Which are the main control theories behind the landing maneuvers of the Falcon 9? For the hovering part, as it approaches the landing surface, I guess the inverted pendulum control approaches would do it. But what about the control from stage separation till it the reentry burn? Any textbook references appreciated!
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7Oddly, no hovering. The engine has a T/W ratio greater than 1. Cannot hover, even if they wanted too. Cannot throttle down low enough to hover. – geoffc Jan 25 '15 at 01:05
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2Duplicate? How will SpaceX achieve landing of the Falcon 9 first stage? – mins Jan 26 '15 at 19:19
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3Not sure, seems to be asking about "control theories", which probably includes the algorithms computing location and guidance. The question you pose as a duplicate is about the hardware. – Stu Jan 26 '15 at 20:10
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2Something like this? -- old stuff. – mins Jan 27 '15 at 07:44
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Well you're right geoffc. I've might have used the term "hovering" wrong. Although at the very last moment the velocity would be zero... and in the previous missions it hovered a little bit on the surface of the ocean. Fantastic thesis mins. Thanks, that will get me definitely started! Old stuff indeed... but the implementation is quite new and exciting! – KonstantinosV Jan 27 '15 at 21:08
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@mins The URL no longer works, any possibility of finding a new link? I'm interested in what you linked. – space_voyager Sep 12 '15 at 07:57
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1@space_voyager: A Predictor-Corrector Guidance Algorithm Design for a Low L/D Autonomous Re-entry Vehicle by Carla Haroz, 1996 – mins Sep 12 '15 at 10:33
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1@KonstantinosV To add to this (old) discussion, I worked with a guy from JPL whose past colleague (Lars Blackmore) is now the guy responsible for Falcon 9 landing. They use real-time convex optimization by harnessing lossless convexification of a non-convex optimal control problem (the non-convexity arises, for example, from a non-zero lower bound on Merlin engine thrust). Here's a paper on the topic – space_voyager Sep 12 '15 at 10:43
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1@space_voyager - Lars Blackmore's page (http://web.mit.edu/larsb/www/) and his publication list give a good approximation of the algos he designed. That's as good as it gets, barring a tweet by Elon. You could convert your comment to an answer... – Deer Hunter Oct 29 '15 at 16:07
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One of the key control algorithms involved is called G-FOLD, or Guidance for Fuel-Optimal Large Diverts. This is something that JPL has been working on for Mars landings, and some people involved have actually went to work for SpaceX a few years ago. Here is a high level description:
http://www.lpi.usra.edu/meetings/marsconcepts2012/pdf/4193.pdf
And you can find more here : https://scholar.google.com/citations?hl=en&user=xZvK9z0AAAAJ&view_op=list_works&sortby=pubdate
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