{"id":1351,"date":"2025-07-30T17:37:47","date_gmt":"2025-07-30T09:37:47","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1351"},"modified":"2025-07-30T17:39:03","modified_gmt":"2025-07-30T09:39:03","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e9%9d%9e%e7%ba%bf%e6%80%a7%e8%a7%84%e5%88%92","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/30\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e9%9d%9e%e7%ba%bf%e6%80%a7%e8%a7%84%e5%88%92\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014\u975e\u7ebf\u6027\u89c4\u5212"},"content":{"rendered":"\n

\u975e\u7ebf\u6027\u89c4\u5212\u7684\u5b9a\u4e49<\/h2>\n\n\n\n

\u6570\u5b66\u89c4\u5212\u662f\u8fd0\u7b79\u5b66\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u5b83\u7528\u6765\u7814\u7a76\u5728\u7ed9\u5b9a\u6761\u4ef6\u4e0b\uff08\u7ea6\u675f\u6761\u4ef6\uff09\uff0c\u5982\u4f55\u6309\u7167\u4e00\u8861\u91cf\u6307\u6807\uff08\u76ee\u6807\u51fd\u6570\uff09\u6765\u5bfb\u6c42\u8ba1\u5212\u3001\u7ba1\u7406\u5de5\u4f5c\u4e2d\u7684\u6700\u4f18\u65b9\u6848\u3002<\/p>\n\n\n\n

[math]\\min [\/math]\u6216[math]\\max f(x), \\text{ s.t. } g_i(x) \\leq 0 [\/math]\uff08\u5982\u679c\u662f\u5927\u4e8e\u7684\u5219\u8981\u624b\u52a8\u6539\u4e3a\u5c0f\u4e8e0\uff09<\/p>\n\n\n\n

\u8fd9\u91cc\u7684[math]x[\/math]\u79f0\u4e3a\u51b3\u7b56\u53d8\u91cf\uff1b[math]f(x)[\/math]\u79f0\u4e3a\u76ee\u6807\u51fd\u6570\uff1b[math]g_i(x) \\leq 0[\/math]\u79f0\u4e3a\u7ea6\u675f\u6761\u4ef6\u3002<\/p>\n\n\n\n

\u5982\u679c[math]f(x)[\/math]\u548c\u7ea6\u675f\u6761\u4ef6\u5747\u4e3a\u975e\u7ebf\u6027\u8868\u8fbe\u5f0f<\/mark>\uff0c\u5219\u6b64\u65f6\u5c31\u662f\u975e\u7ebf\u6027\u89c4\u5212\u3002<\/p>\n\n\n\n

\u975e\u7ebf\u6027\u89c4\u5212\u7684\u5e94\u7528<\/h2>\n\n\n\n

\u4f8b 1. \u5728\u7ea610000m\u9ad8\u7a7a\u7684\u67d0\u8fb9\u957f160km\u7684\u6b63\u65b9\u5f62\u533a\u57df\u5185\uff0c\u7ecf\u5e38\u6709\u82e5\u5e72\u67b6\u98de\u673a\u4f5c\u6c34\u5e73\u98de\u884c\u3002
\u533a\u57df\u5185\u6bcf\u67b6\u98de\u673a\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u5411\u91cf\u5747\u7531\u8ba1\u7b97\u673a\u8bb0\u5f55\u5176\u6570\u636e\uff0c\u4ee5\u4fbf\u8fdb\u884c\u98de\u884c\u7ba1\u7406\u3002\u5f53\u4e00\u67b6
\u6b32\u8fdb\u5165\u8be5\u533a\u57df\u7684\u98de\u673a\u5230\u8fbe\u533a\u57df\u8fb9\u7f18\u65f6,\u8bb0\u5f55\u5176\u6570\u636e\u540e,\u8981\u7acb\u5373\u8ba1\u7b97\u5e76\u5224\u65ad\u662f\u5426\u4f1a\u4e0e\u533a\u57df\u5185
\u7684\u98de\u673a\u53d1\u751f\u78b0\u649e\u3002\u5982\u679c\u4f1a\u78b0\u649e,\u5219\u5e94\u8ba1\u7b97\u5982\u4f55\u8c03\u6574\u5404\u67b6\uff08\u5305\u62ec\u65b0\u8fdb\u4eba\u7684\uff09\u98de\u673a\u98de\u884c\u7684\u65b9\u5411
\u89d2,\u4ee5\u907f\u514d\u78b0\u649e\u3002\u73b0\u5047\u5b9a\u6761\u4ef6\u5982\u4e0b\uff1a
\uff081\uff09\u4e0d\u78b0\u649e\u7684\u6807\u51c6\u4e3a\u4efb\u610f\u4e24\u67b6\u98de\u673a\u7684\u8ddd\u79bb\u5927\u4e8e8km\u3002
\uff082\uff09\u98de\u673a\u98de\u884c\u65b9\u5411\u89d2\u8c03\u6574\u7684\u5e45\u5ea6\u4e0d\u5e94\u8d85\u8fc730\u00b0\u3002
\uff083\uff09\u6240\u6709\u98de\u673a\u98de\u884c\u901f\u5ea6\u5747\u4e3a800km\/h\u3002
\uff084\uff09\u8fdb\u4eba\u8be5\u533a\u57df\u7684\u98de\u673a\u5728\u5230\u8fbe\u533a\u57df\u8fb9\u7f18\u65f6,\u4e0e\u533a\u57df\u5185\u98de\u673a\u7684\u8ddd\u79bb\u5e94\u572860km\u4ee5\u4e0a\u3002
\uff085\uff09\u6700\u591a\u9700\u8003\u86516\u67b6\u98de\u673a\u3002
\uff086\uff09\u4e0d\u5fc5\u8003\u8651\u98de\u673a\u79bb\u5f00\u6b64\u533a\u57df\u540e\u7684\u72b6\u51b5\u3002<\/p>\n\n\n\n

