Trajectory optimization of solid launch vehicle based on Legendre pseudospectral method

Legendre pseudospectral (PS) is a sort of high-order integral approximate rule, and high-precision value can be obtained by using the bigger integral step length. The discontinuous problem was treated by using Knotting Pseudospectral Method, which can convert infinite dimension dynamic optimal control problem into finite dimension static optimization problem so as to reduce the complexity of the problem. This method was used for trajectory optimization of three-stage solid launch vehicle to obtain a general algorithm. Taking three-stage solid launch vehicle as an example, the dynamics model can be derived in the inertia rectangular coordinate system, and trajectory optimization model was gained. The results demonstrate validity of this method for optimizing trajectory time and accuracy.