ATO Using Direct Transcription and Collocation - OTB

Demonstrates the solution of an aerospace trajectory optimization problem using direct transcription and collocation.

This submission describes a technical approach and MATLAB script that demonstrate the use of direct transcription and collocation to solve aerospace optimal control problems. The computer program solves the problem described on pages 66-69 of the classic text, Applied Optimal Control, by Arthur E. Bryson, Jr. and Yu-Chi Ho.

This problem is summarized in the text as follows:

“Given a constant-thrust rocket engine, T = thrust, operating for a given length of time, t, we wish to find the thrust-direction history to transfer a rocket vehicle from a given initial circular orbit to the largest possible circular orbit.”

In the language of optimal control theory, this problem is a “continuous system with functions of the state variables prescribed at a fixed terminal time”. The numerical example given in the text is a continuous, low-thrust coplanar orbit transfer from Earth to Mars. The orbits of the planets are assumed to be circular and coplanar, and the total transfer time is about 193 days.