Real-time optimal guidance

This paper describes an algorithm for repetitive in-flight calculation of optimal rocket steering laws for orbital injection and rendezvous missions. The algorithm is based on a general "indirect" method of solving the optimal-trajectory problem as a boundary-value problem in ordinary differential equations, and it avoids assuming artificial physical simplifications or specialized mission definitions. At each guidance cycle the solution to the boundary-value problem is updated by a single iteration of Newton\´s method using partial derivatives obtained by numerical integration of variational differential equations. Simulation results show that a precalculuted linear steering law provides adequate initialization to assure that this iterative guidance scheme recovers from worst-case in-flight perturbations and achieves desired end conditions with near-minimum cost.