2022-05-20<\/p>\n
\u524d\u8a00\uff1a\u5bf9\u4e8e\u65e0\u4eba\u9a7e\u9a76\u8def\u5f84\u89c4\u5212\u7cfb\u5217\u7684\u7b2c\u4e8c\u7bc7RRT\u7b97\u6cd5\u7684\u6539\u8fdb\u90e8\u5206\uff0c\u7531\u4e8e\u6709\u4e9b\u5185\u5bb9\u5c5e\u4e8e\u4e2a\u4eba\u60f3\u5230\u7684\u521b\u65b0\u70b9\uff0c\u6709\u60f3\u6cd5\u6295\u4e00\u7bc7\u5c0f\u8bba\u6587\u6240\u4ee5\u6682\u65f6\u6ca1\u6709\u516c\u5f00\uff0c\u7b49\u540e\u7eed\u5b8c\u6210\u540e\u6211\u4f1a\u518d\u516c\u5f00\u4ecb\u7ecd\u3002\u4eca\u5929\u7b2c\u4e09\u7bc7\u5185\u5bb9\u5f00\u542f\u4e00\u4e2a\u65b0\u7684\u7b97\u6cd5\u4ecb\u7ecd\uff1aFrenet\u5750\u6807\u7cfb\u4e0b\u7684\u52a8\u6001\u89c4\u5212\u3002\u6211\u82b1\u4e86\u5c06\u8fd1\u534a\u4e2a\u6708\u7684\u65f6\u95f4\u6765\u4e86\u89e3\u3001\u7814\u7a76\u7b97\u6cd5\u539f\u7406\uff0c\u7406\u89e3\u7f51\u4e0apython\u5f00\u6e90\u7684\u4ee3\u7801\uff0c\u6700\u540e\u6839\u636e\u4e2a\u4eba\u7406\u89e3\u5728matlab\u4e0a\u8fdb\u884c\u4e86\u590d\u73b0\u3002\u5982\u679c\u8fd8\u6ca1\u6709\u770b\u8fc7\u6211\u524d\u9762\u6587\u7ae0\u7684\u8bfb\u8005\uff0c\u53ef\u4ee5\u70b9\u51fb\u4e0b\u65b9\u7684\u4f20\u9001\u95e8\uff1a
\n\u65e0\u4eba\u9a7e\u9a76\u8def\u5f84\u89c4\u5212\uff08\u4e00\uff09\u5168\u5c40\u8def\u5f84\u89c4\u5212 – RRT\u7b97\u6cd5\u539f\u7406\u53ca\u5b9e\u73b0
\n\u540c\u6837\uff0c\u5982\u679c\u6587\u4e2d\u6709\u9519\u8bef\u6216\u4fb5\u6743\u7684\u5730\u65b9\u8fd8\u8bf7\u5404\u4f4d\u8bfb\u8005\u6307\u51fa\uff0c\u6211\u4f1a\u53ca\u65f6\u4f5c\u51fa\u4fee\u6539\uff0c\u7b14\u8005\u5728\u8fd9\u5148\u884c\u8c22\u8fc7\u3002
\n\u4e00\u3001\u8f68\u8ff9\u89c4\u5212\u65b9\u6cd5\u7b80\u4ecb
\n\u5728\u7b2c\u4e00\u7bc7\u6587\u7ae0\u4e2d\u6211\u5bf9\u65e0\u4eba\u9a7e\u9a76\u8def\u5f84\u89c4\u5212\u6280\u672f\u505a\u4e86\u4e2a\u7b80\u5355\u7684\u4ecb\u7ecd\uff0c\u5373\u53ef\u4ee5\u5206\u4e3a\u5168\u5c40\u8def\u5f84\u89c4\u5212\u548c\u5c40\u90e8\u8def\u5f84\u89c4\u5212\u4e24\u90e8\u5206\u3002\u4eca\u5929\u4ecb\u7ecd\u7684Frenet\u5750\u6807\u7cfb\u4e0b\u52a8\u6001\u8f68\u8ff9\u89c4\u5212\u5c31\u5c5e\u4e8e\u5c40\u90e8\u8def\u5f84\u89c4\u5212\u7684\u5185\u5bb9\u3002\u5728\u8fd9\u6211\u5148\u7b80\u8981\u4ecb\u7ecd\u4e00\u4e0b\u8f68\u8ff9\u89c4\u5212\u7684\u65b9\u6cd5\u3002\u53c2\u8003\u8bba\u6587\uff1a\u57fa\u4e8e\u6fc0\u5149\u96f7\u8fbe\u7684\u73af\u5883\u8bc6\u522b\u53ca\u5c40\u90e8\u8def\u5f84\u89c4\u5212\u6280\u672f\u7814\u7a76\u3002
\n\u65e0\u4eba\u8f66\u7684\u5c40\u90e8\u8def\u5f84\u89c4\u5212\u4e0d\u4ec5\u9700\u8981\u8003\u8651\u5230\u9053\u8def\u4ea4\u901a\u4e2d\u7684\u9759\u6001\u969c\u788d\u7269\u7684\u907f\u969c\u95ee\u9898\uff0c\u8fd8\u9700\u8981\u5bf9\u73af\u5883\u4e2d\u884c\u4eba\u3001\u8f66\u8f86\u7b49\u52a8\u6001\u969c\u788d\u7269\u672a\u6765\u8f68\u8ff9\u505a\u51fa\u7684\u9884\u5224\uff0c\u5bf9\u672a\u6765\u65f6\u95f4\u6bb5\u5185\u7684\u78b0\u649e\u53ef\u80fd\u6027\u8fdb\u884c\u5206\u6790\uff0c\u4fdd\u8bc1\u8f66\u8f86\u5b89\u5168\u3001\u8212\u9002\u7684\u884c\u9a76\uff0c\u56e0\u800c\u5728\u6c42\u89e3\u8fc7\u7a0b\u4e2d\u9700\u8981\u8003\u8651\u65f6\u95f4\u7ef4\u5ea6 t\u3002\u5f53\u8def\u5f84\u70b9\u589e\u52a0\u4e86\u65f6\u95f4\u8fd9\u4e00\u7ef4\u5ea6\uff0c\u5b9e\u8d28\u4e0a\u8f6c\u53d8\u4e3a\u4e86\u8f68\u8ff9\u70b9\uff0c\u56e0\u800c\u5728\u81ea\u52a8\u9a7e\u9a76\u6280\u672f\u9886\u57df\u5c40\u90e8\u8def\u5f84\u89c4\u5212\u4e5f\u53ef\u4ee5\u79f0\u4e3a\u8f68\u8ff9\u89c4\u5212\u3002\u8f66\u8f86\u5728\u4e09\u7ef4\u7a7a\u95f4\u5185\u7684\u8f68\u8ff9\u89c4\u5212\uff0c\u4e00\u822c\u6709\u4e09\u79cd\u5e38\u7528\u7684\u7b56\u7565\uff1a
