the communication network to the resulting closed-loop control dynamics of the formation. The consequences for the design of the control, communication and coordination are discussed.
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Design of a LQR Controller of Reduced Inputs for Multiple Spacecraft Formation Flying
Regarding multiple spacecraft formation flying, the observation is made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite formation. Without the need for zenith-nadir (radial) thrust, simplifications and reduction of the weight of the propulsion system may be accomplished. This work focuses on the validation of this radial-excluding control system on its own merits, and in comparison to a related system which does provide thrust parallel to the orbital radius. Simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled, leader satellite. The conclusion is drawn that, despite the exclusion of the radial thrust axis, the remaining control thrust available still provides enough control to design a gain matrix of adequate performance using linear-quadratic regulator (LQR) techniques.
Starin, Scott R.↗
Distributed control topologies for deep space formation flying spacecraft
A formation of satellites flying in deep space can be specified in terms of the relative satellite positions and absolute satellite orientations. The redundancy in the relative position specification generates a family of control topologies with equivalent stability and reference tracking performance, one of which can be implemented without requiring communication between the spacecraft. A relative position design formulation is inherently unobservable, and a methodology for circumventing this problem is presented. Additional redundancy in the control actuation space can be exploited for feed-forward control of the formation centroid's location in space, or for minimization of total fuel consumption.
formation flying distributed spacecraft distribute↗
A survey of spacecraft formation flying guidance
This paper is the first comprehensive spacecraft formation flying guidance (FFG) survey. Here by the term guidance we mean both path planning (i. e., reference trajectory generation) and optimal, open loop control design. FFG naturally divides into two areas: Deep Space (DS), in which relative spacecraft dynamics reduce to double integrator form, and Planetary Orbital Environments (POE), in which they do not (e.9. libration point formations). Both areas consider optimal formation reconfigurations. In addition, DS FFG addresses optimal u, v-coverages for multiple spacecraft interferometers and rest-to-rest rotations. The main focus of the POE literature, however, is 'assive apertures.' These are periodic and fuel-eficient relative spacecraft trajectories that accomplish scientific objectives (e.9. synthesizing an aperture).
formation flying guidance optimal control path pla↗
Implementation of Autonomous GPS Guidance and Control for Spacecraft Formation Flying
This paper presents the general relative orbit dynamics equations and GPS (Global Positioning System) orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition and maintenance of spacecraft formation using GPS code pseudoranges are presented. As a practical application of the models and method provided in this paper, the orbit control of the Earth-Orbiter 1(EO-1) / Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3-dimensional initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.
Xing, Guang Q.↗
Distributed control topologies for deep space formation flying spacecraft
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spacecraft formation flying distributed control↗
Local Estimators for Spacecraft Formation Flying
A formation estimation architecture for formation flying builds upon the local information exchange among multiple local estimators. Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are needed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms should rely on a local information-exchange network, relaxing the assumptions on existing algorithms. In this research, it was shown that only local observability is required to design a formation estimator and control law. The approach relies on breaking up the overall information-exchange network into sequence of local subnetworks, and invoking an agreement-type filter to reach consensus among local estimators within each local network. State estimates were obtained by a set of local measurements that were passed through a set of communicating Kalman filters to reach an overall state estimation for the formation. An optimization approach was also presented by means of which diffused estimates over the network can be incorporated in the local estimates obtained by each estimator via local measurements. This approach compares favorably with that obtained by a centralized Kalman filter, which requires complete knowledge of the raw measurement available to each estimator.
Fathpour, Nanaz↗
A survey of spacecraft formation flying guidance and control (Part II): control
This paper provides a comprehensive survey of spacecraft formation flying control, which encompasses design techniques and stability results for these coupled-state control laws.
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Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs
Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.
Starin, Scott R.↗
Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs
Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.
