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In this paper we describe the key technology challenges, the approach to resolving them through analysis and testbed activities, and the results of the testbed activities.
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.
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.
Cooperative formation flying using various methods of filtering spacecraft to spacecraft range have been proposed and techniques from this paper can be extended to support such missions.
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.
Formation flying systems can range from global constellations offering extended service coverage to clusters of highly coordinated vehicles that perform distributed sensing. Recently, the use of groups of micro-satellites in the areas of near Earth explorations, deep space explorations, and military applications has received considerable attention by researchers and practitioners. To date, most proposed control strategies are based on linear models (e.g., Hill-Clohessy-Wiltshire equations) or nonlinear models that are restricted to circular reference orbits. Also, all models in the literature are uncoupled between relative position and relative attitude. In this paper, a generalized dynamic model is proposed. The reference orbit is not restricted to the circular case. In this formulation, the leader or follower satellite can be in either a circular or an elliptic orbit. In addition to maintaining a specified relative position, the satellites are also required to maintain specified relative attitudes. Thus the model presented couples vehicle attitude and orbit requirements. Orbit perturbations are also included. In particular, the J(sub 2) effects are accounted in the model. Finally, a sliding mode controller is developed and used to control the relative attitude of the formation and the simulation results are presented.
Concepts for missions of distributed spacecraft flying in formation abound. From high resolution interferometry to spatially distributed in-situ measurements, these mission concepts levy a myriad of guidance, navigation, and control (GNC) requirements on the spacecraft/formation as a single system. A critical step toward assessing and meeting these challenges lies in realistically simulating distributed spacecraft systems. The Formation Flying TestBed (FFTB) at NASA Goddard Space Flight Center's (GSFC) Guidance, Navigation, and Control Center is a hardware-in-the-loop simulation and development facility focused on GNC issues relevant to formation flying systems. The FFTB provides a realistic simulation of the vehicle dynamics and control for formation flying missions in order to: (1) conduct feasibility analyses of mission requirements, (2) conduct and answer mission and spacecraft design trades, and (3) serve as a host for GNC software and hardware development and testing. The initial capabilities of the FFTB are based upon an integration of high fidelity hardware and software simulation, emulation, and test platforms developed or employed at GSFC in recent years, including a high-fidelity Global Positioning System (GPS) simulator which has been a fundamental component of the GNC Center's GPS Test Facility. The FFTB will be continuously evolving over the next several years from a tool with capabilities in GPS navigation hardware/software-in-the-loop analysis and closed loop GPS-based orbit control algorithm assessment. Eventually, it will include full capability to support all aspects of multi-sensor, absolute and relative state determination and control, in all (attitude and orbit) degrees of freedom, as well as information management for satellite clusters and constellations. A detailed description of the FFTB architecture is presented in the paper.
Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a virtual space telescope. Using precision dual spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts with spacecraft separations from 1000 km to 25,000 km, such as the Milli-Arc-Second Structure Imager (MASSIM) and the New Worlds Observer, and Heliophysics concepts for solar coronagraphs and X-ray imaging with smaller separations (50m 500m). All of these proposed missions require advances in guidance, navigation, and control (GNC) for precision formation flying. In particular, very precise astrometric alignment control and estimation is required for precise inertial pointing of the virtual space telescope to enable science imaging orders of magnitude better than can be achieved with conventional single spacecraft instruments. This work develops design architectures, algorithms, and performance analysis of proposed GNC systems for precision dual spacecraft astrometric alignment. These systems employ a variety of GNC sensors and actuators, including laser-based alignment and ranging systems, optical imaging sensors (e.g. guide star telescope), inertial measurement units (IMU), as well as micro-thruster and precision stabilized platforms. A comprehensive GNC performance analysis is given for Heliophysics dual spacecraft PFF imaging mission concept.
Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a virtual space telescope. Using precision dual spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts with spacecraft separations from 1000 km to 25,000 km, such as the Milli-Arc-Second Structure Imager (MASSIM) and the New Worlds Observer, and Heliophysics concepts for solar coronagraphs and X-ray imaging with smaller separations (50m-500m). All of these proposed missions require advances in guidance, navigation, and control (GNC) for precision formation flying. In particular, very precise astrometric alignment control and estimation is required for precise inertial pointing of the virtual space telescope to enable science imaging orders of magnitude better than can be achieved with conventional single spacecraft instruments. This work develops design architectures, algorithms, and performance analysis of proposed GNC systems for precision dual spacecraft astrometric alignment. These systems employ a variety of GNC sensors and actuators, including laser-based alignment and ranging systems, optical imaging sensors (e.g. guide star telescope), inertial measurement units (IMU), as well as microthruster and precision stabilized platforms. A comprehensive GNC performance analysis is given for Heliophysics dual spacecraft PFF imaging mission concept.
Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing dual-spacecraft precision formation flying (PFF) to enable a 'virtual' telescope (VT). Using precision dual-spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts for X-ray imaging and exo-planet observation with large spacecraft separations (1000 km to 80,000 km), and heliophysics concepts for X-ray or extreme ultra-violet (EUV) imaging or solar coronagraphs with smaller separations (50m - 500m). These proposed missions require advances in guidance, navigation, and control (GN&C) for PFF to enable high resolution science imaging. For many applications, the dual-spacecraft dynamics are coupled through the GN&C system when the relative ranging and position alignment sensor components are not co-located with their respective spacecraft mass centers. We develop a model-based PFF system design approach for the VT application, considering the coupling inherent in precision dual-spacecraft inertial alignment. These systems employ a variety of GN&C sensors and actuators, including laser-based alignment and ranging systems, camera-based imaging sensors, inertial measurement units (IMU), as well as microthruster systems and image motion compensation platforms. Results of a GN&C performance assessment reveal how data from relative position sensors can be employed in a Kalman filter framework to significantly improve alignment estimation performance. The assessment provides a comparison of two different GN&C formation flying architectures, illustrating the performance trades inherent in the choice of PFF system architecture in the VT application.