\n\u4e00\u5c06\u4e09\u7ef4\u7a7a\u95f4\u79bb\u6563\u5316\uff0c\u901a\u8fc7\u542f\u53d1\u5f0f\u641c\u7d22\u7b97\u6cd5\u8fdb\u884c\u6c42\u89e3\u3002\u4e8c\u662f\u5c06\u8f68\u8ff9\u5206\u89e3\u4e3a\u8def\u5f84\u89c4\u5212\u548c\u901f\u5ea6\u89c4\u5212\u4e24\u4e2a\u8fc7\u7a0b\u3002\u8be5\u65b9\u6cd5\u7684\u601d\u60f3\u5728\u4e8e\u901a\u8fc7\u8def\u5f84\u89c4\u5212\u5b8c\u6210\u9759\u6001\u73af\u5883\u4e0b\u8def\u5f84\u6c42\u89e3\uff0c\u7136\u540e\u4f7f\u7528\u901f\u5ea6\u89c4\u5212\u65b9\u6cd5\u89e3\u51b3\u8fd0\u52a8\u969c\u788d\u7269\u7684\u907f\u649e\u95ee\u9898\u3002\u4e09\u662f\u5c06\u8f68\u8ff9\u5206\u89e3\u4e3a\u4e24\u4e2a\u65b9\u5411\u5173\u4e8e\u65f6\u95f4\u7684\u4f18\u5316\u6c42\u89e3\u95ee\u9898\u3002\u6700\u65e9\u7531\u4e8e Werling \u63d0\u51fa\u5c06\u4e09\u7ef4\u7684\u8f68\u8ff9\u89c4\u5212\u5206\u89e3\u4e3a\u6a2a\u5411\u7684\u8fd0\u52a8\u89c4\u5212\u548c\u7eb5\u5411\u7684\u8fd0\u52a8\u89c4\u5212\u95ee\u9898\uff0c\u8fd9\u91cc\u7684\u6a2a\u5411\u662f\u6307\u8f66\u8f86\u76f8\u5bf9\u4e8e\u9053\u8def\u4e2d\u5fc3\u7684\u6cd5\u7ebf\u65b9\u5411\uff0c\u7eb5\u5411\u6307\u4e2d\u5fc3\u7ebf\u7684\u5207\u7ebf\u65b9\u5411\u3002
\n\u90a3\u4e48Frenet\u5750\u6807\u7cfb\u4e0b\u52a8\u6001\u8f68\u8ff9\u89c4\u5212\u5b9e\u9645\u4e0a\u5c31\u5c5e\u4e8e\u7b2c\u4e09\u79cd\uff0c\u5c06\u89c4\u5212\u95ee\u9898\u5206\u89e3\u4e3a\u7eb5\u5411\u548c\u6a2a\u5411\u6765\u5206\u522b\u6c42\u89e3\u3002
\n\u4e8c\u3001Frenet\u5750\u6807\u7cfb\u8f6c\u6362
\n1\u3001Frenet\u5750\u6807\u7cfb\u6982\u5ff5
\n\u5728\u8f68\u8ff9\u89c4\u5212\u8fc7\u7a0b\u4e2d\uff0c\u4f7f\u7528\u7b1b\u5361\u5c14\u76f4\u89d2\u5750\u6807\u7cfb\u5e76\u4e0d\u80fd\u5f88\u597d\u7684\u63cf\u8ff0\u8f66\u8f86\u5f53\u524d\u4f4d\u7f6e\u4e0e\u5f53\u524d\u6240\u5728\u8f66\u9053\u7684\u5173\u7cfb\uff0c\u56e0\u6b64\u9700\u8981\u5f15\u5165Frenet\u5750\u6807\u7cfb\u7684\u6982\u5ff5\u3002\u5728Frenet\u5750\u6807\u7cfb\u4e2d\uff0c\u4f7f\u7528\u9053\u8def\u4e2d\u5fc3\u7ebf\u4f5c\u4e3a\u53c2\u8003\u7ebf\uff0c\u5c06\u8f66\u8f86\u7684\u8f68\u8ff9\u70b9\u6295\u5f71\u5230\u53c2\u8003\u7ebf\u4e0a\u5f97\u5230\u53c2\u8003\u70b9\uff0c\u4ee4\u6cbf\u53c2\u8003\u7ebf\u65b9\u5411\u4e3a\u7eb5\u8f74s\uff0c\u5782\u76f4\u4e8e\u53c2\u8003\u7ebf\u65b9\u5411\u4e3a\u6a2a\u8f74d\u3002Frenet\u5750\u6807\u7cfb\u53ef\u4ee5\u5f88\u5bb9\u6613\u786e\u5b9a\u8f66\u8f86\u504f\u79bb\u8f66\u9053\u4e2d\u5fc3\u7ebf\u7684\u8ddd\u79bb\u53ca\u6cbf\u7740\u8f66\u9053\u7ebf\u884c\u9a76\u7684\u8ddd\u79bb\uff0c\u53ef\u4ee5\u5ffd\u7565\u9053\u8def\u66f2\u7387\u7684\u5f71\u54cd\uff0c\u76f8\u6bd4\u4e8e\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e0b\u7684\u63cf\u8ff0\u66f4\u4e3a\u7b80\u6d01\u548c\u76f4\u89c2\u3002 Frenet\u5750\u6807\u7cfb\u548c\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u5173\u7cfb\u5982\u4e0b\uff1a <\/p>\n
2\u3001Frenet-\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u8f6c\u6362
\n\u5047\u8bbe\u8f66\u8f86\u884c\u9a76\u81f3t\u65f6\u523b\u5b9e\u9645\u8f68\u8ff9\u548c\u53c2\u8003\u8f68\u8ff9\u5982\u4e0b\uff1a <\/p>\n
\u5168\u5c40\u5750\u6807\u7cfb\u4e0b\uff0ct\u65f6\u523b\u8f66\u8f86\u7684\u72b6\u6001\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a\uff0c\u5404\u53c2\u6570\u542b\u4e49\u5982\u4e0b\uff1a
\n\uff0c\u8f66\u8f86\u5f53\u524d\u4f4d\u7f6e\uff1b
\n\u00a0\u65b9\u4f4d\u89d2\uff0c\u901f\u5ea6\u65b9\u5411\u4e0ex\u6b63\u5411\u5939\u89d2\uff1b
\n\u00a0\u66f2\u7387\uff1b\u00a0\u901f\u5ea6\uff1b\u00a0\u00a0\u52a0\u901f\u5ea6\u3002
\n\u00a0Q\u6295\u5f71\u5230\u53c2\u8003\u7ebf\u4e0a\u7684\u70b9\uff0cP\u5728\u5168\u5c40\u5750\u6807\u7cfb\u4e0b\u7684\u4f4d\u7f6e\u5411\u91cf\u3002