Starin, Scott R.↗
A survey of spacecraft formation flying guidance and control (part I): guidance
This paper provides a comprehensive survey of spacecraft formation flying guidance (FTG). Here by the term guidance we mean both path planning and optimal, open loop control design.
formation flying guidance robotic path planning pa↗
Rule-based estimation and control of formation flying spacecraft
This paper addresses some estimation and control problems specific to formation flying of spacecraft that can be approached with rule or logic based methodologies.
formation flying rule-based control rule-based est↗
Spacecraft Formation Flying near Sun-Earth L2 Lagrange Point: Trajectory Generation and Adaptive Full-State Feedback Control
In this paper, we present a method for trajectory generation and adaptive full-state feedback control to facilitate spacecraft formation flying near the Sun-Earth L2 Lagrange point. Specifically, the dynamics of a spacecraft in the neighborhood of a Halo orbit reveals that there exist quasi-periodic orbits surrounding the Halo orbit. Thus, a spacecraft formation is created by placing a leader spacecraft on a desired Halo orbit and placing follower spacecraft on desired quasi-periodic orbits. To produce a formation maintenance controller, we first develop the nonlinear dynamics of a follower spacecraft relative to the leader spacecraft. We assume that the leader spacecraft is on a desired Halo orbit trajectory and the follower spacecraft is to track a desired quasi-periodic orbit surrounding the Halo orbit. Then, we design an adaptive, full-state feedback position tracking controller for the follower spacecraft providing an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield global, asymptotic convergence of the relative position tracking errors.
Wong, Hong↗
Graphs, Matrix Inequalities, and Switching for the Formation Flying Spacecraft
We present several results on the leader-following (LF) paradigm in the formation flying of multiple spacecraft in free space.
formation flying control theory Linear matrix ineq↗
A Hardware-in-the-Loop Testbed for Spacecraft Formation Flying Applications
The Formation Flying Test Bed (FFTB) at NASA Goddard Space Flight Center (GSFC) is being developed as a modular, hybrid dynamic simulation facility employed for end-to-end guidance, navigation, and control (GN&C) analysis and design for formation flying clusters and constellations of satellites. The FFTB will support critical hardware and software technology development to enable current and future missions for NASA, other government agencies, and external customers for a wide range of missions, particularly those involving distributed spacecraft operations. The initial capabilities of the FFTB are based upon an integration of high fidelity hardware and software simulation, emulation, and test platforms developed at GSFC in recent years; including a high-fidelity GPS simulator which has been a fundamental component of the Guidance, Navigation, and Control Center's GPS Test Facility. The FFTB will be continuously evolving over the next several years from a too[ with initial capabilities in GPS navigation hardware/software- in-the- loop analysis and closed loop GPS-based orbit control algorithm assessment to one with cross-link communications and relative navigation analysis and simulation capability. Eventually the FFT13 will provide full capability to support all aspects of multi-sensor, absolute and relative position determination and control, in all (attitude and orbit) degrees of freedom, as well as information management for satellite clusters and constellations. In this paper we focus on the architecture for the FFT13 as a general GN&C analysis environment for the spacecraft formation flying community inside and outside of NASA GSFC and we briefly reference some current and future activities which will drive the requirements and development.
Leitner, Jesse↗
Spacecraft Formation Flying: An Overview of Missions and Technologies
Over the next two decades a revolution is likely to occur in how remote sensing of Earth, other planets or bodies, and a range of phenomena in the universe is performed from space. In particular, current launch vehicle fairing volume and mass constraints will continue to restrict the size of monolithic telescope apertures which can be launched to accommodate only slightly more performance capability than is achievable today, such as by the Hubble Space Telescope. Systems under formulation today, such as the James Webb Space Telescope, will be able to increase aperture size and, hence, imaging resolution, by deploying segmented optics. However, this approach is limited as well, by our ability to control such segments to optical tolerances over long distances with highly uncertain structural dynamics connecting them. Consequently, for orders of magnitude improved resolution as required for imaging black holes, imaging planets, or performing asteroseismology, the only viable approach will be to fly a collection of spacecraft in formation to synthesize a virtual segmented telescope or interferometer with very large baselines. This presentation highlights some of the strategic science missions planned in the National Aeronautics and Space Administration, and identifies some of the critical technologies needed to enable some of the most challenging space missions ever conceived which have realistic hopes of flying.
Leitner, Jesse↗