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This paper presents a novel approach to the robust solution of optimal impulsive control problems under aleatory and epistemic uncertainty. The novel approach uses belief Markov decision processes to reformulate the control problem in terms of uncertainty distributions, called beliefs, rather than the realizations of the system states. This formulation leads to the definition of a belief optimal control problem where the cost function and constraints are functions of the uncertainty distributions. The control formulation encompasses orbit determination arcs as well. The belief optimization is solved with a shooting-like transcription and a nonlinear programming solver to optimize the resulting discretized problem. Both aleatory and epistemic uncertainties are propagated with a nonintrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimization of a flyby trajectory of the Europa Clipper mission in a scenario characterized by knowledge, execution, and observation uncertainty.

The endgame scenario that was explored in this analysis consisted of the part of the trajectory starting at the last Ganymede flyby and ending at the final Europa approach. The basic design components included computing the phasing for the final Ganymede encounter, computing the required intermediate Europa flybys, determining the required maneuvers to transition between the intermediate resonances, and interfacing with a computed portal prior to the final approach. The JPL optimization software, COSMIC, was used in the ephemeris model to optimize solutions computed in the circular restricted three-body problem and compute bounds on the attainable set of solutions by sweeping various design parameters.

For deep-space missions that remain in the vicinity of a target body, solar eclipses might become a source of major concern due to thermal and power constraints. This paper presents a method for minimizing the eclipse duration of periodic trajectories in three-body systems using synodic resonant periodic orbits. The proposed methodology successfully captures the global eclipse structure of synodic resonant periodic orbits in terms of driving parameters such as elongation and phase angles. Two-dimensional Eclipse maps are introduced to identify optimal orbit insertion conditions that avoid or minimize eclipse intervals. The validity and applicability of the proposed method is tested in the full-ephemeris model (DE430) of the Earth–Moon and Mars–Phobos systems, respectively. As a result of these investigations, we propose new science minimum-eclipse trajectories that are under consideration for the upcoming JAXA missions EQUULEUS and MMX.

EQUULEUS (EQUilibriUm Lunar-Earth point 6U Spacecraft) will be the world's smallest spacecraft to explore the Earth-Moon Lagrange point. It is being jointly developed by JAXA (Japan Aerospace Exploration Agency) and the University of Tokyo, and will be launched by NASA's Space Launch System Exploration Mission-1. The spacecraft will fly to a libration orbit around the Earth-Moon L2 point (EML2) and will demonstrate low-energy trajectory-control techniques within the Sun-Earth-Moon region for the first time by a nano-class spacecraft. EQUULEUS also carries three scientific observation missions: imaging of Earth's plasmasphere by extreme ultraviolet wavelength, lunar impact flash observation on the far side of the moon, and micrometeoroid flux measurements in the cis-lunar region. While all these missions have their own scientific objectives, they will also contribute to future human activity and/or infrastructure development in the cis-lunar region. Most parts of the spacecraft system use commercial off-the-shelf components, or are designed based on the experiences of various past space missions, with the exception of the newly developed water resistojet propulsion system. EQUULEUS uses X-band frequency for deep space telecommunication. Japanese deep space antennas (64-m and 34-m) will be nominally used for spacecraft operation, and support from the deep space network of JPL (Jet Propulsion Laboratory) is also being planned, especially for the initial phase of operation. The spacecraft will fly to EML2 in less than one year, and will remain there for scientific observations until shortly before the depletion of the onboard propellant, when the spacecraft will leave the orbit for space-debris compliance.

This paper presents the trajectory design for EQUilibriUm Lunar-Earth point 6U Spacecraft (EQUULEUS), which aims to demonstrate orbit control capability of CubeSats in the cislunar space. The mission plans to observe the far side of the Moon from an Earth-Moon L2 (EML2) libration point orbit. The EQUULEUS trajectory design needs to react to uncertainties of mission design parameters such as the launch conditions, errors, and thrust levels. The main challenge is to quickly design science orbits at EML2 and low-energy transfers from the post-deployment trajectory to the science orbits within the CubeSat’s limited propulsion capabilities. To overcome this challenge, we develop a systematic trajectory design approach that 1) designs over 13,000 EML2 quasi-halo orbits in a full-ephemeris model with a statistical stationkeeping cost evaluation, and 2) identifies families of low-energy transfers to the science orbits using lunar flybys and solar perturbations. The approach is successfully applied for the trajectory design of EQUULEUS.

