Trajectory optimization of the Brazilian multistage launch vehicle VLM-1

The insertion of a payload into orbit is a very complex and costly activity. Therefore, the best performance of the launch vehicle is important for each launch. To achieve this goal, usually the vehicle trajectory is determined via an optimization process which results in the maximum payload mass that can be inserted into orbit or, equivalently, the minimum propellant expenditure to achieve orbit. This is a specially complex problem belonging to the general class of optimal control problems. This work investigates the trajectory optimization of a multistage launch vehicle. The optimal control problem is transformed into a nonlinear programming problem with the use of two different transcription methods: Hermite–Simpson collocation and multiple shooting. To solve the resulting parameter optimization problem, the gradient-based algorithm called sequential conjugate gradient-restoration algorithm is used, and an extension of the algorithm is proposed which enhances its applicability to more general optimization problems. The proposed algorithm is used to optimize the trajectory of the Brazilian microsatellite launcher VLM-1, in missions with different complexities. To validate the methodology, the results are compared with those obtained with a commercial optimization tool.