{"id":404,"date":"2017-11-26T16:59:23","date_gmt":"2017-11-26T08:59:23","guid":{"rendered":"http:\/\/nullthought.net\/?p=404"},"modified":"2024-08-25T10:08:40","modified_gmt":"2024-08-25T02:08:40","slug":"spacex%e7%81%ab%e7%ae%ad%e7%b2%be%e5%87%86%e7%9d%80%e9%99%86%e7%9a%84%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=404","title":{"rendered":"SpaceX\u706b\u7bad\u7cbe\u51c6\u7740\u9646\u7684\u7b97\u6cd5"},"content":{"rendered":"

Lars Blackmore<\/a>\u662fSpaceX\u7684\u9996\u5e2d\u706b\u7bad\u7740\u9646\u5de5\u7a0b\u5e08\uff0c\u4ed6\u64b0\u5199\u7684\u6587\u7ae0\u300a\u706b\u7bad\u81ea\u4e3b\u7cbe\u51c6\u7740\u9646\u300b\uff08Autonomous Precision Landing of Space Rockets<\/a>\uff09\u4e2d\u7c97\u7565\u63d0\u5230\u4e86\u730e\u9e709\u706b\u7bad\u7cbe\u51c6\u7740\u9646\u7684\u7b97\u6cd5\uff0c\u5373\u51f8\u4f18\u5316<\/a>\uff08Convex Optimization\uff09\u3002<\/p>\n

\u51f8\u4f18\u5316\u662f\u673a\u8f7d\u81ea\u4e3b\u6027\u7684\u4e00\u4e2a\u6709\u524d\u9014\u7684\u5de5\u5177\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4fdd\u8bc1\u6536\u655b\u5230\u5168\u5c40\u6700\u4f18\u89e3\u3002\u7136\u800c\uff0c\u8bb8\u591a\u95ee\u9898\u5e76\u4e0d\u5177\u5907\u4f7f\u7528\u51f8\u4f18\u5316\u6240\u9700\u7684\u51f8\u7ed3\u6784\uff0c\u4e00\u79cd\u79f0\u4e3a\u201c\u65e0\u635f\u51f8\u5316\uff08Lossless Convexification\uff09<\/strong>\u201d\u7684\u6280\u672f\u514b\u670d\u4e86\u8fd9\u4e00\u96be\u9898\u3002\u6b64\u6280\u672f\u662fLars Blackmore\u4e0e\u79d1\u7814\u4f19\u4f34Behcet Acikmese<\/a>\u7684\u7814\u7a76\u6210\u679c\uff0c\u5176\u5173\u952e\u601d\u60f3\u662f\u5c06\u975e\u51f8\u95ee\u9898\u91cd\u65b0\u8868\u8ff0\u4e3a\u9ad8\u7ef4\u7684\u51f8\u95ee\u9898<\/strong>\uff0c\u7136\u540e\u8bc1\u660e\u51f8\u95ee\u9898\u7684\u6700\u4f18\u89e3\u4e5f\u662f\u975e\u51f8\u95ee\u9898\u7684\u5168\u5c40\u6700\u4f18\u89e3\u3002\u6240\u8c13\u201c\u65e0\u635f\uff08Lossless\uff09\u201d\uff0c\u5373\u5728\u51f8\u5316\u8fc7\u7a0b\u4e2d\u6ca1\u6709\u53bb\u9664\u53ef\u884c\u7a7a\u95f4\u7684\u4efb\u4f55\u533a\u57df\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u5b58\u5728\u975e\u51f8\u95ee\u9898\u7684\u53ef\u884c\u89e3\uff0c\u53ef\u786e\u4fdd\u80fd\u591f\u627e\u5230\u6b64\u89e3\u3002<\/p>\n