\nFrenet\u5750\u6807\u7cfb\u4e0b\uff0c\u8f66\u8f86\u7684\u72b6\u6001\u91cf\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a\uff0c\u5404\u53c2\u6570\u542b\u4e49\u5982\u4e0b\uff1a
\n\u00a0\u6cbf\u53c2\u8003\u7ebf\u7eb5\u5411\u4f4d\u79fb\uff1b\u00a0\u00a0\u6cbf\u53c2\u8003\u7ebf\u7eb5\u5411\u901f\u5ea6\uff1b\u00a0\u00a0\u6cbf\u53c2\u8003\u7ebf\u7eb5\u5411\u52a0\u901f\u5ea6\uff1b
\n\u00a0\u53c2\u8003\u7ebf\u6cd5\u7ebf\u65b9\u5411\uff08\u6a2a\u5411\uff09\u4f4d\u79fb\uff1b\u00a0\u00a0\u6a2a\u5411\u901f\u5ea6\uff1b\u00a0\u00a0\u6a2a\u5411\u52a0\u901f\u5ea6\uff1b
\n\u00a0\u6a2a\u5411\u4f4d\u79fb\u5bf9\u5e94\u7684\u5f27\u957f\u7684\u4e00\u9636\u5bfc\u6570\uff1b\u00a0\u6a2a\u5411\u4f4d\u79fb\u5bf9\u5e94\u7684\u5f27\u957f\u7684\u4e8c\u9636\u5bfc\u6570\u3002
\n\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e0eFrenet\u5750\u6807\u7cfb\u72b6\u6001\u91cf\u8f6c\u5316\u53ef\u4ee5\u8868\u793a\u4e3a\u5982\u4e0b\u5173\u7cfb\uff1a <\/p>\n
\u7531\u4e8e\u5177\u4f53\u63a8\u5bfc\u8fc7\u7a0b\u6bd4\u8f83\u7e41\u7410\u548c\u5197\u957f\uff0c\u6211\u5728\u8fd9\u4e0d\u8fdb\u884c\u5c55\u5f00\u4ecb\u7ecd\uff0c\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u8bba\u6587\u7684\u5185\u5bb9\uff1a\u57fa\u4e8eFrenet\u5750\u6807\u7cfb\u7684\u81ea\u52a8\u9a7e\u9a76\u8f68\u8ff9\u89c4\u5212\u4e0e\u4f18\u5316\u7b97\u6cd5\u3002
\n\u4e09\u3001\u52a8\u6001\u8f68\u8ff9\u89c4\u5212\u8fc7\u7a0b
\n1\u3001\u57fa\u4e8ejerk\u5b9e\u65f6\u8f68\u8ff9\u89c4\u5212
\n\u8f68\u8ff9\u89c4\u5212\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\u3002\u901a\u5e38\u6765\u8bf4\uff0c\u4e58\u5750\u8212\u9002\u6027\u548c\u5b89\u5168\u6027\u662f\u8f68\u8ff9\u89c4\u5212\u7684\u76ee\u6807\uff0c\u8fc7\u5927\u7684\u52a0\u901f\u5ea6\u53d8\u5316\u4f1a\u4f7f\u5f97\u4e58\u5ba2\u611f\u5230\u4e0d\u9002\u3002\u56e0\u6b64\u8f68\u8ff9\u89c4\u5212\u8fc7\u7a0b\u4e2d\u53ef\u4ee5\u5c06\u52a0\u901f\u5ea6\u53d8\u5316\u7387\uff0c\u4e5f\u5c31\u662f\u201c\u52a0\u52a0\u901f\u5ea6\u201d-jerk\u4f5c\u4e3a\u4f18\u5316\u7684\u76ee\u6807\uff0c\u6765\u4fdd\u8bc1\u4e58\u5750\u7684\u8212\u9002\u6027\u3002
\n\u6839\u636e\u6587\u732e\u4e2d\u7684\u4ecb\u7ecd\uff0c\u7ecf\u8fc7Frenet\u5206\u89e3\u540e\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u4e00\u7ef4\u79ef\u5206\u7cfb\u7edf\uff1a <\/p>\n
\u5176\u4e2d\uff0c\u4e3a\u6a2a\u5411\/\u7eb5\u5411\u8fd0\u52a8\uff0c\uff0c\u4e3ajerk\u3002
\nTakahashi\u5df2\u8bc1\u660e\u5bf9\u4e8e\u4e0a\u8ff0\u7cfb\u7edf\u7531\u65f6\u523b\u521d\u59cb\u914d\u7f6e\u548c\u65f6\u523b\u76ee\u6807\u914d\u7f6e\uff0c\u57fa\u4e8ejerk\u7684\u4f18\u5316\u8f68\u8ff9\u90fd\u5728\u4e00\u4e2a\u4e94\u6b21\u591a\u9879\u5f0f\u4e2d\uff0c\u4e14\u5fc5\u5b58\u5728\u6700\u5c0f\u5316\u7684\u89e3\uff1a <\/p>\n
\u5176\u4e2d\uff0c\u53ef\u4ee5\u7528\u4e8e\u8bc4\u4ef7\u8212\u9002\u6027\uff0c\u662f\u76ee\u6807\u914d\u7f6e\u51fd\u6570\uff0c\u7528\u4ee5\u8bc4\u4ef7\u8f68\u8ff9\u3002
\n2\u3001\u6a2a\u5411\u8f68\u8ff9\u89c4\u5212\u6c42\u89e3
\n\u6a2a\u5411\u89c4\u5212\u4e3b\u8981\u627f\u62c5\u7684\u662f\u907f\u969c\u3001\u6362\u9053\u7b49\u4efb\u52a1\uff0c\u5df2\u77e5\u5728\u65f6\u523b\u7684\u914d\u7f6e\u548c\u65f6\u523b\u76ee\u6807\u914d\u7f6e\uff0c\u5219\u4e94\u6b21\u591a\u9879\u5f0f\u53ef\u4ee5\u5199\u4e3a\uff1a <\/p>\n
\u5219\u6709\uff1a <\/p>\n
\u4e3a\u7b80\u5316\u8fd0\u7b97\uff0c\u4ee4\uff0c\uff0c\u5219\u53ef\u6c42\u5f97\uff1a <\/p>\n
\u4ee3\u5165\u4e0a\u5f0f\uff0c\u53ef\u4ee5\u89e3\u5f97\uff1a <\/p>\n
\u7531\u6b64\u53ef\u4ee5\u6c42\u5f97\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u901a\u5e38\u6765\u8bf4\u5e0c\u671b\u8f66\u8f86\u6cbf\u7740\u53c2\u8003\u7ebf\u884c\u9a76\uff0c\u6a2a\u5411\u901f\u5ea6\u548c\u6a2a\u5411\u52a0\u901f\u5ea6\u5747\u4e3a0\uff0c\u90a3\u4e48\u65f6\u523b\u7684\u76ee\u6807\u914d\u7f6e\u53ef\u4ee5\u5199\u4e3a\u3002