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.

Europa is one of the most scientifically interesting targets of the solar system, as it may possess what are thought to be the three necessary ingredients for life: an extensive ocean of liquid wat...

This is a COSPAR roadmap to advance the frontiers of science through innovation and international collaboration using small satellites. The world of small satellites is evolving quickly and an opportunity exists to leverage these developments to make scientific progress. In particular, the increasing availability of low-cost launch and commercially available hardware provides an opportunity to reduce the overall cost of science missions. This in turn should increase flight rates and encourage scientists to propose more innovative concepts, leading to scientific breakthroughs. Moreover, new computer technologies and methods are changing the way data are acquired, managed, and processed. The large data sets enabled by small satellites will require a new paradigm for scientific data analysis. In this roadmap we provide several examples of long-term scientific visions that could be enabled by the small satellite revolution. For the purpose of this report, the term “small satellite” is somewhat arbitrarily defined as a spacecraft with an upper mass limit in the range of a few hundred kilograms. The mass limit is less important than the processes used to build and launch these satellites. The goal of this roadmap is to encourage the space science community to leverage developments in the small satellite industry in order to increase flight rates, and change the way small science satellites are built and managed. Five recommendations are made; one each to the science community, to space industry, to space agencies, to policy makers, and finally, to COSPAR.

This paper presents a belief-based formulation and a novel approach for the robust solution of optimal control problems under uncertainty. The introduced formulation, based on the Belief Markov Decision Process model, reformulates the control problem directly in terms of uncertainty distributions, called beliefs, rather than on realisations of the system state. Successively, an approach inspired by navigation analysis is developed to transcribe and solve such problem in the presence of observation windows, employing a polynomial expansion for the dynamical propagation. Finally, the developed method is applied to the robust optimisation of a flyby trajectory of Europa Clipper mission in a scenario characterised by knowledge, execution and observation errors.

Low-thrust propulsion is a key technology for space exploration, and much work in astrodynamics has focused on the mathematical modeling and the optimization of low-thrust trajectories. Typically, ...

Following their success in low Earth orbit, nanospacecraft weighing less than 25 kg may soon contribute to the exploration of the Solar System. This paper outlines the necessary technologies that e...

Accepted: 2017-03-17, 資料番号: SA1170152000

Accepted: 2015-11-07, 資料番号: SA1150267000

Akatsuki (“dawn” in Japanese) is the JAXA Venus orbiter that was scheduled to enter orbit around Venus on Dec. 7 th , 2010. Following the failure of the main engine during the orbit insertion maneuver, the spacecraft escaped Venus on a 200-day orbit around the Sun, only to return in early 2017. This paper presents the design and implementation of the recovery trajectory, which involves perihelion maneuvers to re-encounter Venus in late 2015. Relying only on the onboard propellant, the trajectory rescued the mission by (1) anticipating the beginning of the science phase within the nominal lifetime of the spacecraft, and (2) halving the Δv requirements for the orbit insertion maneuver. Several trajectories are designed with an innovative use of a technique called non-tangent V-Infinity Leveraging Transfers (VILTs). Candidate solutions are then recomputed in higher fidelity models, and one solution is finally selected for its low Δv requirements and for programmatic reasons. The results of the perihelion maneuver campaign are also presented.

In early 2013, the European Space Agency (ESA) invited the scientific community to propose themes for the next decades of fag-ship missions (specifically for the next L-class missions, L2 and L3). Researchers from European, American, and Japanese institutions submitted a white paper on the scientific case for a mission to Neptune and Triton. The document included an example mission concept and aimed to demonstrate that the proposed science theme can be addressed with technology that is expected to become available within the L2 and L3 time frames (2028 and 2034). We present here the trajectory design for the mission concept and a high-level discussion on its feasibility, which was included in the white paper. We also present details on the example Triton tour, a new search for interplanetary transfers, and a preliminary analysis of the gravity losses at Neptune orbit insertion (NOI), which suggests the use of a large chemical propulsion system.

Accepted: 2014-11-25, 資料番号: SA1150045000

This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.

