Simone D'Amico

Proximity Operations of Formation-Flying Spacecraft Using an Eccentricity/Inclination Vector Separation

The implementation of synthetic apertures by means of a distributed satellite system requires tight control of the relative motion of the participating satellites. This paper investigates a formation-flying concept able to realize the demanding baselines for aperture synthesis, while minimizing the collision hazard associated with proximity operations. An elegant formulation of the linearized equations of relative motion is discussed and adopted for satellite formation design. The concept of eccentricity/inclination-vector separation, originally developed for geostationary satellites, is here extended to low-Earth-orbit (LEO) formations. It provides immediate insight into key aspects of the relative motion and is particularly useful for orbit control purposes and proximity analyses. The effects of the relevant differential perturbations acting on an initial nominal configuration are presented, and a fuel-efficient orbit control strategy is designed to maintain the target separation. Finally, the method is applied to a specific LEO formation (TanDEM-X/TerraSAR-X), and realistic simulations clearly show the simplicity and effectiveness of the formation-flying concept.

Spaceborne Autonomous Formation-Flying Experiment on the PRISMA Mission

The Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) represents the first European technology demonstration of formation-flying and on-orbit-servicing techniques. Several hardware and software experiments, either at subsystem or system levels, have been successfully conducted since the launch of the dual-satellite mission in June 2010. This paper describes the guidance, navigation, and control functionalities and presents key flight results from the so-called Spaceborne Autonomous Formation-Flying Experiment (SAFE) executed in September 2010 and March 2011 as one of the primary PRISMA mission objectives. SAFE is intended to demonstrate autonomous acquisition, keeping, and reconfiguration of passive relative orbits for advanced remote sensing and rendezvous applications. As shown in the paper, the onboard Global Positioning System navigation system provides relative orbit information in real time with an accuracy better than 10 cm and 1 mm/s (threedimensional, root mean square) in position and velocity, respectively. The impulsive formation control achieves accuracies better than 10m (three-dimensional, root mean square) for separations below 2 km with minimum usage of thrusters, ensuring high predictability for simplified mission operations and minimum collision risk for increased safety

Spaceborne Autonomous Relative Control System for Dual Satellite Formations

two spacecraft flying on near-circular orbits. Emphasis is given to the practical implementation within an onboard embedded computer, which requires a simple, resource-sparing, and robust design of the system. Therefore, the algorithms are tailored to minimize the usage of onboard resources and to allow the harmonious integration of the relative control system within the space segment. The validation of TanDEM-X Autonomous Formation Flying performed using a hardware-in-the-loop testbed shows that control performance at the meter level is expected.

Relative Orbit Control Design for the PRISMA Formation Flying Mission

Time has come for the first European fully autonomous close-range formation flying demonstration in low Earth orbit. The PRISMA technology demonstration mission, originating from an initiative of the Swedish National Space Board and the Swedish Space Corporation, is currently in its development phase and will realize formation flying and rendezvous experiments involving two spacecraft at an altitude of 700km. In the frame of the German Aerospace Center’s contribution to PRISMA, this study addresses the GPS-based guidance, navigation and control (GNC) on-board functionalities for the maintenance of a robust and safe relative motion between two spacecraft with typical accuracies of a few tenths of meters and minimum thrusters usage. After an introduction of the GNC concept based on real-time GPS measurements filtering, relative orbital elements parameterization, and impulsive orbit control, emphasis is given to real world simulations of the system including the modeling of sensors and actuators. Finally, the paper derives realistic estimates of the expected relative orbit control performances and their dependencies on the accuracy of the GPS data filtering and the characteristics of the propulsion system.

GPS-based relative navigation during the separation sequence of the PRISMA formation

PRISMA is a Swedish-led micro-satellite mission that serves as a test platform for autonomous formation flying and rendezvous of spacecraft. It comprises two satellites which are launched together in a clamped configuration and separated in orbit after completion of all checkout operations. The challenge of the subsequent early operations phase is to maintain the formation safety and in particular to minimize the risk of collision using only a reduced subset of the overall guidance, navigation and control functionalities. While not specifically designed for safe mode operations, the PRISMA GPS-based relative navigation system is still considered the best source of relative orbit information during this mission phase. A comprehensive simulation of the separation sequence has been therefore conducted that demonstrates the robust operation of the GPS navigation system under the adverse conditions of the separation event and the subsequent non-nominal spacecraft attitude. While initially based on offline Simulink/C++ software simulations, the employed test approach makes use of the prototype flight software for the GPS navigation system and enables a seamless transition to real-time software simulations as well as hardware-in-the-loop simulations.

