R69-6 Trajectory Optimization by a Direct Descent Process

This paper develops and investigates a practical method by which certain aerospace trajectory optimization problems with terminal constraints can be relatively easily solved on a hybrid computer. If a gradient technique has been selected for the optimization process, then it has generally been the practice to solve the equations adjoint to the equations of motion by utilizing a digital computer. In the present work no utilization is made of the adjoint variables. The gradient is calculated by determining the response of the cost function to approximately impulsive control perturbations, similar to the method used by Wingrove and Raby. The variational problems which are considered are those of the Mayer type where the cost function to be minimized is a function of the terminal state and terminal time. In this paper a technique is developed so that the gradient which is calculated is compatible with imposed terminal constraints. The calculation of this modified gradient, which consists of a linear combination of the cost gradient and the gradients of the terminal constraints, is relatively simple and can be rapidly performed on the hybrid computer. The circuitry required for handling the terminal constraints by this technique, as well as that required to simulate the other equations of the problem, is described in substantial detail.