第17回宇宙科学シンポジウム (2017年1月5日-6日. 宇宙航空研究開発機構宇宙科学研究所(JAXA)(ISAS)相模原キャンパス), 相模原市, 神奈川県, 17th Space Science Symposium (January 5-6, 2017. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency(JAXA)(ISAS)Sagamihara Campus), Sagamihara, Kanagawa Japan, 著者人数: 18名, 資料番号: SA6000060066, レポート番号: P-024

An analysis is presented of gravity assisted flybys in the planar, circular, restricted three-body problem (pcr3bp) that is inspired by the Keplerian map and by the Tisserand- Poincare graph. The new Flyby map is defined and used to give insight on the flyby dynamics and on the accuracy of the linked-conics model. The first main result of this work is using the Flyby map to extend the functionality of the Tisserand graph to low energies beyond the validity of linked conics. Two families of flybys are identified: Type I (direct) flybys and Type II (retrograde) flybys. The second main result of this work shows that Type I flybys exist at all energies and are more efficient than Type II flybys, when both exist. The third main result of this work is the introduction of a new model, called “Conics, When I Can”, which mixes numerical integration and patched conics formulas, and has applications beyond the scope of this work. The last main result is an example trajectory with multiple flybys at Ganymede, all outside the linked-conics domain of applicability. The trajectory is computed with the pcr3bp, and connects an initial orbit around Jupiter intersecting the Callisto orbit, to an approach transfer to Europa. Although the trajectory presented has similar time of flight and radiation dose of other solutions found in literature, the orbit insertion Δv is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.

In response to the scientific interest in Jupiter's Galilean moons, NASA and ESA have plans to send orbiting missions to Europa and Ganymede, respectively. The inter-moon transfers of the Jovian system offer obvious advantages in terms of scientific return, but are also challenging to design and optimize due in part to the large, often chaotic, sensitivities associated with repeated close encounters of the planetary moons. The approach outlined in this paper confronts this shortcoming by exploiting the multi-body dynamics with a patched three-body model to enable multiple “resonant-hopping” gravity assists. Initial conditions of unstable resonant orbits are pre-computed and provide starting points for the elusive initial guess associated with the highly nonlinear optimization problem. The core of the optimization algorithm relies on a fast and robust multiple-shooting technique to provide better controllability and reduce the sensitivities associated with the close approach trajectories. The complexity of the optimization problem is also reduced with the help of the Tisserand–Poincare (T–P) graph that provides a simple way to target trajectories in the patched three-body problem. Preliminary numerical results of inter-moon transfers in the Jovian system are presented. For example, using only 59 m/s and 158 days, a spacecraft can transfer between a close resonant orbit of Ganymede and a close resonant orbit of Europa.

The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple impulsive maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent impulsive maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δv change of

This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture A v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the ν ∞ -leveraging-maneuver approach leads to high-Δ ν, short-time-of-flight transfers, and the multibody technique leads to low-Δν, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the ν ∞ -leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Δν of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

Renewed interest by ESA and NASA in missions to Europa, Ganymede, Enceladus, and Titan poses the question of how to best solve the endgame problem. Endgames typically aim at an inexpensive insertion maneuver into the science orbit and can be designed using either V ∞ -leveraging maneuvers or the multibody dynamics. Although historically linked to insertion maneuvers, the endgame problem is symmetric and equally applies to departure. In this two-part series, we analyze and draw connections between the two apparently separate approaches, providing insight into the dynamics of the multibody gravity-assist problem. In this paper we derive new formulas for the V ∞ -leveraging maneuver and build the leveraging graph to be used as a reference guide for designing endgame tours. We prove that the cost of a V ∞ -leveraging-maneuver sequence decreases when using high-altitude flybys (as done in the multibody technique). Finally, we find a simple quadrature formula to compute the minimum ΔV transfer between moons using V ∞ -leveraging maneuvers, which is the main result of the paper, and a method to estimate transfer times. The leveraging graphs and associated formulas are derived in canonical units and therefore apply to any celestial system with a smaller body in a circular orbit around a primary. Specifically, we demonstrate the new method to provide rapid calculations of the theoretical boundary values for ΔV requirements and estimated transfer times for moon tours in the Saturn and Jupiter systems using the V ∞ -leveraging-maneuver model.

