@inproceedings{schattel2016lowthrust,
  title        = {Low Thrust Trajectory Optimization for Autonomous Asteroid Rendezvous Missions},
  author       = {Schattel, A. and Echim, M. and B{\"u}skens, C.},
  booktitle    = {6th International Conference on Astrodynamics Tools and Techniques (ICATT), Darmstadt, Germany},
  year         = {2016},
  abstract     = {The demand for deep space missions and the desire to investigate small space objects like asteroids and comets is increasing constantly. Such exploration missions open up the possibility to gain further scientific knowledge about the origin
of our solar system as well as to find and eventually mine rare earth elements that are narrow on Earth or even to discover novel resources. To realize such missions, trajectory
planning and optimization are of utmost importance. When flying further into outer space, the spatial distances become enormously huge while fuel is very limited and signal runtimes are increasing rapidly. These conditions impose an unmanned and autonomously working spacecraft. The mathematical field of optimization and optimal control provides
the foundation for autonomous decisions and facilitates more safety and minimal resource consume. Solutions may additionally be transferred to other, earth-bound applications
like e.g. deep sea navigation and autonomous driving with minor additional expenses. The aspects investigated in the present paper focus on the specific challenges of guidance and
control regarding the cruise and approach phase of a spacecraft starting in a parking orbit around the Sun and reaching for an asteroid in the main belt. The underlying optimal control problems are solved using so called direct methods also known as transcription techniques. Those transform
an infinite-dimensional optimal control problem (OCP) into a finite-dimensional non-linear optimization problem (NLP) via discretization methods. The resulting high dimensional
non-linear optimization problems can be solved efficiently by special methods like sequential quadratic programming (SQP) or interior point methods (IP). For solving the problems introduced in this paper the NLP solver WORHP, which
stands for "We Optimize Really Huge Problems", is used, a software routine combining SQP at an outer level and IP to solve underlying quadratic sub problems. Within this paper
the transcription is performed using the robust method of full discretization. The trajectory optimization and optimal control problems are modeled and solved using low thrust electric
propulsion on the one hand and chemical propulsion on the other hand for comparison. The movement of the spacecraft is described through ordinary differential equations (ODE) considering the gravitational influences of the Sun and the planets Mars, Jupiter and Saturn as well as the different thrust
commands. Competitive mission aims like short flight times and low energy consumption can be provided with a weighting factor within the optimization process. The varying challenges of the two propulsion types are analyzed and comparative solutions and results introduced. Several mission trajectories are compared, optimizing with different weighting
factors for energy cost and flight time duration, in order to investigate the different possibilities of an asteroid rendezvous mission. The results show the huge gain of trajectory optimization as input for on-board autonomous decision making
during deep space missions as well as the great increase in possibilities for flight maneuvers by providing solutions for changing and contradictory mission objectives. Furthermore,
trajectory optimization can be used to analyze the potentials of different propulsion systems beforehand.}
}