\u8bf7\u5bf9\u8fd9\u4e2a\u907f\u514d\u78b0\u649e\u7684\u98de\u884c\u7ba1\u7406\u95ee\u9898\u5efa\u7acb\u6570\u5b66\u6a21\u578b\uff0c\u5217\u51fa\u8ba1\u7b97\u6b65\u9aa4\uff0c\u5bf9\u4ee5\u4e0b\u6570\u636e\u8fdb\u884c\u8ba1\u7b97\uff08\u65b9\u5411\u89d2\u8bef\u5dee\u4e0d\u8d85\u8fc7 0.01 \u5ea6\uff09\uff0c\u8981\u6c42\u98de\u673a\u98de\u884c\u65b9\u5411\u89d2\u8c03\u6574\u7684\u5e45\u5ea6\u5c3d\u91cf\u5c0f\u3002
\u8bbe\u8be5\u533a\u57df 4 \u4e2a\u9876\u70b9\u7684\u5750\u6807\u4e3a[math](0,0)[\/math]\uff0c[math](160,0)[\/math]\uff0c[math](160,160)[\/math]\uff0c[math](0,160)[\/math]\u3002\u8bb0\u5f55\u6570\u636e\u89c1\u4e0b\u8868\u3002<\/p>\n\n\n\n\n \n \n \n \n \n \n \n \n \n
\u98de\u673a\u7f16\u53f7<\/th>\n \u6a2a\u5750\u6807x<\/th>\n \u7eb5\u5750\u6807y<\/th>\n \u65b9\u5411\u89d2[math]\/(^{\\circ})[\/math]<\/th>\n <\/tr>\n <\/thead>\n
1<\/td>\n 150<\/td>\n 140<\/td>\n 243<\/td>\n <\/tr>\n
2<\/td>\n 85<\/td>\n 85<\/td>\n 236<\/td>\n <\/tr>\n
3<\/td>\n 150<\/td>\n 155<\/td>\n 220.5<\/td>\n <\/tr>\n
4<\/td>\n 145<\/td>\n 50<\/td>\n 159<\/td>\n <\/tr>\n
5<\/td>\n 130<\/td>\n 150<\/td>\n 230<\/td>\n <\/tr>\n
\u65b0\u8fdb\u5165<\/td>\n 0<\/td>\n 0<\/td>\n 52<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n\n\n

\u89e3\u9898\u601d\u8def<\/mark><\/strong><\/p>\n\n\n\n

\u7531\u9898\u610f\u77e5\uff0c\u4efb\u610f\u4e24\u67b6\u98de\u673a [math] i, j [\/math] \u4e0d\u53d1\u751f\u78b0\u649e\u7684\u6761\u4ef6\u4e3a [math]\\min d_{ij}(t) > 8 [\/math]\uff0c\u5373\u4efb\u610f\u65f6\u523b\u8ddd\u79bb\u6700\u8fd1\u65f6\u4e5f\u8981\u5927\u4e8e 8 \u516c\u91cc\u3002\u8fd8\u8981\u6c42\u65b9\u5411\u89d2\u5ea6\u8c03\u6574\u5c3d\u53ef\u80fd\u5c0f\u3002\u6240\u4ee5\u76ee\u6807\u51fd\u6570\u4e3a [math]\\min \\sum_{i = 1}^{6} |\\Delta \\theta_i|[\/math] \u6216 [math]\\min \\sum_{i = 1}^{6} (\\Delta \\theta_i)^2 [\/math]\uff0c\u4e00\u822c\u9009\u540e\u8005\u3002<\/p>\n\n\n\n

