Event-Driven Network Model for Space Mission Optimization with High-Thrust and Low-Thrust Spacecraft

Numerous high-thrust and low-thrust space propulsion technologies have been developed in the recent years with the goal of expanding space exploration capabilities; however, designing and optimizing a multi-mission campaign with both high-thrust and low-thrust propulsion options are challenging due to the coupling between logistics mission design and trajectory evaluation. Specifically, this computational burden arises because the deliverable mass fraction (i.e., final-to-initial mass ratio) and time of flight for low-thrust trajectories can can vary with the payload mass; thus, these trajectory metrics cannot be evaluated separately from the campaign-level mission design. To tackle this challenge, this paper develops a novel event-driven space logistics network optimization approach using mixed-integer linear programming for space campaign design. An example case of optimally designing a cislunar propellant supply chain to support multiple lunar surface access missions is used to demonstrate this new space logistics framework. The results are compared with an existing stochastic combinatorial formulation developed for incorporating low-thrust propulsion into space logistics design; our new approach provides superior results in terms of cost as well as utilization of the vehicle fleet. The event-driven space logistics network optimization method developed in this paper can trade off cost, time, and technology in an automated manner to optimally design space mission campaigns.Comment: 38 pages; 11 figures; Journal of Spacecraft and Rockets (Accepted); previous version presented at the AAS/AIAA Astrodynamics Specialist Conference, 201

Space logistics network optimization with embedded propulsion technology selection

Establishing long-term human presence beyond low Earth-orbit will require cooperative use of emerging technologies, such as low-thrust solar electric propulsion, along with existing space exploration technologies. Trajectory analysis plays a key role in deciding the costs of using different propulsion technologies. Traditional trajectory design methods are usually confined to analyzing individual missions using high-thrust or low-thrust propulsion options --- these techniques also do not usually consider the architectural aspects of the in-space network. On the other hand, determination of network architecture and mission sequence often relies on the expertise of mission designers. Thus, formulating and optimizing the problem as a multi-mission campaign can guide top-level decisions through rigorous mathematical modeling. However, designing a multi-mission campaign with both propulsion options is generally computationally challenging due to the coupling of logistics network design and space transportation costs. Specifically, conventional space logistics planning methods are unable to account for the use of low-thrust vehicles for transportation due to the inherent nonlinear nature of associated costs. The aim of this work is to develop ways of handling low-thrust trajectory models within space logistics frameworks, so that propulsion technology trade-offs can be conducted internally. This work develops two new frameworks for optimizing the combined use of low-thrust and high-thrust propulsion options within campaign-level space logistics planning tools. The first framework uses a chromosomal representation of network arc parameters to drive a multiobjective genetic algorithm that explores the tradespace. The second framework combines the generalized multicommodity network flow model with novel event-based time steps for dynamic space logistics optimization in the presence of nonlinear flight times associated with low-thrust transportation. These methodologies are applied to the case study of Apollo-style crew missions to the lunar surface supported by in-space refueling via predeployed tanks delivered by cargo tugs. Although the costs for high-thrust trajectories are a part of the inputs to the formulation, the costs for low-thrust trajectories are determined internally because of their dependence on the thrust-to--mass ratio. For an efficient evaluation of low-energy, low-thrust transfers in the Earth–moon system, an approximation method is implemented based on a Lyapunov feedback control law called Q-law, and dynamical systems theory. This preliminary trajectory design technique is validated against literature sources and is then used to closely estimate the costs associated with cargo deliveries using low-thrust tugs. Numerical results from the new space logistics frameworks reveal campaign profiles where high-thrust and low-thrust propulsion options can be used cooperatively to achieve substantial improvement over the baseline no-refuel cases. These results also present multiple options that involve in-space propellant storage and transfer, deep-space rendezvous, and solar electric propulsion tugs for cargo delivery. By trading mission costs with campaign duration, these methods help quantify the impact of low-thrust solar electric propulsion in logistics supply planning

Solar radiation pressure, drag and gravitational effects on a dust particle in Earth orbit