\u5b9e\u73b0\u7cbe\u51c6\u7740\u9646\u7684\u5173\u952e\u5728\u4e8e\u63a7\u5236\u504f\u79bb\u53d8\u91cf(Dispersions)\u3002\u964d\u843d\u8fc7\u7a0b\u4e2d\u7684\u73af\u5883\u4e0d\u786e\u5b9a\u6027\u5bfc\u81f4\u504f\u79bb\u53d8\u91cf\u589e\u52a0\u3002\u5728\u7740\u9646\u524d\u7684\u4e00\u77ac\u95f4\uff0c\u81f3\u5c11\u898199%\u7684\u504f\u79bb\u53d8\u91cf\u503c\u7b26\u5408\u8981\u6c42\uff0c\u5426\u5219\u7740\u9646\u5c06\u4f1a\u5931\u8d25\u3002\u63a7\u5236\u504f\u79bb\u53d8\u91cf\u7684\u4e09\u4e2a\u5173\u952e\u8fc7\u7a0b\u662f\uff1a1)\u8fd4\u56de\u524d\u53d1\u52a8\u673a\u70b9\u706b\u53ca\u5927\u6c14\u5c42\u5916\u7684\u8f68\u9053\u63a7\u5236\uff1b2)\u5927\u6c14\u5c42\u5185\u91c7\u7528\u6805\u683c\u7ffc(Grid Fin)\u7684\u7a7a\u6c14\u52a8\u529b\u63a7\u5236\uff1b3)\u7740\u9646\u524d\u53d1\u52a8\u673a\u70b9\u706b\u53ca\u8f6c\u5411\u63a7\u5236\uff08\u6216\u6a2a\u5411\u79fb\u52a8\uff09\u3002<\/p>\n

\u5f88\u663e\u7136\uff0c\u5bf9\u964d\u843d\u8fc7\u7a0b\u4e2d\u7684\u706b\u7bad\u8fdb\u884c\u8fdc\u7a0b\u63a7\u5236\u662f\u4e0d\u73b0\u5b9e\u7684\uff0c\u5fc5\u987b\u91c7\u7528\u81ea\u4e3b\u63a7\u5236\uff0c\u6240\u6709\u7684\u8ba1\u7b97\u548c\u63a7\u5236\u5747\u987b\u706b\u7bad\u81ea\u884c\u5b8c\u6210\uff0c\u4e14\u5fc5\u987b\u77ac\u95f4\u5b8c\u6210\u3002Lars Blackmore\u63d0\u5230\uff0c\u964d\u843d\u7684\u9ad8\u901f\u63a7\u5236\u8ba1\u7b97\u662f\u51f8\u4f18\u5316\u8ba1\u7b97\uff0c\u91c7\u7528\u4e86CVXGEN<\/a>\u751f\u6210\u98de\u63a7\u4ee3\u7801\uff08Flight Code\uff09\u3002CVXGEN\u662f\u4e00\u5957\u81ea\u52a8\u751f\u6210\u89e3\u51b3\u51f8\u4f18\u5316\u95ee\u9898\u7a0b\u5e8f\u4ee3\u7801\u7684\u8f6f\u4ef6\uff0c\u4f5c\u8005\u662f\u65af\u5766\u798f\u5927\u5b66\u7684Jacob Mattingley\u535a\u58eb\u3002CVXGEN\u9002\u5408\u89e3\u51b3\u5c11\u4e8e2000\u4e2a\u7cfb\u6570\u56e0\u5b50\u7684\u51f8\u4f18\u5316\u95ee\u9898\u3002<\/p>\n

\u730e\u9e709\u706b\u7bad\u91c7\u7528CVXGEN\u751f\u6210\u7684\u98de\u63a7\u4ee3\u7801\u662f\u9759\u6001\u7684\u8fd8\u662f\u52a8\u6001\u7684\uff1f\u524d\u8005\u662f\u4e00\u6b21\u6027\u751f\u6210\u3001\u5b89\u88c5\u5e76\u6267\u884c\uff0c\u540e\u8005\u662f\u5728\u964d\u843d\u548c\u7740\u9646\u8fc7\u7a0b\u4e2d\u52a8\u6001\u751f\u6210\u5e76\u6267\u884c\u3002\u4e2a\u4eba\u5224\u65ad\u503e\u5411\u4e8e\u540e\u8005\u3002<\/p>\n

CVXGEN\u4f5c\u8005Jacob Mattingley\u535a\u58eb\u7684\u6307\u5bfc\u8001\u5e08\u662f\u65af\u5766\u798f\u5927\u5b66\u6559\u6388Stephen Boyd<\/a>\u3002Stephen Boyd\u6559\u6388\u6240\u8457\u7684\u300a\u51f8\u4f18\u5316\u300b\uff08Convex Optimization<\/a>\uff09\u4e00\u4e66\u662f\u51f8\u4f18\u5316\u95ee\u9898\u65b9\u9762\u7684\u6743\u5a01\u8457\u4f5c\u3002<\/p>\n\n\n