\u8bbe [math] i [\/math] \u548c [math] j [\/math] \u4e24\u67b6\u98de\u673a\u7684\u521d\u59cb\u5750\u6807\u4e3a [math](x_i^0, y_i^0)[\/math]\u3001[math](x_j^0, y_j^0)[\/math]\uff0c\u5219\u7ecf\u8fc7 [math] t [\/math] \u65f6\u95f4\u540e\uff0c[math] x_i (t) = x_i^0 + vt \\cos \\theta_i [\/math]\uff0c[math] y_i (t) = y_i^0 + vt \\sin \\theta_i [\/math]\uff0c[math]\\theta_i = \\theta_i^0 + \\Delta \\theta_i [\/math]\uff0c[math]|\\Delta \\theta_i| \\leqslant \\frac {\\pi}{6}[\/math]\uff0c[math] i = 1, 2, \\cdots, n [\/math]\u3002<\/p>\n\n\n\n

\u6240\u4ee5\u4e24\u673a\u8ddd\u79bb [math] d_{ij}(t) = \\sqrt {(x_i – x_j)^2 + (y_i – y_j)^2}[\/math]\uff0c\u4e3a\u4e86\u8ba1\u7b97\u65b9\u4fbf\uff0c\u5c06\u5176\u5e73\u65b9\u540e\u518d\u4ee4 [math] d_{ij}^{(2)}(t) = [x_i (t) – x_j (t)]^2 + [y_i (t) – y_j (t)]^2 [\/math]\uff0c\u7136\u540e\u518d\u6c42 [math]\\min d_{ij}^{(2)}(t)[\/math]\uff0c\u8f6c\u6362\u4e3a\u6c42\u4e00\u5143\u51fd\u6570\u6781\u503c\u95ee\u9898 \u3002<\/p>\n\n\n

\n
\"\"<\/div><\/figure>\n<\/div>\n\n\n

\uff08\u8fd9\u91cc\u516c\u5f0f\u592a\u590d\u6742\uff0c\u5c31\u9009\u62e9\u76f4\u63a5\u622a\u56fe\u4e86\uff09<\/s><\/p>\n\n\n\n

\u540c\u7406\uff0c\u5bf9\u4e8e\u8fd9 6 \u67b6\u98de\u673a\uff0c\u4e24\u4e24\u7ec4\u5408\u5206\u522b\u4ee3\u5165\u4e0a\u9762\u7684[math]d_{ij}(t)[\/math]\u5c31\u53ef\u5f97\u5230 15 \u4e2a\u7ea6\u675f\u5173\u7cfb\u5f0f\u3002\u4e8e\u662f\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n\n\n\n

[math] \\min \\sum_{i = 1}^{6} (\\Delta \\theta_i)^2 \\ \\text{s.t.} \\begin{cases} d_{12}^{(2)} > 64 \\\\ d_{13}^{(2)} > 64 \\\\ d_{14}^{(2)} > 64 \\\\ \\cdots \\\\ d_{56}^{(2)} > 64 \\end{cases} [\/math]<\/p>\n\n\n\n

\u6700\u540e\u4f7f\u7528MATLAB\u7b49\u5de5\u5177\u5bf9\u8be5\u5f0f\u6c42\u89e3\u5373\u53ef\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u975e\u7ebf\u6027\u89c4\u5212\u7684\u5b9a\u4e49 \u6570\u5b66\u89c4\u5212\u662f\u8fd0\u7b79\u5b66\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u5b83\u7528\u6765\u7814\u7a76\u5728\u7ed9\u5b9a\u6761\u4ef6\u4e0b\uff08\u7ea6\u675f\u6761\u4ef6\uff09\uff0c\u5982\u4f55\u6309\u7167\u4e00\u8861\u91cf\u6307\u6807\uff08\u76ee\u6807\u51fd\u6570 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-1351","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1351"}],"version-history":[{"count":47,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1351\/revisions"}],"predecessor-version":[{"id":1399,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1351\/revisions\/1399"}],"wp:attachment":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}