Although the idea of a planetary satellite tour had been the subject of technical consideration since the early 1970s, the Galileo mission to Jupiter marked the first time that gravity assists were used to enable a scientific tour of a planetary satellite system. From December 1995 to September 2003, Galileo performed 33 flybys of Io, Europa, Ganymede and Callisto during its survey of the Jovian system. The Galileo tour design was a manual process where STOUR was employed to perform the initial ballistic patched-conic design 2. This solution was then input to MOSES, which used the multiconic method to produce a trajectory that approximated the influence of other gravitating bodies, SRP etc [22], before finally being forward integrated in high-fidelity.
The Cassini spacecraft is currently completing the final week of its twenty year mission, most of which has been spent orbiting the planet Saturn. Cassini’s tour of Saturn’s moons is significantly more sophisticated than Galileo’s. To respond to this, the Computer Algorithm for Trajectory Optimization (CATO) software was developed, which integrated the spacecraft’s equations of motion subject to the point mass gravitational effects of other bodies, SRP and the oblateness of the central body [122, 123].
1.4.1 Flyby Combinatorics
The human lifespan, combined with a general unwillingness to wait large spans of time before receiving scientific returns from a mission, limits the number of gravity-assists that interplanetary spacecraft missions can reasonably use (to perhaps not greater than ten)3. By contrast, a planetary satellite tour can include hundreds of gravity-assists, as was the case with the Cassini mission where the orbiter performed 162 targeted moon flybys over the course of its 13 year exploration of the Saturnian system. As a result of this disparity,
2Prior to its automation by Steve Williams [121], the STOUR search process was entirely user-interactive
3The most number of GAs used by a spacecraft during its interplanetary cruise, to date, is six by the MESSENGER spacecraft.
many of the search techniques that have been shown to be effective for interplanetary MGA design encounter severe limitations when applied to satellite tour problems.
Heuristic methods such as genetic algorithms were first applied to the interplanetary MGA problem in order to help cope with the large dimension of the flyby pathfinding problem. Even for relatively modest problems where the chromosome length is perhaps only 10-15 bits in length, a genetic algorithm run can last days or weeks in order to ensure that the design space has been properly explored and that the population has maturely evolved. Tour problems represent a significantly more complex pathfinding problem, and some variation of the branch and bound method remains the only practical approach to contend with such a large design space in an acceptable amount of time. Of course, as discussed in section 1.2.3, the branch and bound method does not consider the entire search space and so any advances made in methods that more thoroughly explore the design space of extremely high dimensional pathfinding problems, such as planetary satellite tours, are valuable.
In order to illustrate the computational complexity associated with different MGA problems, first consider a mission from Earth to Jupiter, where we limit valid intermediate flyby targets to Earth, Venus or Mars.
If the choice during each phase of the problem is to just flyby either Earth, Venus or Mars, and we let the spacecraft perform up to five flybys on its way to Jupiter, there exist 243 different flyby combinations of Earth, Venus and Mars (e.g E-EVEEM-J). For comparison, let’s assume that the Galileo spacecraft had exactly four flyby options for each phase of its Jupiter tour: perform a flyby of either Io, Europa, Ganymede or Callisto. For its 33 flyby tour, there exists 7.3786976 × 1019unique flyby combinations of the four Galilean moons.
1.4.2 Automation
Automation of the flyby sequence search for gravity-assist trajectories is a highly desirable capability, and is the subject of several ongoing research efforts. Regarding interplanetary trajectories, the work of Englander and Conway is arguably the most advanced. Certainly it has enjoyed the most success to date, with their methods being applied to produce the final optimized trajectory for the recently selected NASA Discovery class Lucy mission. That body of research has shown that a HOC automaton is capable of automating the interplanetary mission design process. These methods have not yet been extended to the design of planetary satellite tours.
