Space Missions Engineering Laboratory

• Astrodynamics
• Space Robotics
• On-Board Autonomy
• Optimization
  • Multiobjective Optimization
  • Multidisciplinary Optimization
  • Global Optimization
  • Local Optimization
  • Heuristic Methods
• Soft Computing
• Autonomous Navigation

Local Optimization

Local Optimization methods are used whenever the nature of the optimization problem assures the existence of a unique solution or a good first guess of the problem is available. Local optimization methods are all based on Newton’s method for the solution of nonlinear equations, and for this reason they show quadratic convergence.

Our group of research uses local optimizer for solving huge parametric optimization problems which are the result of direct numerical transcription of optimal control problems. We have applied local optimizer to different optimization problems including low-thrust interplanetary transfers, atmospheric phases guidance determination, formation flying reconfiguration and station keeping, and trajectory optimization in chaotic dynamical systems.

We have achieved particular skills in the numerical transcription of control problems using collocation methods, pseudo-spectral methods, multiple shooting, and parallel multiple shooting techniques and in dealing with problems with huge set of equality and inequality constraints. Furthermore we can formulate optimization problems in order to be numerically solved by different commercial local optimizer (i.e. Matlab Optimization Toolbox and SNOPT), and we have developed an in house optimizer based on an interior point algorithm to solve inequality-constrained problem. As an example, Figure 5 shows the optimal low-thrust trajectory for the encounter of two asteroids in the same mission. The dynamics have been transcribed using a pseudo-spectral technique, and the resulting parametric optimization problem has been solved using SNOPT.