\n\u901a\u8fc7\u8bbe\u7f6e\u91c7\u6837\u95f4\u9694\u548c\u6a2a\u5411\u8ddd\u79bb\u95f4\u9694\uff0c\u53ef\u4ee5\u751f\u6210\u4e00\u7cfb\u5217\u7684\u5907\u9009\u66f2\u7ebf\uff1a <\/p>\n
3\u3001\u7eb5\u5411\u8f68\u8ff9\u89c4\u5212\u6c42\u89e3
\n\u5bf9\u4e8e\u7eb5\u5411\u8f68\u8ff9\u89c4\u5212\uff0c\u9700\u8981\u8003\u8651\u5230\u8f66\u8f86\u7684\u5b9e\u9645\u884c\u9a76\u573a\u666f\u9700\u6c42\uff0c\u4f8b\u5982\u8ddf\u8f66\u3001\u5b9a\u901f\u5de1\u822a\u3001\u505c\u8f66\u3001\u6c47\u6d41\u7b49\u7b49\u3002\u4e0d\u540c\u7684\u884c\u9a76\u60c5\u666f\u6709\u4e0d\u540c\u7684\u671f\u671b\u914d\u7f6e\u3002\u5728\u8fd9\u6211\u4ec5\u9488\u5bf9\u6700\u7b80\u5355\u7684\u5b9a\u901f\u5de1\u822a\u60c5\u666f\u8fdb\u884c\u4ecb\u7ecd\u3002
\n\u7531\u4e8e\u662f\u5b9a\u901f\u5de1\u822a\uff0c\u90a3\u4e48\u6b64\u65f6\u6cbf\u7740\u53c2\u8003\u7ebf\u65b9\u5411\u7684\u4f4d\u7f6e\u914d\u7f6e\u5219\u65e0\u9700\u8003\u8651\uff0c\u4ec5\u9700\u8981\u914d\u7f6e\u7eb5\u5411\u901f\u5ea6\u548c\u7eb5\u5411\u52a0\u901f\u5ea6\u3002\u540c\u65f6\uff0c\u7531\u4e8e\u51cf\u5c11\u4e86\u4e00\u4e2a\u914d\u7f6e\u91cf\uff0c\u8f68\u8ff9\u591a\u9879\u5f0f\u53ef\u4ee5\u964d\u4e3a\u4e00\u4e2a4\u6b21\u591a\u9879\u5f0f\u6765\u8003\u8651\u3002\u7531\u65f6\u523b\u7684\u914d\u7f6e\u548c\u65f6\u523b\u76ee\u6807\u914d\u7f6e\uff0c4\u6b21\u591a\u9879\u5f0f\u53ef\u4ee5\u5199\u4e3a\uff1a <\/p>\n
\u5219\u6709\uff1a <\/p>\n
\u540c\u6837\uff0c\u4ee4\uff0c\uff0c\u5219\u53ef\u6c42\u5f97\uff1a <\/p>\n
\u4ee3\u5165\u4e0a\u5f0f\uff0c\u53ef\u4ee5\u89e3\u5f97\uff1a <\/p>\n
\u901a\u8fc7\u8bbe\u7f6e\u91c7\u6837\u95f4\u9694\u548c\u901f\u5ea6\u53d8\u5316\u95f4\u9694\uff0c\u4e5f\u53ef\u4ee5\u751f\u6210\u4e00\u7cfb\u5217\u7684\u5907\u9009\u66f2\u7ebf\uff1a <\/p>\n
4\u3001\u6700\u4f18\u8f68\u8ff9\u9009\u62e9
\n\u5bf9\u4e8e\u6a2a\u5411\u548c\u7eb5\u5411\u8f68\u8ff9\u89c4\u5212\uff0c\u90fd\u751f\u6210\u4e86\u4e00\u7cfb\u5217\u7684\u5907\u9009\u8f68\u8ff9\uff0c\u901a\u8fc7\u8bbe\u5b9a\u8bc4\u4ef7\u51fd\u6570\u6765\u786e\u5b9a\u6bcf\u4e00\u65f6\u523b\u7684\u6700\u4f18\u8def\u5f84\u3002
\n\u6839\u636e\u53c2\u8003\u8bba\u6587\uff0c\u6a2a\u5411\u8f68\u8ff9\u8bc4\u4ef7\u51fd\u6570\u5982\u4e0b\uff1a <\/p>\n
\u5176\u4e2d\uff1a\uff0c\u5373jerk\u5728\u91c7\u6837\u65f6\u95f4\u5185\u7684\u53d8\u5316\u5e45\u5ea6\uff0c\u7528\u6765\u8bc4\u4ef7\u8212\u9002\u6027\uff1b\u8868\u793a\u76ee\u6807\u72b6\u6001\u504f\u79bb\u4e2d\u5fc3\u7ebf\u7684\u6307\u6807\uff1b\u4e3a\u8f66\u8f86\u884c\u9a76\u6548\u7387\u8bc4\u4ef7\u6307\u6807\u3002
\n\u7eb5\u5411\u8f68\u8ff9\u8bc4\u4ef7\u51fd\u6570\u5982\u4e0b\uff1a <\/p>\n
\u4e0e\u6a2a\u5411\u8bc4\u4ef7\u51fd\u6570\u552f\u4e00\u4e0d\u540c\u7684\u662f\u4ee3\u8868\u76ee\u6807\u914d\u7f6e\u901f\u5ea6\u4e0e\u8bbe\u5b9a\u671f\u671b\u901f\u5ea6\u7684\u5dee\u8ddd\u635f\u5931\u3002
\n\u6700\u540e\u5c06\u4e8c\u8005\u8fdb\u884c\u5408\u5e76\uff0c\u52a0\u5165\u6743\u91cd\u7cfb\u6570\uff0c\u5373\u53ef\u5f97\u5230\u6700\u4f18\u8def\u5f84\u8bc4\u4ef7\u51fd\u6570\uff1a <\/p>\n
\u901a\u5e38\u8f68\u8ff9\u8bc4\u4ef7\u51fd\u6570\u8d8a\u5c0f\uff0c\u4ee3\u8868\u8be5\u8f68\u8ff9\u7684\u4ee3\u4ef7\u8d8a\u5c0f\uff0c\u4f18\u5148\u5ea6\u8d8a\u9ad8\u3002
\n5\u3001\u78b0\u649e\u68c0\u6d4b
\nAtsushi Sakai\u5728Python\u4ee3\u7801\u4e2d\u8bbe\u7f6e\u7684\u78b0\u649e\u68c0\u6d4b\u65b9\u6cd5\u662f\uff1a
