Optimal Control via Direct Methods for Low-Thrust Interplanetary Trajectories

The increasing interest in large interplanetary missions, coupled with the need for efficient propellant consumption to achieve substantial DeltaVs, has driven the increasing adoption of electric propulsion systems. While these high specific impulse and low-thrust technologies significantly enhance mission efficiency, they also introduce substantial design challenges. These challenges necessitate the use of more complex and costly trajectory optimization models and tools compared to the traditional methods employed for impulsive maneuver mission analysis. Within this thesis a flexible low-thrust interplanetary trajectory optimization tool is proposed and developed, designed for seamless integration and implementation in industrial contexts, particularly for preliminary mission analysis studies. To achieve this objective, an optimization approach using direct methods and collocation techniques is adopted. The mathematical model describing the optimal control problem for interplanetary low-thrust trajectories is presented, with a focus on the reduction of the continuous problem to a finite-dimension nonlinear programming (NLP) problem formulation through direct collocation transcription. Experimental analyses of the problem are conducted. The model is implemented employing Sequential Quadratic Programming (SQP) algorithms that leverage the sparse structure of the large-scale problem at hand. An environmental analysis is proposed to compare the performance of the WORHP solver with the Matlab Optimization Toolbox, with a particular focus on the effectiveness of exploiting sparsity in problems of this scale. This analysis aims to demonstrate the importance and necessity of such specific tools in an industrial context to effectively address the problem of low-thrust trajectories optimization. The optimization tool developed for the low-thrust interplanetary rendezvous maneuver problem is presented. The architecture and operation of the tool are described, with a focus on the global optimum search through a multi-start approach and a refinement of the optimal solution to enhance its accuracy. Several case studies of interest are described and analyzed to test the developed tool, with a particular focus on missions to Mars and Apophis, either accounting for constant allowable thrust models (e.g., nuclear electric propulsion) or Sun-distance-dependent thrust levels (e.g., solar electric propulsion).