PRISMA Mission Research Articles

Closed-Form Solution of the l1-Optimal Bi-Impulsive Coplanar Orbital Transfer Problem

S ATELLITE orbital transfer has been studied based on two main approaches: impulsive maneuvers and continuous-thrust maneuvers. Impulsive models, in spite of being approximate, are important because they enable mission designers to obtain a preliminary fuel budget as well as maneuver scheduling. Coplanar maneuvers usually consume less propellant than more general transfers wherein the orbital planes are modified. In this context, bi-impulsive maneuvers, such as the Hohmann transfer, are useful because they require a minimum number of thruster firings for each transfer between nonintersecting orbits. Under certain conditions, Hohmann transfers are optimal in the sense of minimizing the total velocity change. However, Hohmann transfers are designed to transfer a satellite between two collinear position vectors. When the initial and final position vectors are not collinear, one should consider other strategies. Several authors have studied the problem of optimal impulsive transfers. Munick et al. [1] provided a solution for optimal transfers from elliptic orbits to coplanar nonintersecting circular orbits using two velocity impulses. Lawden [2] derived a set of algebraic equations whose solution yields the optimal bi-impulsive transfer between two coplanar elliptic orbits. The obtained set of equations must be numerically solved. Battin [3] wrote an ‘2 cost function for a bi-impulsive transfer between twopositionvectors, assuming that the initial and final position and velocity vectors are all coplanar. The minimization of this cost function relies on numerical methods, since an eight-order algebraic equation must be solved. Battin’s development leads to necessary conditions, but no closed-form expressions for the optimal solution are provided. Broucke and Prado [4] studied the optimal coplanar transfer problem with two, three, and four impulses. They also obtained sets of algebraic equations that need to be numerically solved. Won [5] derived analytical conditions for the bi-impulsive transfer between elliptic coplanar coaxial orbits that minimize either the required velocity change or the transfer time. Ma et al. [6] developed an approach using the eccentricity vector, and derived equations to obtain the optimal bi-impulsive transfer between coplanar orbits. As in the previouslymentioned cases, the equationsmust be numerically solved.Conway and Pontani [7] derived optimal four-impulse orbital rendezvous maneuvers when both the chaser and target are in the same circular orbit with an initial phase difference of rad. They obtained general expressions for the change of velocity required by each impulse, and numerically optimized the total velocity change. An implicit assumption in most of the aforementioned works is that the propellant consumption is measured by the Euclidean norm of the velocity change vectors. This is appropriate if the satellite uses a single thruster to perform themaneuver, i.e., it regulates the attitude to align the nozzle with the required vector thrust. However, as also noted by others [8], in satellites that use multiple body-fixed orthogonal thrusters the mass consumption is measured by the ‘1-norm of the thrust vector rather than Euclidean norm. Thus, if Euclidean norms were used to find the fuel-optimal transfers for satellites equipped with body-fixed orthogonal thrusters (e.g., the Mango satellite in the PRISMA mission [9]), a nonfuel-optimal maneuver would be determined. Therefore, for satellites using orthogonal thrusters the optimization approach should be modified. With this consideration in mind, this work formulates the ‘1 cost function for a general coplanar transfer between two noncollinear position vectors with prescribed terminal velocities, and analytically determines the set of points that satisfy the necessary conditions for minima. Since this set includes only 14 points, it is easy to evaluate all of theminima candidates and obtain the globally optimal bi-impulsive maneuver for the mentioned scenario, avoiding numerical optimization processes. The derived analytical solution enables real-time onboard implementation.

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

AbstractThis 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.

Flight demonstration of new thruster and green propellant technology on the PRISMA satellite

The concept of a storable liquid monopropellant blend for space applications based on ammonium dinitramide (ADN) was invented in 1997, within a co-operation between the Swedish Space Corporation (SSC) and the Swedish Defense Research Agency (FOI). The objective was to develop a propellant which has higher performance and is safer than hydrazine. The work has been performed under contract from the Swedish National Space Board and ESA. The progress of the development has been presented in several papers since 2000. ECAPS, a subsidiary of the Swedish Space Corporation was established in 2000 with the aim to develop and market the novel “high performance green propellant” (HPGP) technology for space applications. The new technology is based on several innovations and patents w.r.t. propellant formulation and thruster design, including a high temperature resistant catalyst and thrust chamber. The first flight demonstration of the HPGP propulsion system will be performed on PRISMA. PRISMA is an international technology demonstration program with Swedish Space Corporation as the Prime Contractor. This paper describes the performance, characteristics, design and verification of the HPGP propulsion system for PRISMA. Compatibility issues related to using a new propellant with COTS components is also discussed. The PRISMA mission includes two satellites in LEO orbit were the focus is on rendezvous and formation flying. One of the satellites will act as a “target” and the main spacecraft performs rendezvous and formation flying maneuvers, where the ECAPS HPGP propulsion system will provide delta-V capability. The PRISMA CDR was held in January 2007. Integration of the flight propulsion system is about to be finalized. The flight opportunity on PRISMA represents a unique opportunity to demonstrate the HPGP propulsion system in space, and thus take a significant step towards its use in future space applications. The launch of PRISMA scheduled to 2009.

