A multi-objective approach to the design of low thrust space trajectories using optimal control

Abstract

In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L 2 halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to V and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the 123 34 M. Dellnitz et al.challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.

Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control

“…An extension of invariant manifold techniques to account for a continuously applied control force is presented in Dellnitz et al [27] and employed to design a trajectory from Earth to Venus and from Earth to L 2 in [28]. However, so far, techniques like this are only computationally reasonable for a constant one-dimensional control force.…”

“…In addition, control effort and V are fundamentally different quantities, and thus should not be summed up in one single objective function. To consider different objective functions simultaneously requires multi-objective optimization (see, e.g., [27]), which enables the computation of an entire set of Pareto-optimal solutions being optimal compromises between different objective functions. A multi-objective optimization of this problem is out of the scope of this work, but can be considered in the future.…”

Trajectory planning for multiple unmanned vehicles under reciprocal constraints

“…Castillo 2007, Dellnitz 2009, Saravanan et al 2009). In those studies, different path descriptions have been coded within the solution-related chromosome code.…”

Analytical results for solar sail optimal missions with modulated radial thrust

“…The trajectory design of a solar sail based mission is usually addressed in an optimal framework (Dellnitz et al, 2009;Racca, 2003). Because the solar sail uses no propellant, the aim of the optimization process is to find suitable relationships between the sail performance, as the maximum propelling acceleration at A.…”