SpaceX\u7cfb\u5217\u6587\u7ae0<\/a><\/div>\n\n\n\n
\n\n\n\n

Algorithm for Precise Landing of SpaceX Rockets<\/strong><\/p>\n\n\n\n

Lars Blackmore<\/a>, the Chief Rocket Landing Engineer at SpaceX, briefly mentions the algorithm for the precise landing of the Falcon 9 rocket, which is based on convex optimization, in his article “Autonomous Precision Landing of Space Rockets.<\/a>“<\/p>\n\n\n\n

Convex optimization is a promising tool for onboard autonomy because it ensures convergence to a global optimum. However, many problems do not possess the convex structure required for convex optimization. A technique known as “Lossless Convexification<\/strong>” overcomes this challenge. This technique, a result of research by Lars Blackmore and his scientific partner Behcet Acikmese<\/a>, involves reformulating a non-convex problem into a high-dimensional convex problem<\/strong> and then proving that the optimal solution to the convex problem is also the global optimum of the non-convex problem. The term “lossless” indicates that no feasible region of the problem is discarded during convexification. In other words, if a feasible solution to the non-convex problem exists, it can be found.<\/p>\n\n\n\n

The key to achieving precise landing is controlling dispersions. Environmental uncertainties during the descent increase the dispersion variables. At least 99% of the dispersion values must meet the requirements just before landing, or the landing will fail. The three critical processes for controlling dispersions are: 1) engine ignition and orbital control outside the atmosphere before reentry; 2) aerodynamic control using grid fins within the atmosphere; and 3) engine ignition and steering control (or lateral movement) before landing.<\/p>\n\n\n\n

It is clear that remotely controlling the rocket during the landing process is impractical. Autonomous control is necessary, with all calculations and controls performed by the rocket itself in real-time. Lars Blackmore mentioned that the high-speed control calculations for landing are convex optimization calculations, implemented using flight code generated by CVXGEN<\/a>. CVXGEN is software developed by Dr. Jacob Mattingley from Stanford University for automatically generating program code to solve convex optimization problems. CVXGEN is suitable for solving convex optimization problems with fewer than 2000 coefficients.<\/p>\n\n\n\n

Is the flight control code generated by CVXGEN for the Falcon 9 rocket static or dynamic? The former is generated, installed, and executed once, while the latter is dynamically generated and executed during descent and landing. Maybe the latter is a better choice.<\/p>\n\n\n\n

Dr. Jacob Mattingley, the author of CVXGEN, was supervised by Professor Stephen Boyd<\/a> at Stanford University. Professor Stephen Boyd’s book “Convex Optimization<\/a>” is an authoritative text on convex optimization problems.<\/p>\n","protected":false},"excerpt":{"rendered":"

Lars Blackmore\u662fSpaceX\u7684\u9996\u5e2d\u706b\u7bad\u7740\u9646\u5de5\u7a0b\u5e08\uff0c\u4ed6\u64b0\u5199\u7684\u6587\u7ae0\u300a\u706b\u7bad\u81ea\u4e3b\u7cbe\u51c6\u7740\u9646\u300b\uff08Autono […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[21,12,30,69],"class_list":["post-404","post","type-post","status-publish","format-standard","hentry","category-tech","tag-onehourresearch","tag-spacex","tag-space","tag-engineering"],"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"NullThought","author_link":"https:\/\/nullthought.net\/?author=1"},"rttpg_comment":0,"rttpg_category":"Tech<\/a>","rttpg_excerpt":"Lars Blackmore\u662fSpaceX\u7684\u9996\u5e2d\u706b\u7bad\u7740\u9646\u5de5\u7a0b\u5e08\uff0c\u4ed6\u64b0\u5199\u7684\u6587\u7ae0\u300a\u706b\u7bad\u81ea\u4e3b\u7cbe\u51c6\u7740\u9646\u300b\uff08Autono…","_links":{"self":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/404","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=404"}],"version-history":[{"count":13,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/404\/revisions"}],"predecessor-version":[{"id":3888,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/404\/revisions\/3888"}],"wp:attachment":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}