SIMBOL-X is a high energy new generation telescope covering by a single instrument a continuous energy range starting at classical X-rays and extending to hard X-rays, i.e. from 0.5 to 80 keV. It is using in this field a focalizing payload which until now was used for energy below 10 keV only, via the construction of a telescope distributed on two satellites flying in formation. SIMBOL-X permits a gain of two orders of magnitude in sensibility and spatial resolution in comparison to state of the art hard X-rays instruments. The mirror satellite will be in free flight on a high elliptical orbit and will target the object to observe very precisely, thus focusing the hard X-ray emission thanks to this mirror module. At the focal point area which is situated 20 meters behind the mirror satellite, the detector satellite maintains its position on a forced orbit thanks to a radio link with the mirror satellite and a lateral displacement sensor using a beam emitted onboard the mirror satellite. This configuration is said "formation flying". The location of the detector satellite shall be very finely tuned as it carries the focal plane of this distributed telescope. To provide science measurements, the Simbol-X orbit has been chosen High elliptic (HEO), which means elliptical orbit with a high perigee altitude. Preliminary studies where made with an orbit with an altitude of the perigee of 44000km and altitude of the apogee of 253000km. The orbit was seven days ground track repeated in order to maintain a perigee pass over the Malindi ground station to download scientific telemetry. But as studies went on, difficulties in mass budget, link budget, perigee maintenance and formation flying maintenance were raised. This was mainly due to the vicinity of the Moon and its disturbing effect on the satellites orbits. Alternative orbits have been proposed in order to demonstrate the feasibility of the mission. The problematic of bringing the two satellites from their injection orbit to their operational orbit 20 m apart from each other and then maintain this configuration is very challenging. It requires theoretical development of the relative motion between two satellites in high eccentric orbit with large differential disturbance on the two bodies. This paper will present the mission analysis for the Simbol-X satellites with the complex problematic of doing formation flying in high elliptic orbit.
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.
The problem of flying an earth observing mission using a group of observatories flying in formation, rather than a single observatory, is addressed. Contraints placed on the design of the observatories and of the mission, if it is required that the instantaneous field of views of the two instruments overlap by a specified amount, are determined. The complexities of formation flying are found to greatly outweigh simpler solutions which combine instruments on a single spacecraft payload. While formation flying may be beneficial when crossing times and simultaneity arguments are not stringent, it is not practical for EOS. Accomplishment of the EOS scientific mission requires the simultaneous measurement of a basic set of earth system science parameters; it also requires that many events be observed by groups of instruments looking through the same atmospheric path.
The seventh orbital flight of the Space Shuttle had as one of its primary objectives the testing of the vehicle's capability for proximity operations (defined as anytime the Orbiter is within 1000 feet of another satellite). The goals of these tests were to obtain flight data on different techniques for separation from, stationkeeping with, and approach and capture of a free-flying satellite. This included the acquisition of data on technique evaluation as to propellant usage, time required, crew workload, plume disturbance to the payload by the reaction control system, and jet plume impingement. The tests were also to provide data on the rendezvous radar and optical sighting devices performance in this environment. It is concluded that the Orbiter proved to be a very responsive vehicle that ws straightforward to fly in the vicinity of another satellite given the proper experience base with ground simulations.
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.
The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.
Software for a system to control the trajectories of multiple spacecraft flying in formation is being developed to reflect underlying concepts of (1) a decentralized approach to guidance and control and (2) reconfigurability of the control system, including reconfigurability of the software and of control laws. The software is organized as a modular network of software tasks. The computational load for both determining relative trajectories and planning maneuvers is shared equally among all spacecraft in a cluster. The flexibility and robustness of the software are apparent in the fact that tasks can be added, removed, or replaced during flight. In a computational simulation of a representative formation-flying scenario, it was demonstrated that the following are among the services performed by the software: Uploading of commands from a ground station and distribution of the commands among the spacecraft, Autonomous initiation and reconfiguration of formations, Autonomous formation of teams through negotiations among the spacecraft, Working out details of high-level commands (e.g., shapes and sizes of geometrically complex formations), Implementation of a distributed guidance law providing autonomous optimization and assignment of target states, and Implementation of a decentralized, fuel-optimal, impulsive control law for planning maneuvers.
A conceptual space telescope having an aperture tens of meters wide and a focal length of hundreds of meters would be implemented as a group of six separate optical modules flying in formation: a primary-membrane-mirror module, a relay-mirror module, a focal-plane-assembly module containing a fast steering mirror and secondary and tertiary optics, a primary-mirror-figure-sensing module, a scanning-electron-beam module for controlling the shape of the primary mirror, and a sunshade module. Formation flying would make it unnecessary to maintain the required precise alignments among the modules by means of an impractically massive rigid structure. Instead, a control system operating in conjunction with a metrology system comprising optical and radio subsystems would control the firing of small thrusters on the separate modules to maintain the formation, thereby acting as a virtual rigid structure. The control system would utilize a combination of centralized- and decentralized-control methods according to a leader-follower approach. The feasibility of the concept was demonstrated in computational simulations that showed that relative positions could be maintained to within a fraction of a millimeter and orientations to within several microradians.