Optimal trajectory solutions exist for solar electric propulsion in interplanetary travel.
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Peer-reviewed literature demonstrates that optimal trajectory solutions and mathematical frameworks exist for low-thrust and solar electric propulsion in interplanetary travel.
Electric sail-based propulsion is an innovative propellant-less propulsion technology that generates continuous thrust through the interaction between an artificial electric field and the solar wind. In an electric sail, the propulsive acceleration is adjusted by controlling the attitude of its normal plane and the coefficient determining the maximum thrust. However, the attitude adjustment speed of the electric sail is relatively small and the direction of the normal vector is constrained. Consequently, the electric sail is required to maintain a continuous propulsive acceleration vector when flying by the intermediate targets in multitarget interplanetary exploration. Therefore, an indirect optimization of three-dimensional optimal continuous interplanetary trajectory for electric sails with refined thrust model is investigated in this article. First, the optimal propulsive angles and thrust adjustment coefficient of electric sails with a refined thrust model are derived using Pontryagin's minimum principle. Second, a homotopy function is introduced in the process of trajectory optimization with an indirect method to approximate the step of the thrust adjustment coefficient to improve the accuracy of numerical integration. Additionally, the initial costates of the electric sail are transformed from the numerical simulation results of the Bezier shaping approach (BSA) and integrative BSA (IBSA) using the Karush–Kuhn–Tucker condition. The numerical simulation results for the Earth–Mars rendezvous mission and the multitarget flyby mission reveal that the initial values of the costates are effective to implement an indirect optimization process of the optimal continuous trajectory for the rapid convergence of the electric sail. According to the numerical simulation results for multitarget mission, the indirect method is on average 2.5% better than the Gauss pseudospectral method (GPM) in overall index, and the calculation time is only 1.06% of GPM.
Abstract It is attractive to use a hybrid propulsion system (HPS) consisting of solar electric propulsion (SEP) and solar radiation pressure (SRP) in interplanetary and near-Earth missions. Compared with the equivalent pure sail and pure SEP trajectories, HPS can reduce fuel consumption and transfer time. A multi-objective optimization model for the three-dimensional rendezvous mission of hybrid propulsion system is established in this paper. The optimization index is defined as a weighted sum of transfer time and the fuel consumption. Solutions with the bang-bang thrust profile are obtained under the specific mission constraints of time and fuel consumption. The influence of weights on the optimization results is discussed, and a reasonable weight range is given based on the magnitude analysis. By combining the homotopy approach with time-optimal solar sail trajectory, the initial value of the covariates are well estimated. Numerical simulations are performed both on Earth–2000SG344 and Earth–Apophis rendezvous. The results indicate that the proposed method is advantageous to obtain solutions with different mission time and fuel consumption flexibility.
Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.
Low thrust solar system missions are particularly difficult to plan. The trajectories require careful planning and very accurate simulation predictions. Progress in two specific topics will be reviewed. The first is the development of simulation methods that optimize the total energy requirement and mission time simultaneously. The method uses variational calculus to derive a set of equations that can be used to find optimal trajectories. Escape from deep gravitational wells will use high thrust bimodal nuclear thermal propulsion. Thereafter the transit between targets in the solar systems will use low thrust high specific impulse engines that run using constant power output. Hence minimizing the low thrust trajectory for power will also minimize the transit time. A second problem that needs to be considered is the use of low thrust for landing on objects with a small gravitational field. In this case a low thrust propulsion system is sufficient, but matching the motion, or rotation, of the target (e.g., an asteroid) is particularly difficult. Exact solutions exist for the free rotation of rigid bodies can be used to match the motion of the object at the landing point. A method for accomplishing this objective can he developed and will be presented.
Patch-conic trajectory analysis for the 2029 primary and 2031 backup launch windows and pork chop plot evaluation and interplanetary return trajectory trade study (ballistic coast vs. continued electric propulsion thrusting) with gravity loss and drag corrections results in a total mission ΔV of 9.14 km/s. According to Edelbaum’s low-thrust approximation, with validation against numerical propagation of orbits (2%–5% discrepancy), within the wider literature of electric propulsion trajectory optimization, eclipse, J2 perturbation, and thrust degradation sensitivity analysis, prediction of Mars escape occurs in approximately 270 days (85% thrust duty cycle) using 49 kg Xe at 5.0 kW input power. A three-degrees-of-freedom Monte Carlo EDL simulation (10,000 cases), complemented by qualitative six-degrees-of-freedom sensitivity analysis and parametric thermal protection system (TPS) mass sizing, results in a 99th-percentile landing ellipse of 8.7 km × 4.2 km with peak heat flux within PICA-class thermal protection limits.
Impact of Pitch Angle Limitation on E-Sail Interplanetary Transfers
The Electric Solar Wind Sail (E-sail) deflects charged particles from the solar wind through an artificial electric field to generate thrust in interplanetary space. The structure of a spacecraft equipped with a typical E-sail essentially consists in a number of long conducting tethers deployed from a main central body, which contains the classical spacecraft subsystems. During flight, the reference plane that formally contains the conducting tethers, i.e., the sail nominal plane, is inclined with respect to the direction of propagation of the solar wind (approximately coinciding with the Sun–spacecraft direction in a preliminary trajectory analysis) in such a way as to vary both the direction and the module of the thrust vector provided by the propellantless propulsion system. The generation of a sail pitch angle different from zero (i.e., a non-zero angle between the Sun–spacecraft line and the direction perpendicular to the sail nominal plane) allows a transverse component of the thrust vector to be obtained.
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