\n\u5047\u8bbe\u8f66\u8f86\u5728\u5907\u9009\u8f68\u8ff9\u4e00\u4e2a\u91c7\u6837\u65f6\u523b\u5185\u6cbf\u53c2\u8003\u7ebf\u65b9\u5411\u884c\u9a76\u7eb5\u5411\u8ddd\u79bbs\uff0c\u82e5\u7ed3\u675f\u540e\u8f66\u8f86\u4e0e\u969c\u788d\u7269\u7684\u8ddd\u79bb\u5c0f\u4e8e\u8bbe\u5b9a\u7684\u9608\u503c\uff0c\u5219\u8be5\u8f68\u8ff9\u4e0d\u6ee1\u8db3\u78b0\u649e\u68c0\u6d4b\u9700\u6c42\uff0c\u8fdb\u884c\u5254\u9664\u3002\u5bf9\u6240\u6709\u5907\u9009\u8f68\u8ff9\u8fdb\u884c\u8be5\u9879\u64cd\u4f5c\u3002
\n\u6211\u5728matlab\u79fb\u690d\u4ee3\u7801\u7684\u65f6\u5019\uff0c\u6ca1\u6709\u5bf9\u8fd9\u90e8\u5206\u8fdb\u884c\u4fee\u6539\u3002
\n\u56db\u3001Python-Matlab\u4ee3\u7801\u79fb\u690d
\n\u6211\u5728\u7f51\u4e0a\u627e\u5230\u7684\u7b97\u6cd5\u7684Python\u4ee3\u7801\u662f\u65e5\u672c\u65e0\u4eba\u9a7e\u9a76\u5de5\u7a0b\u5e08Atsushi Sakai\u7f16\u5199\u7684\uff0c\u5e76\u5df2\u7ecf\u5728github\u4e0a\u5f00\u6e90\u3002\u6211\u5728\u6587\u672b\u4e5f\u7ed9\u51fa\u4e86\u6e90\u7801\u7684\u94fe\u63a5\uff0c\u6709\u9700\u8981\u7684\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u83b7\u53d6\u3002
\n\u4e3a\u4e86\u52a0\u6df1\u5bf9\u7b97\u6cd5\u7684\u7406\u89e3\uff0c\u540c\u65f6\u4fdd\u6301\u4e4b\u524d\u6240\u6709\u7b97\u6cd5\u9a8c\u8bc1\u5e73\u53f0\u7684\u4e00\u81f4\u6027\uff0c\u6211\u5c06Python\u6e90\u7801\u79fb\u690d\u5230\u4e86matlab2019\u3002\u5728\u8fd9\u6211\u4e0d\u5bf9Python\u6e90\u7801\u8fdb\u884c\u89e3\u91ca\uff0c\u4ec5\u5bf9\u6211\u79fb\u690d\u540e\u7684matlab\u4ee3\u7801\u8fdb\u884c\u4e00\u4e2a\u4ecb\u7ecd\u3002
\n1\u3001\u521d\u59cb\u53c2\u6570\u5b9a\u4e49\uff08\u5b8f\u5b9a\u4e49\uff09
\n\u5728\u7a0b\u5e8f\u6700\u5f00\u59cb\u5148\u7ed9\u51fa\u9700\u8981\u7528\u5230\u7684\u53c2\u6570\u7684\u5b9a\u4e49\u53ca\u6570\u503c\uff0c\u4f8b\u5982\u6700\u5927\u91c7\u6837\u6a2a\u5411\u8ddd\u79bb\u3001\u6a2a\u5411\u8ddd\u79bb\u91c7\u6837\u95f4\u9694\u3001\u6700\u5927\u91c7\u6837\u65f6\u95f4\u3001\u91c7\u6837\u65f6\u95f4\u95f4\u9694\u3001\u6700\u5927\u52a0\u901f\u5ea6\/\u901f\u5ea6\u7b49\u7b49\uff0c\u5177\u4f53\u5982\u4e0b\uff1a
\nSIM_LOOP = 500; MAX_SPEED = 50.0 \/ 3.6; % \u6700\u5927\u901f\u5ea6 [m\/s]MAX_ACCEL = 2.0; % \u6700\u5927\u52a0\u901f\u5ea6 [m\/ss]MAX_CURVATURE = 1.0; % \u6700\u5927\u66f2\u7387 [1\/m]MAX_ROAD_WIDTH = 7.0; % \u6700\u5927\u91c7\u6837\u6a2a\u5411\u8ddd\u79bb [m]D_ROAD_W = 1.0; % \u6a2a\u5411\u8ddd\u79bb\u91c7\u6837\u95f4\u9694 [m]DT = 0.2; % \u91c7\u6837\u65f6\u95f4\u95f4\u9694 [s]MAX_T = 5.0; % \u6700\u5927\u91c7\u6837\u65f6\u95f4 [s]MIN_T = 4.0; % \u6700\u5c0f\u91c7\u6837\u65f6\u95f4 [s]TARGET_SPEED = 30.0 \/ 3.6; % \u671f\u671b\u901f\u5ea6 [m\/s]D_T_S = 5.0 \/ 3.6; % \u7eb5\u5411\u901f\u5ea6\u91c7\u6837\u95f4\u9694 [m\/s]N_S_SAMPLE = 1;ROBOT_RADIUS = 2; % \u78b0\u649e\u68c0\u6d4b\u9608\u503c [m]robot_width = 1; % \u673a\u5668\u4eba\u5bbd [m]robot_length = 2; % \u673a\u5668\u4eba\u957f [m] % \u8bc4\u4ef7\u51fd\u6570\u6743\u91cdK_J = 0.1;K_T = 0.1;K_D = 1.0;K_LAT = 1.0;K_LON = 1.0; %% \u53c2\u6570\u8303\u56f4\u786e\u5b9ac_speed = 10.0 \/ 3.6; % \u5f53\u524d\u901f\u5ea6c_d = 2.0; % \u5f53\u524d\u6a2a\u5411\u4f4d\u79fbc_d_d = 0.0; % \u5f53\u524d\u6a2a\u5411\u901f\u5ea6c_d_dd = 0.0; % \u5f53\u524d\u6a2a\u5411\u52a0\u901f\u5ea6s0 = 0.0; % \u5f53\u524d\u6cbf\u8f66\u9053\u7ebf\u4f4d\u79fbarea = 20.0;
\n2\u3001\u969c\u788d\u7269\u70b9\u53ca\u53c2\u8003\u8def\u5f84\u751f\u6210
\n\u539f\u6587\u4e2d\u662f\u7ed9\u5b9a\u4e86\u51e0\u4e2a\u53c2\u8003\u8def\u5f84\u70b9\uff0c\u91c7\u7528\u4e09\u6b21\u6837\u6761\u7684\u65b9\u6cd5\u751f\u6210\u53c2\u8003\u8def\u5f84\u3002
\n%% \u53c2\u8003\u8def\u5f84\u70b9nodes = [0, 0; 10, -6; 20.5 5; 35, 6.5; 70.5, 0; 100, 5]; %% \u8bbe\u7f6e\u969c\u788d\u7269\u5750\u6807\u70b9ob = [20, 10 30, 9; 30, 6; 35, 9; 50, 3; 75, 0];%% \u751f\u6210\u671f\u671b\u8def\u5f84csp = Cubic_spline(nodes);
