Given the current technological limitations, launch missions are extremely costly: rockets are huge, being about 100 times more massive than the payload, and most of the times expendable. The specific cost required to place a spacecraft in LEO is between 10 and 25 k€/kg. Consequently, trajectory optimization plays a major role in the design of a launch mission. Universities, companies, agencies and research centers have their own optimization software and continuously try to improve the existing methods. In this context, the main objective of the presented research is to assess advantages and disadvantages of using a pseudospectral approach for launcher trajectory optimization in an industrial context by applying it to the Vega launcher family, namely Vega, Vega C and mini-Vega E.
The software GPOPS is chosen for the transcription of the continuous optimal control problem and SNOPT for the solution of the associated non-linear programming problem. The launcher ascent problem is formulated considering all the main constraints: angle of attack, pitch rate, aerodynamic loads and heat flux. In addition, the dynamic model includes thrust profiles and drag curves of the aforementioned vehicles. The control to be optimized is the direction of thrust and it is formulated in two different ways, allowing to select the most suited for the specific application: Cartesian x-y-z components or pitch-yaw angles.
After numerous tests with all kinds of target orbits (Sun-synchronous, polar, equatorial, escape, etc.), it can be concluded that the PS method and the software composed by GPOPS and SNOPT are suited for practical ascent trajectory optimization: first, all the typical constraints are included and fulfilled; second, the problem formulation is general enough to be easily applied to all kinds of configurations (number of stages, types of motors, etc.) and number of phases (single/multiple boosts, coast, etc.); third, problem formulation allows for both payload mass maximization (preliminary studies) and propellant reserve maximization with fixed payload (industrial application); finally, the obtained performances do match perfectly with the performance maps of ELV. In conclusion, this research provides the hosting company with a validated method and a complete tool, ready for a daily utilization.