The Adjoint Method and Its Application to Trajectory Optimization

A method is presented for the systematic evaluation of two-point boundary value problems. Emphasis is placed on solving trajectory optimization problems formulated by the calculus of variations. The method presented in this paper, termed the adjoint method, iteratively converts the two-point boundary value problem into an initial value one, thus allowing a solution to be achieved in one run on a digital computer. Two sample problems that were solved by using the method are given: the case of a boost mission and that of an orbit transfer mission, both to be done in a minimum amount of time.