\nCubic_spline\u662f\u6211\u81ea\u5b9a\u4e49\u7684\u4e09\u6b21\u6837\u6761\u751f\u6210\u51fd\u6570\u3002
\n3\u3001\u5b9a\u4e49FrenetPath\u7ed3\u6784\u4f53
\n\u5b9a\u4e49FrenetPath\u7ed3\u6784\u4f53\uff0c\u5b58\u50a8\u6bcf\u4e00\u4e2a\u5907\u9009\u8def\u5f84\u7684\u6a2a\u5411\u3001\u7eb5\u5411\u89c4\u5212\u7ed3\u679c\uff0c\u53ca\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e0b\u7684\u72b6\u6001\u91cf\uff1a
\n%% Frenet\u8f68\u8ff9\u7ed3\u6784\u4f53FrenetPath.t = [];FrenetPath.d = [];FrenetPath.d_d = [];FrenetPath.d_dd = [];FrenetPath.d_ddd = [];FrenetPath.s = [];FrenetPath.s_d = [];FrenetPath.s_dd = [];FrenetPath.s_ddd = [];FrenetPath.cd = 0.0;FrenetPath.cv = 0.0;FrenetPath.cf = 0.0; FrenetPath.x = [];FrenetPath.y = [];FrenetPath.yaw = [];FrenetPath.ds = [];FrenetPath.c = [];
\n4\u3001Frenet\u52a8\u6001\u8f68\u8ff9\u89c4\u5212\u7b97\u6cd5
\n\u8fd9\u4e00\u90e8\u5206\u662f\u8be5\u7b97\u6cd5\u7684\u6838\u5fc3\u51fd\u6570\uff0c\u5373\u5b8c\u6210\u4e86\u7eb5\u5411\u3001\u6a2a\u5411\u8f68\u8ff9\u7684\u89c4\u5212\u8fc7\u7a0b\uff0c\u5907\u9009\u8f68\u8ff9\u7684\u8bc4\u4ef7\u8fc7\u7a0b\u53ca\u78b0\u649e\u68c0\u6d4b\u8fc7\u7a0b\u3002\u6700\u540e\u5c06\u5f53\u524d\u65f6\u523b\u6700\u4f18\u8f68\u8ff9\u8f93\u51fa\u7ed9path\uff0cpath\u5c5e\u4e8eFrenetPath\u7ed3\u6784\u4f53\u7c7b\u578b\u3002
\npath = calc_frenet_paths_fixed_velocity(csp, c_speed, c_d, c_d_d, c_d_dd, … s0,MAX_ROAD_WIDTH,D_ROAD_W, MIN_T, MAX_T, DT, … FrenetPath, TARGET_SPEED,D_T_S, N_S_SAMPLE, … K_D, K_J, K_LAT, K_LON, K_T, ob, MAX_ACCEL, … MAX_SPEED, MAX_CURVATURE,ROBOT_RADIUS);
\ncalc_frenet_path_fixed_velocity\u51fd\u6570\u5177\u4f53\u5185\u5bb9\u5982\u4e0b\uff1a
\nfunction fplist = calc_frenet_paths_fixed_velocity(csp, c_speed, c_d, c_d_d, c_d_dd, … s0,MAX_ROAD_WIDTH,D_ROAD_W, MIN_T, MAX_T, DT, … FrenetPath, TARGET_SPEED,D_T_S, N_S_SAMPLE, … K_D, K_J, K_LAT, K_LON, K_T, ob, MAX_ACCEL, … MAX_SPEED, MAX_CURVATURE,ROBOT_RADIUS); min_cost = [inf,inf]; cost = []; flag = 1; for di=-MAX_ROAD_WIDTH:D_ROAD_W:MAX_ROAD_WIDTH for Ti = MIN_T:DT:MAX_T fp = FrenetPath; lat_qp = QuinticPolynomial(c_d, c_d_d, c_d_dd, di, 0, 0, Ti); for t=0:DT:Ti-DT fp.t(1,end+1) = t; end for t=fp.t(1,1):DT:fp.t(1,end) fp.d(1,end+1) = lat_qp.a0 + lat_qp.a1*t + lat_qp.a2*t^2 + lat_qp.a3*t^3 + lat_qp.a4*t^4 + lat_qp.a5*t^5; fp.d_d(1,end+1) = lat_qp.a1 + 2*lat_qp.a2*t + 3*lat_qp.a3*t^2 + 4*lat_qp.a4*t^3 + 5*lat_qp.a5*t^4; fp.d_dd(1,end+1) = 2*lat_qp.a2 + 6*lat_qp.a3*t + 12*lat_qp.a4*t^2 + 20*lat_qp.a5*t^3; fp.d_ddd(1,end+1) = 6*lat_qp.a3 + 24*lat_qp.a4*t + 60*lat_qp.a5*t^2; end for tv = TARGET_SPEED – D_T_S * N_S_SAMPLE : D_T_S: TARGET_SPEED + D_T_S * N_S_SAMPLE tfp = fp; lon_qp = QuarticPolynomial(s0, c_speed, 0.0, tv, 0.0, Ti); for t=fp.t(1,1):DT:fp.t(1,end) tfp.s(1,end+1) = lon_qp.b0 + lon_qp.b1*t + lon_qp.b2*t^2 + lon_qp.b3*t^3 + lon_qp.b4*t^4; tfp.s_d(1,end+1) = lon_qp.b1 + 2*lon_qp.b2*t + 3*lon_qp.b3*t^2 + 4*lon_qp.b4*t^3; tfp.s_dd(1,end+1) = 2*lon_qp.b2 + 6*lon_qp.b3*t + 12*lon_qp.b4*t^2 ; tfp.s_ddd(1,end+1) = 6*lon_qp.b3 + 24*lon_qp.b4*t; end Jp = sum(tfp.d_ddd .^2); Js = sum(tfp.s_ddd .^2); ds = (TARGET_SPEED – tfp.s_d(1,end))^ 2; tfp.cd = K_J * Jp + K_T * Ti + K_D * tfp.d(1,end)^2; tfp.cv = K_J * Js + K_T * Ti + K_D * ds; tfp.cf = K_LAT * tfp.cd + K_LON * tfp.cv; tfp = calc_global_paths(tfp, csp); flag = check_paths(tfp, ob, MAX_ACCEL, MAX_SPEED, MAX_CURVATURE,ROBOT_RADIUS); if (flag == 1) cost(end+1,:) = [tfp.cf, di]; if min_cost(end,1) >= tfp.cf min_cost(end+1,:) = [tfp.cf, di]; fplist = tfp; end else flag = 1; end end end endend
