This paper proposes two adaptive nonlinear control algorithms based on a variable-structure control design for multiple spacecraft formation flying. The nonlinear dynamics describing the motion of the follower spacecraft relative to the leader spacecraft are considered for the case in which the leader spacecraft is in an elliptical reference orbit, and the stability of such a formation in the presence of external perturbations is investigated. This paper presents fault-tolerant control schemes to account for accidental or degradation faults in spacecraft sensors and thrusters. The nonlinear analytical model describing the system is used to develop two adaptive fault-tolerant control laws (continuous sliding mode control and nonsingular terminal sliding mode control) that guarantee global asymptotic convergence of the position tracking error in the presence of unknown follower spacecraft mass and external disturbances. Several numerical examples are presented to demonstrate the efficacy of the proposed controllers to maintain the relative motion by correcting for initial offsets and external perturbation effects that tend to disperse the formation. Simulation results confirm that the suggested methodologies yield submillimeter formation, keeping precision and effectiveness in ensuring formation maneuvering. In addition, an abrupt blockage of the relative position sensors, thruster failure for a period of time, and thruster degradation (amidst formation keeping and reconfiguration maneuvers) are simulated to demonstrate the fault recovery capability of the controllers. The numerical results clearly establish the robustness of the proposed reconfigurable adaptive control scheme for precise formation keeping in the event of sensor and thruster faults.

Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques

In this paper, the use of differential aerodynamic drag is proposed for multiple satellite formation flying in low Earth orbit. The nonlinear dynamics describing the motion of the follower satellite relative to the leader satellite is considered, and the control methodology is developed based on sliding mode control. The stability of such a formation in the presence of external perturbations is analyzed. Several cases are considered to examine the performance of the proposed control strategy to maintain the relative motion of the follower satellites by correcting for any initial offset errors and external perturbation effects that tend to perturb the formation. Results of the numerical simulation along with hardware-in-the loop testing confirm that the suggested methodology using differential aerodynamic drag yields reasonable formation-keeping precision and its effectiveness in ensuring formation maneuvering.

Multiple Satellite Formation Flying Using Differential Aerodynamic Drag

The formation tracking problem for multiple spacecraft in the framework of networked control systems (NCSs) is investigated. A reference trajectory is generated by the force-free linearized equations of the relative motion (known as Hill's equations). A sampled-data representation of the NCS is considered for the tracking control of relative motion between the leader and follower spacecraft in the presence of variable communication delays and bounded external disturbances. By adding a buffer which is longer than the worst case delay and augmenting the system model to include past values of system input as additional states, a new discrete time-invariant model is formulated, and a digital controller is developed to guarantee the exponentially uniformly ultimate boundedness (UUB) of the tracking errors and to ensure desired formation objectives. Numerical simulations are presented to demonstrate the effectiveness of the controller. The proposed controller is successful in establishing projected circular formation with the maximum magnitude of the steady-state tracking error 0.056 and the control forces remain bounded within 50 mN.

Network-Based Tracking Control of Spacecraft Formation Flying with Communication Delays

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 little or no greater size than that of the Hubble Space Telescope, the largest aperture currently flying in space. 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 paper provides some basic definitions in the area of formation flying, describes 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.

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Formation Flying: The Future of Remote Sensing from Space

Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations

NASA's first autonomous formation flying mission, the New Millennium Program's (NMP) Earth Observing-1 (EO-1) spacecraft, recently completed its principal goal of demonstrating advanced formation control technology. This paper provides an overview of the evolution of an onboard system that was developed originally as a ground mission planning and operations tool. We discuss the Goddard Space Flight Center s formation flying algorithm, the onboard flight design and its implementation, the interface and functionality of the onboard system, and the implementation of a Kalman filter based GPS data smoother. A number of safeguards that allow the incremental phasing in of autonomy and alleviate the potential for mission-impacting anomalies from the on- board autonomous system are discussed. A comparison of the maneuvers planned onboard using the EO-1 autonomous control system to those from the operational ground-based maneuver planning system is presented to quantify our success. The maneuvers discussed encompass reactionary and routine formation maintenance. Definitive orbital data is presented that verifies all formation flying requirements.

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NASA's Autonomous Formation Flying Technology Demonstration, Earth Observing-1(EO-1)

Spacecraft missions are seeking alternative and innovative ways to rapidly reduce mission costs. Automating maneuver planning processes plays a significant role in achieving that goal. FreeFlyer™ and AutoCon™, developed by AI Solutions, are tools being used by current National Aeronautics and Space Administration (NASA) missions to efficiently perform flight dynamics processes, while reducing costs. The Earth Observing System (EOS) AM-l spacecraft and Landsat-7 spacecraft are using FreeFlyer™, while the Earth Orbiter 1 (EO-1) is using AutoCon™, a precursor to FreeFlyer™, for orbital analysis, maneuver planning and product generation. EOS AM-l will perform frequent ground track maintenance maneuvers to maintain orbital constraints. Additional orbital and operational constraints will be taken into account while planning these maneuvers. FreeFlyer™ uses a robust natural scripting language to model mission environments while performing maneuver planning Advanced targeting capabilities and fuzzy logic are incorporated into FreeFlyer™ to resolve and achieve complex mission constraints. EO-1 will be using AutoCon1™ both on ground and on board. A unique targeting algorithm incorporated into AutoCon M, developed by Goddard Space Flight Center (GSFC), will plan maneuvers for formation flying with Landsat7. A sequential progression towards autonomous maneuver planning, including formation flying using AutoCon™, will be demonstrated with the EO-1 mission.

Greg Dell

Papers

NASA's Autonomous Formation Flying Technology Demonstration, Earth Observing-1(EO-1)

EOS AM-l AND EO-1 SUPPORT USING FreeFlyer™ and AutoCon™