PRISMA: An In-Orbit Test Bed for Guidance, Navigation, and Control Experiments

This paper presents system-level hardware-in-the-loop real-time simulation results for three different guidance, navigation, and control experiments designed for in-flight demonstration on the PRISMA formation-flying satellite mission. The mission consists of two spacecraft: Main and Target The Main satellite has full orbit control capability, whereas Target is attitude-controlled only. Launch is planned for November 2009. The simulation results presented demonstrate the feasibility and readiness for flight as well as the expected in-flight performance. The three experiments include Global Positioning System and vision-based formation flying for two spacecraft in both passive and forced motion. In addition to these simulation results, the paper gives an overview of the PRISMA mission in general and the guidance, navigation, and control experiments in particular. The hardware-in-the-loop real-time test environment is also presented.

The precise autonomous orbit keeping experiment on the PRISMA mission

This paper analyzes the problem of autonomous control of the longitude of the ascending node (LAN) for a satellite in low Earth orbit (LEO) by means of along-track and anti-alongtrack velocity increments which adjust the semimajor axis. The problems related to the possibility of generating the reference orbit (RO) on-board and with the estimation of the atmospheric drag are considered. The Autonomous Orbit Keeping (AOK) experiment of the PRISMA formation flying mission will be the test platform of the control strategy here exposed. The AOK on-board software shall demonstrate autonomous orbit control using a guidance law for the orbit’s LAN and shall implement a deterministic control algorithm using along-track and anti-along-track velocity increments. Using GPS-based absolute navigation data, AOK shall command thruster activations in the orbital frame to autonomously control the orbit within a predefined window. The AOK experiment paves the way to the accurate and autonomous orbit control of LEO satellites on a routine basis. The main requirement of the experiment is to demonstrate an orbit control accuracy of the osculating ascending node of 10 m (1σ). The paper shows results from real-world software simulations where the accuracy of the reference orbit is limited and GPS sensors and hydrazine actuators are accurately modeled. The fundamental approach on which the software design, validation and testing is based, is also explained.

Autonomous Formation Flying for the PRISMA Mission

PRISMA is a technology demonstration mission for satellite formation flying and in-orbit servicing. The space segment comprises the fully maneuverable Main minisatellite and the smaller Target satellite in a low Earth orbit at 700-km altitude. A key mission objective is to demonstrate onboard, fully autonomous, robust, safe, and precise formation flying of spacecraft. This is accomplished by spaceborne global positioning system navigation, guidance, and control functionalities for the maintenance of the relative motion between the two spacecraft. An innovative estimation approach employs a common Kalman filter for the absolute states of Main and Target, which accounts for the interdependency of absolute and relative navigation without the need for an explicit relative state. As a result, the onboard navigation system provides absolute and relative orbit information in real time with a position accuracy of 2 and 0.1 m, respectively. The formation control achieves accuracies of a few tenths of meters with minimum usage of thrusters. The guidance and control concept is detailed with emphasis on a relative eccentricity and inclination vector separation strategy. The paper derives estimates of the expected relative orbit control performances based upon realworld simulations using typical global positioning system receiver and propulsion system characteristics.

FORMATION FLYING NAVIGATION AND CONTROL PROBLEMATICS AND APPLICATIONS

This paper describes issues encountered for Formation Flying missions when focusing on the impulsive relative positioning. To fulfil the stringent requirements imposed by the distributed instrument, efforts have been made to correctly model the dynamics, to perform onboard navigation filtering and to develop control algorithms. Direct application of these techniques is showed for the Prisma mission, and possible future extensions are presented for the Simbol-X and Pegase missions.

PRISMA: A Mission to Study Interior and Surface of Stars

AbstractNew technics such as asteroseismology are able to sound the deep interior of stars and to provide the data that will constrain the modelisation of the core. This information will be combined with data collected from the stellar surface which give direct access to measurements of the radiative losses, angular momentum losses and distribution of active structures. From the two sets of data, the key role of the convection zone will be clarified, as the convection zone excites the waves that propagate through the whole star and generates the magnetic field that structures the stellar surface. The PRISMA mission was developed to collect the data needed for detecting the oscillations by very accurate photometry (micromagnitude) and to derive the surface activity and rotation from accurate ultraviolet spectroscopy. A short description of the model payload is given with the observational constraints related to the needed accuracy of measurements. Following the non-selection by ESA in may 1993, some following perspectives are described.

Prisma-probing rotation and interior of stars: Microvariability and activity

The measurement of frequencies, amplitudes and lifetimes of solar oscillations has proven to be a very powerful tool to sound the properties of the solar internal structure. Combined with observations of emerging solar magnetic field parameters of the solar internal structure and dynamo can be inferred. The same techniques may be used to sound stellar interiors: asteroseismology and observation of magnetic activity (emerging magnetic fields). The observation of photometric fluctuations down to micromagnitudes on stars along or near the main sequence when complemented with measurements of activity levels will provide a wealth of information on the internal structure and rotation rates, and its evolutions with age. The PRISMA mission is an ESA Assessment Study currently underway. We present here the scientific objectives of the mission, the measurements to be made, the techniques to be used, and the main characteristics of a model payload.