\n\u5176\u4e2dQuinticPolynomial\u548cQuarticPolynomial\u51fd\u6570\u5c31\u662f\u8f68\u8ff9\u89c4\u5212\u7684\u5177\u4f53\u6c42\u89e3\u516c\u5f0f\uff1a
\nfunction lat_qp = QuinticPolynomial(xs, vxs, axs, xe, vxe, axe, time) lat_qp.a0 = xs; lat_qp.a1 = vxs; lat_qp.a2 = axs\/2; A = [time^3, time^4, time^5; 3*time^2, 4*time^3, 5*time^4; 6*time, 12*time^2, 20*time^3]; B = [xe – lat_qp.a0 – lat_qp.a1*time – lat_qp.a2*time^2; vxe – lat_qp.a1 – 2*lat_qp.a2*time; axe – 2*lat_qp.a2]; temp = A^(-1)*B; lat_qp.a3 = temp(1,1); lat_qp.a4 = temp(2,1); lat_qp.a5 = temp(3,1); end
\nfunction lon_qp = QuarticPolynomial(xs, vxs, axs, vxe, axe, time) lon_qp.b0 = xs; lon_qp.b1 = vxs; lon_qp.b2 = axs \/ 2.0; A = [3*time^2, 4*time^3 6*time, 12*time^2]; B = [vxe – lon_qp.b1 – 2*lon_qp.b2*time; axe – 2*lon_qp.b2]; temp = A^(-1)*B; lon_qp.b3 = temp(1,1); lon_qp.b4 = temp(2,1);end
\ncalc_global_paths\u7528\u4e8e\u6c42\u89e3\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e0b\u7684\u72b6\u6001\u91cf\uff1a
\nfunction fplist = calc_global_paths(fplist, csp) for i = 1:1:size(fplist.s,2) [idx] = findPoint(fplist.s(1,i), csp); i_x = csp(idx,1); i_y = csp(idx,2); i_yaw = (csp(idx+1,2) – csp(idx,2))\/(csp(idx+1,1) – csp(idx,1)); di = fplist.d(1,i); fplist.x(1,end+1) = i_x – di * sin(i_yaw); fplist.y(1,end+1) = i_y + di * cos(i_yaw); end for i = 1:1:size(fplist.x,2)-1 dx = fplist.x(1,i+1) – fplist.x(1,i); dy = fplist.y(1,i+1) – fplist.y(1,i); fplist.yaw(1,end+1) = atan(dy\/dx); fplist.ds(1,end+1) = sqrt(dx^1 + dy^2); end fplist.yaw(1,end+1) = fplist.yaw(1,end); fplist.ds(1,end+1) = fplist.ds(1,end); for i=1:1:size(fplist.yaw,2)-1 fplist.c(1,end+1) = (fplist.yaw(1,i+1) – fplist.yaw(1,i+1))\/fplist.ds(1,i); end fplist.c(1,end+1) = fplist.c(1,end);end
\ncheck_paths\u7528\u4e8e\u78b0\u649e\u68c0\u6d4b\uff0c\u5728\u8fd9\u91cc\u8fd8\u52a0\u5165\u4e86\u6700\u5927\u7eb5\u5411\u52a0\u901f\u5ea6\u3001\u6700\u5927\u7eb5\u5411\u901f\u5ea6\u548c\u6700\u5927\u66f2\u7387\u7ea6\u675f\u3002\u6211\u8bbe\u7f6e\u4e86\u4e00\u4e2a\u6807\u5fd7\u4f4dflag\uff0c\u53ea\u6709\u5f53\u901a\u8fc7\u78b0\u649e\u68c0\u6d4b\uff0c\u5373\u6807\u5fd7\u4f4d\u4e3a1\u7684\u65f6\u5019\uff0c\u624d\u4f1a\u8fdb\u884c\u540e\u7eed\u7684\u5224\u65ad\uff0c\u5426\u5219\u8be5\u8f68\u8ff9\u5c31\u88ab\u820d\u5f03\uff1a
\nfunction flag = check_paths(fplist, ob, MAX_ACCEL, MAX_SPEED, MAX_CURVATURE,ROBOT_RADIUS) flag = 1; for i=1:1:size(fplist.s_d ,2) if (fplist.s_d(1,i) > MAX_SPEED) flag = 0; break end if (fplist.s_dd(1,i) > MAX_ACCEL) flag = 0; break end if (fplist.c(1,i) > MAX_CURVATURE) flag = 0; break end end if (flag == 1) for i=1:1:size(fplist.x,2) for j=1:1:size(ob) d = sqrt((ob(j,1)-fplist.x(1,i))^2 + (ob(j,2)-fplist.y(1,i))^2); if(d <= ROBOT_RADIUS) flag = 0; break end end if (flag == 0) break end if (flag == 0) break end end endend \n\u82e5\u5f53\u524d\u8f68\u8ff9\u901a\u8fc7\u78b0\u649e\u68c0\u6d4b\u5373\u6807\u5fd7\u4f4d\u4e3a1\uff0c\u5219\u4e0e\u622a\u81f3\u76ee\u524d\u6700\u5c0f\u4ee3\u4ef7\u7684\u8f68\u8ff9\u8fdb\u884c\u6bd4\u8f83\uff0c\u5982\u679c\u65b0\u7684\u8f68\u8ff9\u7684\u4ee3\u4ef7\u5c0f\u4e8e\u5f53\u524d\u7684\u6700\u5c0f\u4ee3\u4ef7\uff0c\u5219\u628a\u5f53\u524d\u8f68\u8ff9\u9009\u4f5c\u4e34\u65f6\u6700\u4f18\u8f68\u8ff9\uff0c\u5e76\u628a\u5176\u4ee3\u4ef7\u503c\u8d4b\u7ed9\u6700\u5c0f\u4ee3\u4ef7\uff1b\u82e5\u6807\u5fd7\u4f4d\u4e3a0\uff0c\u5219\u5c06\u5176\u590d\u4f4d\u4e3a1\uff0c\u5e76\u4e0d\u8fdb\u884c\u6700\u5c0f\u4ee3\u4ef7\u7684\u5224\u65ad\u8fc7\u7a0b\uff1a \nif (flag == 1) cost(end+1,:) = [tfp.cf, di]; if min_cost(end,1) >= tfp.cf min_cost(end+1,:) = [tfp.cf, di]; fplist = tfp; endelse flag = 1;end