New State Transition Matrices for Relative Motion of Spacecraft Formations in Perturbed Orbits

This paper presents new state transition matrices that model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J2 and differential drag for three state definitions based on relative orbital elements. These matrices are derived by first performing a Taylor expansion on the equations of relative motion including all considered perturbations and subsequently computing an exact, closed-form solution of the resulting linear differential equations. Both density-model-specific and density-model-free differential drag formulations are included. Density-model-specific formulations require a-priori knowledge of the atmosphere, while density-model-free formulations remove this requirement by augmenting the relative state with a set of parameters which are estimated in flight. The resulting state transition matrices are used to generalize the geometric interpretation of the effects of J2 and differential drag on relative motion in near-circular orbits provided in previous works to arbitrarily eccentric orbits. Additionally, this paper harmonizes current literature by demonstrating that a number of state transition matrices derived by previous authors using various techniques can be found by subjecting the models presented in this paper to more restrictive assumptions. Finally, the presented state transition matrices are validated through comparison with a high-fidelity numerical orbit propagator. It is found that the models including density-model-free differential drag exhibit much better performance than their density-model-specific counterparts. Specifically, these state transition matrices are able to reduce propagation errors by at least an orderof-magnitude when compared to models including only J2 and are able to match or exceed the accuracy of comparable models in literature over a broad range of orbit scenarios.

System design of a miniaturized distributed occulter/telescope for direct imaging of star vicinity

The Space Rendezvous Laboratory (SLAB) at Stanford is investigating the feasibility of a miniaturized distributed occulter/telescope system (mDOT) to directly image exozodiacal dust and Jovian exoplanets. The mDOT mission relies on formation flying in Earth orbit and promises a drastic decrease of the expected mission cost compared to large scale missions, such as NWO and Exo-S (NASA). The preliminary system design of mDOT, described in this paper, is complemented by concurrent novel studies of optimal formation dynamics and diffractive optics design. mDOT consists of a microsatellite carrying a 1 meter radius petal shaped occulter at a distance of 500 km from a 6U CubeSat carrying a 10 cm diameter aperture telescope designed to image at short visible and ultraviolet wavelengths. Following a systems analysis, based on the definition of mission requirements and a survey of CubeSat capabilities, the telescope spacecraft provides 80 days of operation with 50 W solar cells, 31 m/s of delta-v capability using cold gas thrusters. Together with ad-hoc relative metrology instruments, these are used for lateral alignment with the occulter spacecraft at 15 cm position control accuracy. The goal of the mDOT mission is to prove that a space telescope with an external star occulter can be miniaturized, greatly reducing the mission cost and complexity. As shown in this paper, the proposed mission has the capability to directly image the vicinity of nearby stars and, at the same time, prove that miniaturized space systems are capable of executing complex missions. mDOT can serve as a first-of-a-kind precursor, paving the way for larger missions with higher scientific return.

Optimal impulsive closed-form control for spacecraft formation flying and rendezvous

This paper addresses the design of novel optimal closed-form multi-impulsive maneuvers for satellite formation-flying and rendezvous. A new method to derive the state transition matrix for the relative motion in J2-perturbed eccentric orbits is shown and used to compute (semi-)analytical solutions for formation control. In addition, a delta-v lower bound for eccentric orbits is formulated which provides direct insight into the optimality of the control solutions. The functionality and performance of the resulting maneuvering schemes are numerically analyzed through comparisons with state-of-the-art optimal control. The results of this paper show how closed-form maneuver solutions have the potential to fulfil the requirements posed by future distributed space systems at a fraction of the computational cost and overall complexity.

Relative control of a virtual telescope using Global Positioning System and Optical Metrology

A = plant matrix a = semimajor axis B = deterministic matrix e = eccentricity ec = control error vector GM = gravitational parameter i = inclination K = gain matrix l = reference separation between the occulter and the coronagraph M = mean anomaly Q = control error weighting matrix R = control input weighting matrix r = position in Earth-centered inertial coordinates u = control input v = velocity in Earth-centered inertial coordinates x = state vector in Earth-centered inertial coordinates

Navigation and Control of the PRISMA formation: In-Orbit Experience

This paper presents flight results and lessons learned from the Spaceborne Autonomous Formation Flying Experiment (SAFE) conducted by the German Space Operations Center in the frame of the Swedish PRISMA mission. SAFE represents one of the first demonstrations in low Earth orbit of an advanced guidance, navigation and control system for dual-spacecraft formations. Innovative techniques based on carrier-phase differential GPS, relative eccentricity/inclination vectors and impulsive maneuvering are validated and tuned in orbit to achieve centimeter accurate real-time relative navigation, reliable formation keeping at the meter level and flexible formation reconfiguration capabilities.