Optimal Low-Thrust Orbit Transfers Made Easy: A Direct Approach

AAS/AIAA Space Flight Mechanics Meeting, 2016

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.

Journal of Guidance, Control, and Dynamics, 2017

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto.

Acta Astronautica, 2010

In this work, the problem of optimization of interplanetary trajectories with minimum fuel consumption, but with a time limit is studied. It was used a methodology known as the Patched Conics, where the trajectory is divided into three parts: (1) departure phase, inside of the sphere of influence of the departure planet; (2) heliocentric phase, during the journey between the planets; and (3) arrival phase, inside of the sphere of influence of the arrival planet. Furthermore, the possibility of gravitational assisted maneuvers (swing-by) was considered to reduce fuel consumption. In this case the full trajectory would be divided into more parts, depending on the number of maneuvers. Therefore, the goal of this work is to find a combination of conical trajectories, using gravitational assisted maneuvers, which perform the transfer close to the departure planet to the vicinity of the arrival planet, spending minimal fuel with minimal time for the journey. Considering the minimization of time, the solution cannot be the solution of minimum fuel consumption, because the minimization of time and the minimization of fuel are conflicting objectives. Thus, a multi-objective problem must be solved. Hence, a methodology based on the Non Inferiority Criterion (Pareto, 1909 [2]) and the Smallest Loss Criterion (Rocco et al., 2002 [6]) was used, capable of considering multiple objectives simultaneously, without reducing the problem to the case of optimizing a single objective as occur in most methods found in the literature. A mission to Pluto, similar to NASA's New Horizons Mission, was studied considering gravitational assisted maneuvers in Mars, Jupiter and Saturn. Simulating the trajectories and the maneuvers using the Transfer Trajectory Design Programs (Sukhanov, 2004 [13]), several possibilities were analyzed for many combinations of fuel consumption, time of departure, time of arrival and planet used for the swing-by. Then, using the Multiobjective Optimization Program (Rocco et al., 2002 [6]) the problem was solved seeking the best combination. The results can provide good assistance for mission analysis reducing the cost and time.

The Journal of the Astronautical Sciences

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earth's J2 perturbation and lunar gravity.

Materials research proceedings, 2023

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The work proposes a systematic method to compute an optimal transfer trajectory between two non-Keplerian halo orbits in the Circular Restricted Three body formulation of the Earth-Moon dynamics. The paper exploits the knowledge of the natural non-linear dynamics and the primer vector theory applied to the Circular Restricted Three Body Problem to design optimal Halo-to-Halo transfers with fixed and limited, compared with the rest of the literature, Time of flight, from every point of the departure orbit to every point of the arrival orbit. With the goal

2000

A method for approximate analytical optimization of low-thrust transfers, described in [1] and based on linearization of the equations of motion, is considered. A more precise method of reducing the errors due to linearization is suggested. The method of optimization is generalized for the case of a mission to several celestial bodies.

International Conference on Aerospace Sciences and Aviation Technology, 2007

The feedback optimal control problem in low-thrust interplanetary trajectory design is studied in this paper. The problem is tackled by solving the Hamilton-Jacobi-Bellman equation via a generating function technique devised for linear systems. Instead of solving the classical optimal control problem, this technique allows us to derive closed loop control laws in the preliminary design phase. The idea of the work consists in applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear two-body dynamics into a linear system of ordinary differential equations written in new variables. The generating function technique is then applied to this new dynamical system, the feedback optimal control is solved, and the variables are back transformed in the original ones. We circumvent in this way the problem of expanding the vector field and truncating higher-order terms because no accuracy is lost in the undertaken approach. This technique can be applied to any planet-to-planet transfer; it has been successfully tested here for the classical Earth-Mars low-thrust transfer.

2013

This paper presents a method of trajectory optimization based on a well known theory, primer vector, which is modified to accommodate weights in the cost function; arising from the need of a more accurate analysis that takes into account the velocity increment used for the planet’s departure and, particularly for flyby missions, the disregard of the last rendezvous impulse. A detailed derivation of the weighted cost function and its gradient is presented, followed by a discussion on the adjustment of the weights specifically for flyby missions. In order to test the optimization method, a realistic test case is selected and its results are compared against a trajectory using the solution of the Lambert problem and classical primer vector optimization. It is possible to clearly evaluate from the results the advantages of the proposed method, enabling to design a trajectory with a midcourse impulse which costs less than the trajectories calculated by the other methods and provides a mo...

1999

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimi...