Journal of Optimization Theory and Applications

, Volume 151, Issue 2, pp 353–372 | Cite as

Optimal Guidance for Quasi-planar Lunar Ascent

  • David G. HullEmail author


The minimum-time controls (thrust pitch angle and thrust yaw angle) for the three-dimensional transfer of a constant-thrust rocket from one state to another over a flat moon are used to develop guidance laws for operation over a spherical moon. The objective is to evaluate the effect of making approximations on the size of the thrust pitch angle on the suitability of the resulting control law as a guidance law. After assuming small out-of-plane motion (small yaw angle), three pitch angle control laws (exact, first-order, and zeroth-order) are developed. The three laws are employed in the sample and hold guidance of a lunar ascent vehicle. All three laws satisfy the final conditions and give essentially the same pitch and yaw control histories. Since the zeroth-order law can be obtained completely analytically (no iteration processes), it merits consideration for ascent guidance.


Optimal control Lunar ascent Optimal guidance 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

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