19 research outputs found
On the advantages of exploiting the hierarchical structure of astrodynamical models
No full textIn this paper an algorithm is developed that combines the capabilities and advantages of several different astrodynamical models of increasing complexity. Splitting these models in a strict hierarchical order yields a clearer grasp on what is available. With the effort of developing a comprehensive model overhead, the equations for the spacecraft motion in simpler models can be readily obtained as particular cases. The proposed algorithm embeds the circular and elliptic restricted three-body problems, the four-body bicircular and concentric models, an averaged n-body model, and, at the top hierarchic ladder, the full ephemeris SPICE-based restricted n-body problem. The equations of motion are reduced to the assignment of 13 time-varying coefficients, which multiply the states and the gravitational potential to reproduce the proper vector field. This approach yields an efficient and quick way to check solutions for different dynamics and parameters. We show that in bottom-up applications, a gradual increase of model complexity benefits accuracy, the chances of success and the convergence rate of a continuation algorithm. Case studies are simple periodic orbits and low-energy transfers
On the Advantages of Using a Strict Hierarchy to Model Astrodynamical Problems
No full textIn this paper an algorithm is developed that combines the capabilities and advantages of several different astrodynamical models of increasing complexity. Splitting these models in a strict hierarchical order yields a clearer grasp on what is available. With the effort of developing a comprehensive model overhead, the equations for the spacecraft motion in simpler models can be readily obtained as particular cases. The proposed algorithm embeds the circular and elliptic restricted three-body problems, the four-body bicircular and concentric models, an averaged n-body model, and, at the top hierarchic ladder, the full ephemeris spice-based restricted n-body problem. The equations of motion are reduced to the assignment of 13 time-varying coefficients, which multiply the states and the gravitational potential to reproduce the proper vector field. This approach is powerful because it allows, for instance, an efficient and quick way to check solutions for different dynamics and parameters. It is shown how a gradual increase of the dynamics complexity greatly improves accuracy, the chances of success and the convergence rate of a continuation algorithm, applied to low-energy transfers
Trajectory Refinement of Three-Body Orbits in the Real Solar System Model
No full textIn this paper, an automatic algorithm for the correction of orbits in the real solar system model is described. The differential equations governing the dynamics of a massless particle in the n-body problem are written as perturbation of the circular restricted three-body problem in a non-uniformly rotating, pulsating frame by using a Lagrangian formalism. The refinement is carried out by means of a modified multiple shooting technique, and the problem is solved for a finite number of trajectory states at several time instants. The analysis involves computing the dynamical substitutes of the collinear points, as well as several Lagrange point orbits, for the the Sun–Earth, Sun–Jupiter, and Earth–Moon gravitational systems
Automated Trajectory Refinement of Three-Body Orbits in the Real Solar System Model
No full textIn this paper, an automatic algorithm for the correction of orbits in the real solar system model is described. The differential equations governing the dynamics of a massless particle in the n-body problem are written as perturbation of the restricted three-body problem in a non-uniformly rotating, pulsating frame by using a Lagrangian formalism. The refinement is carried out by means of a multiple shooting technique, and the problem is solved for a finite set of variables. Results are given for the dynamical substitutes of the collinear points of several gravitational systems, as well as for periodic three-body orbits
Survey of Mars Ballistic Capture Trajectories using Periodic Orbits
No full textA systematic approach is devised to find ballistic captures in the planar elliptic restricted three-body problem. Simple symmetric periodic orbits around the secondary body of the circular problem, computed through a global grid search, are used as generators for ballistic captures in the elliptic problem. Combining a scaling factor that maps states from the circular to the elliptic case and restricting the motion to emanate from periodic solutions, the search space for ballistic capture is reduced to three dimensions. Results in the Sun-Mars system indicate an abundance of long time-of-flight regular solutions with a variety of characteristics, including low osculating eccentricities
Design and Validation of Ultra Low Thrust Transfers to the Sun-Earth Saddle Point with Application to LISA PathFinder Mission Extension
