Research paperLow-thrust trajectory optimization for the solar system pony express
Introduction
Telecommunications is a fundamental aspect of space exploration. Satellites, interplanetary spacecraft, landers and rovers are crucial assets designed to acquire data and transmit it back to Earth, where thorough analysis and investigation helps further our collective knowledge of the Solar System and the Universe. Often, the impact of a scientific mission is assessed based on the amount of data it returned over its lifetime and the number of publications that made use of the data. The data volumes generated by a mission depend on several factors, such as the design of the spacecraft, the technology used for telecommunication, and the distance from Earth.
Currently, NASA supports interplanetary spacecraft missions using the Deep Space Network (DSN). The DSN is a global radio telecommunication network composed of three ground complexes, spaced apart by about 120 around the Earth, and each facility operates several 34-m antennas and one 70-m antenna. Thanks to the strategic placement of the facilities and the large dish antennas, the DSN is able to constantly communicate with spacecraft over interplanetary distances. However, the use of radio waves and the large distances between the antenna and the probes mean that the links are power-starved, which restricts the maximum data volume, and as a result restricts the maximum data volume that a mission can return. In addition, the DSN is a resource that is shared by many missions which further reduces the data volume that can be returned by a single probe.
The Solar System Pony Express (SSPE) [1] is a mission concept that is being investigated at the Jet Propulsion Laboratory as part of the NASA Innovative Advanced Concepts (NIAC) program. The objective of the study is to augment the data transmission rates of the DSN using the idea of data mules. Data mules are small spacecraft that travel to a remote location (e.g., Mars) where they acquire data in close range to the probe’s transmitter and then carry the data back to Earth where it is downlinked in close range to the receiver. This enables high latency and high bandwidth communication. In the case of a space network, the data transmission rates can be further increased by utilizing optical telecommunications (e.g., Gbps have been demonstrated in an optical link between the Moon and Earth, a value at least one order of magnitude larger than with RF communication systems), which allows for a larger bandwidth but also requires strict pointing accuracy [2].
A network of interplanetary data mules could be established by exploiting cycler orbits [3]. These are trajectories that regularly encounter two or more celestial bodies along their path and require a modest amount of propellant for trajectory correction maneuvers. For the purpose of this study we simulate a network of Earth–Mars cyclers, but the concept could be extended to Venus [4] or the outer planets [5]. In the current mission scenario, one or more smallsats could be launched as a secondary payload onboard a mission bound for Mars. A simplified diagram of the mission concept is shown in Fig. 1. After launch, the data mules use their own low-thrust propulsion system to inject into a cycler orbit and target subsequent flybys of Earth and Mars. During the Mars flybys, data is uplinked from spacecraft already operating at Mars (in orbit or on the surface) and during Earth flybys data is downlinked back to Earth.
In this paper we focus specifically on the trajectory design and optimization of Earth–Mars cycler orbits for the SSPE mission. We simulate trajectories that make use of low-thrust propulsion and include a high-fidelity model that incorporates the gravity of the Sun, Earth and Mars. Low-thrust space missions are becoming more common due to the benefits afforded by ion engines, which are more efficient than chemical engines due to their high specific impulse. They are also much smaller/lighter which allows for the design of smaller spacecraft that can be launched economically as a secondary payload.
Two main classes of methods are used to solve for low-thrust spacecraft trajectories. The first class, direct methods, transcribes the system dynamics into a nonlinear programming problem. Generally, direct methods are robust to an initial guess, but are computationally expensive and are not guaranteed to result in an optimal solution. The second class, indirect methods, seeks to satisfy the necessary conditions for optimality. Although indirect methods ensure that the solution is at least locally optimal, they are extremely sensitive to initial guesses and convergence can be difficult. To overcome this challenge, we apply hyperbolic tangential smoothing to the thrust profile and generate the optimal bang–bang thrust profile by continuation [6], [7], which improves convergence significantly. The indirect method with continuation has proven to be very reliable and is the method of choice for this paper.
Section snippets
Indirect optimal control formulation
Modified Equinoctial Elements (MEEs) [8] are chosen to propagate the dynamics of the spacecraft. Compared to other element sets, such as the classical orbital elements or Cartesian coordinates, the MEEs present several advantages that make them well-suited for multi-revolution low-thrust trajectory optimization. The first five elements behave as slow variables, in contrast to Cartesian coordinates which are all fast variables. Slow variables are particularly attractive from a numerical
Trajectory design
In this section we investigate the use of solar electric propulsion (SEP) as a means to inject the data mule spacecraft into the Earth–Mars cycler orbit and to maintain the cycler orbit by targeting selected Earth and Mars flybys. Our aim is to design trajectories in the ephemeris model that minimize the amount of propellant required for injection and cycler maintenance while maximizing the amount of data that can be uplinked and downlinked during the respective Earth and Mars flybys. During
Results
Following the steps above, we were able to converge 278 out of 2225 STAR’s patched conic trajectories in the ephemeris model using impulsive thrust only (i.e. up to step 3), and 3 trajectories all the way through step 5. An overview of the fully converged solutions is shown in Table 1. Our investigation revealed that most of the propellant budget is required for COI, and once the spacecraft is on the cycler orbit a minimal amount of fuel ( kg) is needed to maintain the orbit and target flybys.
Cross-link analysis
We now demonstrate the communication performance achievable from a data mule flying according to solution A in Table 1. In particular, Fig. 16 shows the distance of the data mule from Earth and Mars respectively, as a function of mission duration. Two Earth flybys and three Mars flybys are apparent, which correspond to the different entries of Table 1.
To estimate the total data volume returnable using the data mule we first assume that the optical crosslink at Mars limits the overall system
Future work
The minimal amount of propellant required for cycler orbit targeting in the ephemeris model opens the door to considering even smaller and cheaper classes spacecraft. As mentioned previously, the bulk of the propellant mass for the mission was needed for the COI. Other technology such as using a space tug to inject multiple smaller spacecraft (i.e. kg) into the cycler orbit would eliminate the need for a large on board COI propulsion system, thus further reducing the size of the cycler
Conclusion
We have developed a method for designing and optimizing Earth–Mars cycler trajectories for the Solar System Pony Express (SSPE). For this mission concept, data mules are launched as a rideshare payload with another Mars-bound mission. Each data mule flying in the SSPE network is equipped with a low-thrust propulsion system that is used for cycler orbit injection and for targeting the flybys of Earth and Mars. Cycler orbits are first computed using a patched conic approximation and impulsive
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, and at the University of Illinois at Urbana-Champaign, under a contract with the National Aeronautics and Space Administration. This work was funded by the NASA NIAC Program (80NM0018D0004).
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