What are the best computational methods to optimize space mission trajectories?

1 Direct methods

Direct methods are based on discretizing the trajectory into segments or nodes, and then solving a nonlinear programming problem to find the optimal values of the control variables, such as thrust, angle, or velocity. Direct methods can handle complex dynamics, nonlinear constraints, and multiple objectives. However, they also require a large number of variables and constraints, which can make the problem difficult to solve and sensitive to the choice of the initial guess and the discretization scheme. Some examples of direct methods are collocation, pseudospectral, and direct shooting methods.

2 Indirect methods

Indirect methods are based on applying the calculus of variations and the Pontryagin's maximum principle to derive the necessary conditions for optimality. Indirect methods can provide high-accuracy solutions and theoretical insights into the optimal control problem. However, they also require solving a two-point boundary value problem, which can be challenging and computationally intensive. Moreover, indirect methods may not be able to handle multiple objectives, nonlinear constraints, or discontinuous control inputs. Some examples of indirect methods are primer vector, adjoint, and Hamiltonian methods.

3 Hybrid methods

Hybrid methods are based on combining direct and indirect methods to exploit their advantages and overcome their limitations. Hybrid methods can use indirect methods to generate initial guesses, refine solutions, or analyze the structure and sensitivity of the optimal trajectory. On the other hand, hybrid methods can use direct methods to handle complex dynamics, nonlinear constraints, or multiple objectives. Hybrid methods can also switch between different methods depending on the phase or segment of the trajectory. Some examples of hybrid methods are direct-collocation with smoothing-splines, indirect-differential evolution, and direct-indirect shooting methods.

4 Metaheuristic methods

Metaheuristic methods are based on applying stochastic or evolutionary algorithms to search for the optimal or near-optimal solution in a large and complex solution space. Metaheuristic methods can handle non-smooth, multimodal, or noisy objective functions, as well as mixed-integer or discrete variables. However, they also require a large number of function evaluations, which can be time-consuming and computationally expensive. Moreover, metaheuristic methods may not guarantee convergence, optimality, or feasibility of the solution. Some examples of metaheuristic methods are genetic algorithms, particle swarm optimization, and simulated annealing.

5 Software tools

Software tools are based on implementing and integrating various computational methods and models to facilitate the design and optimization of space mission trajectories. Software tools can provide user-friendly interfaces, graphical visualization, data analysis, and verification and validation functions. However, they also require careful selection, configuration, and customization of the methods and models, as well as testing and debugging of the software. Some examples of software tools are MATLAB, GMAT, PyGMO, and Copernicus.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?