Improving strategies on PSO for suborbit launch vehicle trajectory optimization

Solving the optimal control problem with a free final time, such as suborbital launch vehicle (SLV) trajectory optimization with two control variables and multi-constraints ones based on particle swarm optimization (PSO), the smoothness of control variable can not be satisfied by linear interpolation method. A novel method including some improving strategies based on PSO for trajectory optimization is proposed, named LCPSO which is a kind of Cooperate PSO based on Legendre orthogonal polynomials. An additional control variable is introduced and transcribes the original optimal problem to a problem with fixed final time, and one dimension searching method based on interval analysis is used to optimize the additional control variable. Furthermore, a theorem on how to find the boundaries of the coefficient of polynomials is proved. Compared with basic PSO, LCPSO has traits of lower dimensions and smoother control variable. An example of trajectory optimization shows the effectiveness of the LCPSO algorithm.