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LOTOS Optimization

Fast and reliable optimization of low-thrust orbit transfers under consideration of a comprehensive set of constraints and with varying objective functions is one of the key features of LOTOS. To control and interact with the optimal control problem, the software acts as dedicated graphical editor to change parameters, states, controls, phase durations, etc. Furthermore with the iteration monitor a feature is provided to easily investigate the behaviour of dynamic optimization entities (states, controls, objective, constraints, etc.) already during the optimization process.

With the multi-phase optimization it is possible to break down the trajectory for example into its thrust and coast arcs. Also eclipses might be considered in this process such that begin and end of an eclipse event are perfectly matched through additional boundary constraints.

An overview of the available optimization methods and solvers as well as a brief summary of the provided cost functions and constraints is given below.

Methods

  • Direct collocation with SOS developed by John T. Betts, Applied Mathematical Analysis, LLC
  • Direct collocation and multiple-shooting with CAMTOS developed by P. Gath and Astos Solutions
  • Automatic mesh refinements (SOS, CAMTOS)

Solvers

  • State of the art NLP solver SPRNLP (part of SOS) for several 100,000 parameters
  • Alternative supported sparse NLP solvers are WORHP (developed by Steinbeis Research Center Optimization, Control and Adjustment Control) and SNOPT (from Stanford University)
  • MIDACO: random search and mixed integer solver based on ant colony optimization algorithms developed by M. Schlueter
  • CGA: classical genetic algorithm developed by D. Fischer and Astos Solutions
  • PSO: particle swarm optimization

Constraints

  • Final Keplerian and equinoctial orbit elements
  • Final geographic longitude
  • Transfer duration
  • Sub-synchronous transfer
  • Slew rates during burn and coast arcs
  • Eclipse begin and end conditions
  • Battery capacity

Cost Functions

  • Fuel consumption
  • Transfer duration
  • Final Keplerian and equinoctial orbit elements
  • Final geographic longitude
  • Van Allen belt dwell time
  • Slew rates during burn and coast arcs
  • Sub-synchronous transfer