An efficient algorithm for optimum trajectory computation

This paper describes a variation to the steepest-descent method for generating optimum trajectories. The steepest-descent approach to trajectory optimization was formulated by Kelley, Bryson et al., for numerically solving a variety of two-point boundary-value problems. The procedure is iterative, requiring repeated forward numerical integrations of the state differential equations and backward integrations of the adjoint equations. In many applications, however, convergence was slow; thus, several techniques for speeding convergence were devised.