This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application, this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories.

著者人数: 26名, Accepted: 2014-05-12, 資料番号: SA1005020000

Several Hall thrusters (e.g. BPT-4000, BHT-600, SPT-100, etc.) are able that operate with useful thrust at the sub-kilowatt power levels that would be available from solar arrays at Jupiter distance. We have found that a combination of a multi-kilowatt thruster (e.g. the BPT-4000) for the interplanetary trajectory with a sub-kilowatt thruster (e.g. the BHT-600) is sufficient for a Europa flyby mission. A roughly 1200 kg spacecraft using this propulsion approach would be able to launch on a Falcon 9 and reach Jupiter in 4.9 years. We demonstrate the feasibility of a Solar Electric Propulsion (SEP) Jovian tour with an example tour that reaches Europa 1.6 years after Jupiter arrival with a remaining capability of 400 m/s of ΔV for additional flybys.

[1] This paper presents the expected accuracy of the tides and gravity of Europa that can be measured by tracking a spacecraft during close flybys of Europa. A reference trajectory was designed for flyby science observations and consists of a total of 36 flybys of Europa at 100 km altitude. Earth-based Doppler measurements were created during ±2 hours of each periapsis passage and were simulated with realistic dynamical and measurement assumptions. The result shows that the degree 2 tidal Love number,k2, can be estimated to σk2 = 0.045 and σk2= 0.009 (1-sigma formal uncertainty) assuming X-band and Ka-band tracking capabilities, respectively, which is sufficient to confirm the existence of a global subsurface ocean.

The BepiColombo mission to Mercury includes a lunar swingby before leaving the Earth-Moon system. This paper summarizes the launch window design, which is based on a phasing loop strategy: the spacecraft remains in a highly eccentric Earth orbit for several loops before lunar the gravity assist. To control the luni-solar perturbations, tangential manoeuvres are introduced at the pericentre passages. An optimization tool is used to generate, for each launch date, a numerically integrated trajectory that matches the subsequent heliocentric trajectory while minimizing the total ? V of the manoeuvres. Additional trajectories for a ±3σ launcher error in the apogee altitude are calculated for each launch date. Two different types of trajectories are investigated: in the first approach, the apogee altitude of the initial orbit is esse ntially unconstrained, so that, for most of the launch dates, the initial apogee lies above the Moon distance. In the second approach, the initial apogee is constrained to be below the Moon distance. The results obtained show that, for both options and due to the different effect of the Sun perturbation, the lunar swingby opportunities in June and July 2012 are clearly more favorable than those in August, September and October. Comparing both options, an initial apogee below the Moon distance leads to more possible launch dates per launch window and a smaller ΔV cost to correct for the launcher dispersion.

In this paper a preliminary analysis of a wide range of mission opportunities, offered by either aerogravity assist or gravity assist manoeuvres, has been carried out. After an accurate validation of aerogravity assist traditional analytical models, according to several different criteria an extensive global search for optimal trajectories has been performed for highenergy missions, resorting to gravity and aerogravity manoeuvres. To this aim, the new preliminary analysis tool PAMSIT, based on some simplified hypotheses, has been developed. This is capable of efficiently and exhaustively exploring the solutions space for this particular problem, considering the feasibility of a trajectory from both the orbital energy and phasing points of view. Then, all found solutions have been classified according to launch and arrival velocities, time of flight and planetary encounters. A comparison between the opportunities offered by gravity manoeuvres and aerogravity manoeuvres will be presented showing the advantages of the latter in all analysed cases. In particular some interesting options for missions to Jupiter and Neptune will be presented.

This paper shows how the BepiColombo trajectory near Mercury follows the invariant manifolds to its final capture. The BepiColombo gravitational capture provides several recovery opportunities at nominal conditions and was designed by exploring the solution space entirely, without knowledge of the invariant manifolds. In this work we reproduced the trajectory in the model of the elliptic restricted three body- problem ( due to the high eccentricity of Mercury’s orbit) and showed t hat it does follow the manifolds. Consequently we envision that manifolds should be used to give insight on the solution space, speeding up the design and optimization process and there by saving cost. Copyright line will be provided by the publisher