Significant work has been performed that has enabled automated pathfinding and pathsolving of the satellite tour problem. The most conceptually straightforward methods are based on exhaustive grids. The
STOUR software was used during the preliminary design phase of the Galileo tour [22] albeit as a user-in-the-loop application. As previously mentioned, STOUR was eventually automated and served as one of the many inspirations for what is probably the most advanced pathsolving tools capable of preliminary design of a gas giant moon tour, Explore [9]. Explore is similar to STOUR in that it is an exhaustive grid-based MGA search method. In addition to patched Lambert C3 matching routines, Explore incorporates more sophisticated trajectory elements such as v-infinity leveraging maneuver (VILM)s [124] and nπ transfers [66]
as well as advanced search logic such as Pareto pruning algorithms. Explore was employed to produce the third place solution for the GTOC 6 problem. That competition also saw other groundbreaking work in satellite tour design. Izzo et al. [74] developed a completely automated tree search algorithm that employed a parallel asynchronous island optimization algorithm.
Where the previously mentioned studies have focused on the design of the entire tour, there have also been studies that focused on the automation of specific aspects of a moon tour mission. The work of Lynam [125,126] and Didion and Lynam [127] was specifically concerned with exhaustive searches for double and triple flyby capture sequences at the beginning of a tour. These works produced an extensive library of precomputed capture sequences spanning several decades. Valid interplanetary trajectories were then identified for a particular capture solution via backwards propagation. These studies relied on analytic derivations of the required satellite phasing constraints and incoming interplanetary velocity asymptotes required to produce a feasible capture. While interesting, this body of work is not particularly conducive to a rapid preliminary design cadence.
The state-of-the-art for automated capture design was recently advanced by Scott et al. [128], who developed a strategy for designing a capture sequence that is subject to practical constraints that are placed on the interplanetary trajectory. That is to say, their method is flexible enough to design a capture trajectory based deviations from an already-established nominal interplanetary arrival asymptote. In that respect, their work represents a significant increase in utility from a practical preliminary mission design standpoint over Lynam’s exhaustive solution database methods.
Automatic design of satellite capture and tour trajectories is one of the most challenging problems in modern astrodynamics, and remains an active research area. This work revisits the automated tour pathsolving problem in part where Lantukh’s work on Explore left off, by investigating parallelization of the underlying flyby tree search algorithm as well as the transition from a C3 matching Lambert grid solution to a direct optimization transcription that is capable of locally optimizing an entire end-to-end moon tour problem.
1.4.3 Path Constraints and Hazard Avoidance
The development of an automated method for designing planetary satellite tours must be flexible enough to accommodate practical engineering considerations, such as environmental hazards. Formulating a useful tour solution is not as simple as stringing together as many flybys as possible given a certain quantity of propellant. The environment around the giant planets Jupiter and Saturn are hostile regions for spacecraft to operate in. The Jupiter-Io plasma torus is one of the most radioactively hazardous areas for a spacecraft to fly through. Extended periods of time spent in this region close to the planet will rapidly degrade all but the most radiation-hardened electronics, and practical tour design in the Jovian system must take this into account [129]. High relative-velocity collisions with the debris and dust that can be found in planetary ring structures can be catastrophic to spacecraft and present another navigational hazard when designing and flying trajectories in close proximity to the giant planets. A particularly interesting example of an environmental factor that will impact future mission design is the high-inclination of the Uranian system caused by the planet’s 97 degree axial tilt relative to the ecliptic plane. Any spacecraft that will go into orbit around Uranus in the future will have to avoid the planet’s rings and also contend with inclination reduction should one of its goals be close-proximity exploration of Uranus’s moons [130].
In addition to natural phenomena that require the imposition of path constraints on a trajectory, other mission requirements also place constraints on a spacecraft performing a satellite tour. One of the most common of these is line-of-sight communications constraints. In order to communicate wih the ground, a spacecraft’s high gain antenna must point towards Earth. Since most interplanetary spacecraft buses do not have articulating high-gain mounts, this means slewing the entire spacecraft, which then places restrictions on when maneuvers can occur. Perhaps even more consequential is whether a particular obtained tour solution is viable from a navigational perspective. The short encounter to encounter times during a tour can become a serious concern when assessing the risk associated with the navigation of the spacecraft. This is one of the major concerns with multiple satellite-aided captures at a gas giant, as studied by Lynam [126].
The automated methods described in chapter 6 do not directly address these concerns, however, the general automated tour solving framework described in that chapter does not preclude the future inclusion of environmental and operational constraints into the search process.