No full textIn this paper we present methods and concepts to design and validate highly nonlinear orbits characterized by ultra low control. These features are met when flying through the Saddle Points, which are location in the Solar System when gravitational accelerations balance. Trajectory optimization is embedded into high-fidelity environments, where accurate description of the spacecraft natural and controlled motion is achieved. Orbit determination and navigation analysis rely on high-fidelity models for both the space and ground segments assets as well. Tools have been developed and applied to the case of the possible mission extension of Lisa Pathfinder
Optimal injection into Quasi-Satellite Orbits around Phobos: application to MMX mission
No full textThe Japan Aerospace Exploration Agency is aiming to launch in 2024 the Martian Moons eXploration mission. The main scientific objective is to survey the two Martian moons and to return a sample from the surface of Phobos. As nominal scientific orbits, several Quasi-Satellite Orbits around Phobos have been computed and adopted in consideration of the complex dynamical environment characteristic of the Mars--Phobos system. This paper explores the performance capability of a multi-impulsive control strategy to inject the MMX probe into a host of QSOs around Phobos, after a heliocentric journey from the Earth. A perturbation analysis in the vicinity of Phobos is performed using several gravitational models of increasing fidelity. Results show that the CR3BP is a suitable model for this analysis. Finally, a control strategy for the multi-impulsive transfer to Phobos QSOs is presented and, starting from a grid of initial states, optimal QSO injection trajectories are evaluated and discussed
A Note on a Geometrical Method to Solve Spacecraft Formation Flying Control
No full textSpacecraft formation flying is becoming more important since the use of multiple satellites has been demonstrated to be cost-effective. In some applications, the spacecraft need to satisfy certain geometrical constraints; e. g. regarding formation pointing. In this paper an efficient method has been devised that minimises the variation of orbital elements to achieve the requested states. The positions that minimise displacement from a reference plane are computed, and the compatible velocities that reduce shape and plane variation for all S/C are evaluated. This allows to find optimal values for a TPBVP. The algorithm has been applied to close-range GEO formations
Design of robust maneuvers for the MMX mission: a chance-constraint optimization perspective
No full textThe design of spacecraft trajectories in nonlinear dynamical systems subject to model uncertainty and disturbances is a complex and demanding task. Methods based on robust optimization consist in accounting, within the optimization process, for the possibility of having an imperfect knowledge of state and control variables. This allows to obtain a solution in which, a priori, a small amount of propellant is traded for reduced sensitivity to uncertainties and state errors, mitigating in this way the risk of partial or complete mission failure.
In this manuscript, a chance-constraint optimization method is conceived and applied to design a robust impulsive approaching trajectory for a spacecraft aimed at the Martian moon Phobos. The trajectory starts at the end of the heliocentric journey from the Earth with given uncertainty on initial conditions. Spacecraft states and control are regarded as probability distributions over time while unscented transformation is used for efficient propagation of these distributions through nonlinear stochastic system dynamics. Numerical results are presented for a case study related to the future sample return mission MMX of the Japanese Aerospace Explorations Agency (JAXA)
Mission design of DESTINY+: toward active asteroid (3200) Phaethon and multiple small bodies
No full textDESTINY+ is an upcoming JAXA Epsilon medium-class mission to fly by the Geminids meteor shower parent body (3200) Phaethon. It will be the world’s first spacecraft to escape from a near-geostationary transfer orbit into deep space using a low-thrust propulsion system. In doing so, DESTINY+ will demonstrate a number of technologies that include a highly efficient ion engine system, lightweight solar array panels, and advanced asteroid flyby observation instruments. These demonstrations will pave the way for JAXA’s envisioned low-cost, high-frequency space exploration plans. Following the Phaethon flyby observation, DESTINY+ will visit additional asteroids as its extended mission. The mission design is divided into three phases: a spiral-shaped apogee-raising phase, a multi-lunar-flyby phase to escape Earth, and an interplanetary and asteroids flyby phase. The main challenges include the optimization of the many-revolution low-thrust spiral phase under operational constraints; the design of a multi-lunar-flyby sequence in a multi-body environment; and the design of multiple asteroid flybys connected via Earth gravity assists. This paper shows a novel, practical approach to tackle these complex problems, and presents feasible solutions found within the mass budget and mission constraints. Among them, the baseline solution is shown and discussed in depth; DESTINY+ will spend two years raising its apogee with ion engines, followed by four lunar gravity assists, and a flyby of asteroids (3200) Phaethon and (155140) 2005 UD. Finally, the flight operations plan for the spiral phase and the asteroid flyby phase are presented in detail
