Launch vehicle trajectory optimization

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Three dimensional trajectory optimization problem is solved through a diagonalized multiplier method in which the multiplier update formula of Tapia and Han is employed over a BFGS Hessian update. The diagonalized multiplier method (DMM) is a single sequence minimization technique for nonlinear programming and avoids the sequence of minimization problems inherent in the classical augmented Lagrangian methods. To avoid violent initial multiplier corrections in DMM, a new modification is proposed in which we minimize the Kuhn-Tucker vector norm along the Han-Tapia multiplier update direction. A software package PYOPT is developed and validated at the Indian Space Research Organisation (ISRO) employing the concepts of diagonalised multiplier method for constrained pitch and yaw steering optimization of launch vehicle trajectories. The system dynamic model for trajectory optimization allows for effective and routine operational studies. The optimality of the solutions of PYOPT is established through sufficiency conditions of optimality in nonlinear programming via saddle point optimality theorem and augmentability theorem. The robustness of the package is demonstrated. The present package, which is faster than programmes based on techniques like projected gradient methods and recursive quadratic programming, has become a standard tool at ISRO for mission design studies.