The purpose of this course is to develop theoretical and applied skills in optimization and control for spacecraft guidance.
This video introduces two rocket ascent problems. The first is Goddard’s problem from 1919. This problem maximizes the rocket’s final altitude, and we see that optimal solutions involve a singular arc. The second problem is to maximize the rocket’s final energy. The analysis results in the linear tangent law, which was used to guide the Saturn V rocket to orbit during the Apollo days.
This video presents a recent modification of the Shuttle era ascent guidance algorithm known as Powered Explicit Guidance or PEG. Through various approximations, the guidance problem is reduced to a boundary value problem with five unknowns – 3 can be solved analytically and 2 numerically. A final observation leads to an approximation so that the modified PEG method is completely analytical.