This work aims to further the research done on evaluating the effects of various perturbing forces on Earth-orbiting particles by numerical integration. One of the predominant perturbations on particle orbits is the solar radiation pressure (SRP), which is defined as the pressure exerted by the photons constituting the light from the Sun. Colombo et. al studied the orbital dynamics of ``smart-dust'' under the effects of SRP and atmospheric drag. The numerical model developed here will expand on that work, but will use Hamiltonian equations of motion instead of Gauss’ equations. This approach easily incorporates forces such as drag, SRP and J2 perturbations. Solar radiation pressure is switched off while the particle passes through the Earth's shadow. The model is developed in an Earth-Centric Inertial frame, where the Sun and the Moon are averaged to lie in the ecliptic plane with an obliquity of 23.6 degrees. None of the effects of perturbation are averaged, thus this study can provide the entire set of initial orbital elements of particles in Earth-orbit required to ensure a long lifespan. The differential equations of motion are numerically integrated using MATLAB's pre-packaged ode45. These formulations and assumptions are tested against results found in existing literature. The application of this model so far described is to select a set of initial orbital elements that will balance the dissipative effects of drag with coupling of SRP, J2 and Moon's gravity, thereby ensuring longer orbital lifetimes. The methodology employs Montecarlo simulations over the possible regime of some known initial conditions, while varying the others. A ``goldilocks'' region is chosen by superimposing the results from different Montecarlo runs that produce the least departure from the initial set of orbital elements at the end of one simulated orbit. These orbits are conjectured to have the longest lifespans; in a sample calculation, the orbital lifetime was increased by ~30 times by selecting a set of initial elements from this ``goldilocks'' region, as compared to an arbitrary set of initial conditions outside it. The eventual goal of this work is to aid precise orbital propagation of swarms of nano-satellites through the use of heavier computational resources. Due to the non-specific nature of all parameters used, this model can also be utilized for missions at other planetary bodies or those in lunar orbit. Inclusion of higher-order integrators or variational integrators (over the Runge-Kutta methods used here) may improve accuracy

Space logistics network optimization with embedded propulsion technology selection

Establishing long-term human presence beyond low Earth-orbit will require cooperative use of emerging technologies, such as low-thrust solar electric propulsion, along with existing space exploration technologies. Trajectory analysis plays a key role in deciding the costs of using different propulsion technologies. Traditional trajectory design methods are usually confined to analyzing individual missions using high-thrust or low-thrust propulsion options --- these techniques also do not usually consider the architectural aspects of the in-space network. On the other hand, determination of network architecture and mission sequence often relies on the expertise of mission designers. Thus, formulating and optimizing the problem as a multi-mission campaign can guide top-level decisions through rigorous mathematical modeling. However, designing a multi-mission campaign with both propulsion options is generally computationally challenging due to the coupling of logistics network design and space transportation costs. Specifically, conventional space logistics planning methods are unable to account for the use of low-thrust vehicles for transportation due to the inherent nonlinear nature of associated costs. The aim of this work is to develop ways of handling low-thrust trajectory models within space logistics frameworks, so that propulsion technology trade-offs can be conducted internally. This work develops two new frameworks for optimizing the combined use of low-thrust and high-thrust propulsion options within campaign-level space logistics planning tools. The first framework uses a chromosomal representation of network arc parameters to drive a multiobjective genetic algorithm that explores the tradespace. The second framework combines the generalized multicommodity network flow model with novel event-based time steps for dynamic space logistics optimization in the presence of nonlinear flight times associated with low-thrust transportation. These methodologies are applied to the case study of Apollo-style crew missions to the lunar surface supported by in-space refueling via predeployed tanks delivered by cargo tugs. Although the costs for high-thrust trajectories are a part of the inputs to the formulation, the costs for low-thrust trajectories are determined internally because of their dependence on the thrust-to--mass ratio. For an efficient evaluation of low-energy, low-thrust transfers in the Earth–moon system, an approximation method is implemented based on a Lyapunov feedback control law called Q-law, and dynamical systems theory. This preliminary trajectory design technique is validated against literature sources and is then used to closely estimate the costs associated with cargo deliveries using low-thrust tugs. Numerical results from the new space logistics frameworks reveal campaign profiles where high-thrust and low-thrust propulsion options can be used cooperatively to achieve substantial improvement over the baseline no-refuel cases. These results also present multiple options that involve in-space propellant storage and transfer, deep-space rendezvous, and solar electric propulsion tugs for cargo delivery. By trading mission costs with campaign duration, these methods help quantify the impact of low-thrust solar electric propulsion in logistics supply planning.U of I OnlyAuthor requested U of Illinois access only (OA after 2yrs) in Vireo ETD syste