\n5\u3001\u4e3b\u5faa\u73af\u90e8\u5206
\n\u5f53\u5faa\u73af\u6b21\u6570\u5c0f\u4e8e\u6700\u5927\u5faa\u73af\u6b21\u6570\u65f6\uff0c\u91cd\u590d\u8fdb\u884c\u8f68\u8ff9\u52a8\u6001\u89c4\u5212\u7684\u8fc7\u7a0b\uff0c\u5982\u679c\u8f66\u8f86\u5230\u8fbe\u4e86\u53c2\u8003\u8f68\u8ff9\u7684\u6700\u540e\u4e00\u4e2a\u70b9\uff0c\u5219\u63d0\u524d\u8df3\u51fa\u5faa\u73af\u8fc7\u7a0b\u3002\u6bcf\u6b21\u5faa\u73af\u90fd\u5bf9\u8f66\u8f86\u5f53\u524d\u7684\u4f4d\u7f6e\u548c\u6700\u4f18\u8f68\u8ff9\u8fdb\u884c\u663e\u793a\uff1a
\n%% \u5faa\u73af\u8fc7\u7a0bfor i=1:1:SIM_LOOP path = calc_frenet_paths_fixed_velocity(csp, c_speed, c_d, c_d_d, c_d_dd, s0,MAX_ROAD_WIDTH, … D_ROAD_W, MIN_T, MAX_T, DT, FrenetPath, TARGET_SPEED,… D_T_S, N_S_SAMPLE,K_D, K_J, K_LAT, K_LON, K_T, ob,… MAX_ACCEL, MAX_SPEED, MAX_CURVATURE,ROBOT_RADIUS); s0 = path.s(1,2); c_d = path.d(1,2); c_d_d = path.d_d(1,2); c_d_dd = path.d_dd(1,2); c_speed = path.s_d(1,2); plot(csp(:,1), csp(:,2),’-.b’); hold on plot(csp(:,1), csp(:,2)+8,’-k’); plot(csp(:,1), csp(:,2)-8,’-k’); plot(ob(:,1), ob(:,2),’*g’); plot_robot(robot_length, robot_width, path.yaw(1,1) , path.x(1,1), path.y(1,1)); plot(path.x(1,1), path.y(1,1),’vc’,’MarkerFaceColor’,’c’,’MarkerSize’,6); plot(path.x(1,:), path.y(1,:),’-r’,’LineWidth’,2); plot(path.x(1,:), path.y(1,:),’ro’,’MarkerFaceColor’,’r’,’MarkerSize’,4); set(gca,’XLim’,[path.x(1,1) – area, path.x(1,1) + area]); set(gca,’YLim’,[path.y(1,1) – area, path.y(1,1) + area]); grid on title(‘Frenet’); xlabel(‘\u6a2a\u5750\u6807 x’); ylabel(‘\u7eb5\u5750\u6807 y’); pause(0.01); hold off if sqrt((path.x(1,1) – nodes(end,1))^2+ (path.y(1,1) – nodes(end,2))^2) <= 1.5 disp(\"Goal\"); break endend \n6\u3001\u7b97\u6cd5\u8fd0\u884c\u6548\u679c \nPython\u6e90\u7801\u8fd0\u884c\u6548\u679c\u5982\u4e0b\uff1a \n \nmatlab2019\u4ee3\u7801\u79fb\u690d\u8fd0\u884c\u6548\u679c\u5982\u4e0b\uff1a \n \n\u4e94\u3001\u7ed3\u8bed \n\u7531\u4eff\u771f\u7ed3\u679c\u53ef\u4ee5\u770b\u51fa\uff0c\u8f66\u8f86\u5728\u5b9a\u901f\u5de1\u822a\u7684\u6a21\u5f0f\u4e0b\u53ef\u4ee5\u6309\u7167\u671f\u671b\u7684\u901f\u5ea6\u6cbf\u7740\u53c2\u8003\u7ebf\u884c\u9a76\uff0c\u5f53\u9047\u5230\u969c\u788d\u7269\u7684\u65f6\u5019\u7531\u4e8e\u5b9e\u65f6\u89c4\u5212\u91c7\u6837\u7684\u7f18\u6545\uff0c\u5373\u4f7f\u6700\u4f18\u8f68\u8ff9\u4f1a\u4e0e\u969c\u788d\u7269\u76f8\u4ea4\uff0c\u8f66\u8f86\u4e5f\u53ef\u4ee5\u505a\u51fa\u5224\u65ad\u4ece\u800c\u9009\u62e9\u5176\u4ed6\u5907\u9009\u8f68\u8ff9\uff0c\u4ece\u800c\u907f\u5f00\u969c\u788d\u7269\uff0c\u4fdd\u8bc1\u884c\u9a76\u7684\u5b89\u5168\u6027\u3002 \n\u5bf9\u4e8e\u5176\u4ed6\u7684\u8f66\u8f86\u884c\u9a76\u60c5\u666f\uff0c\u5747\u53ef\u4ee5\u6839\u636e\u9700\u6c42\u8fdb\u884c\u76ee\u6807\u914d\u7f6e\u548c\u8bc4\u4ef7\u51fd\u6570\u7684\u4fee\u6539\uff0c\u5728\u8fd9\u6211\u4e0d\u5728\u505a\u66f4\u591a\u7684\u8bf4\u660e\u3002 \n \n \nPS\uff1a Frenet\u5750\u6807\u7cfb\u4e0b\u52a8\u6001\u8f68\u8ff9\u89c4\u5212\u6280\u672f\u662f\u57282010\u5e74\u7684ICRA\uff08\u673a\u5668\u4eba\u9886\u57df\u9876\u4f1a\uff09\u4e0a\u9996\u6b21\u63d0\u51fa\u5e76\u5f97\u5230\u5e7f\u6cdb\u7684\u5173\u6ce8\uff0c\u4f1a\u8bae\u539f\u6587\u94fe\u63a5\u5982\u4e0b\uff1aOptimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frames \nTakahashi\u5173\u4e8ejerk\u4f18\u5316\u8fc7\u7a0b\u4e94\u6b21\u591a\u9879\u5f0f\u63a8\u5bfc\u539f\u6587\u94fe\u63a5\u5982\u4e0b\uff1a \nLocal Path Planning And Motion Control For Agv In Positioning \nAtsushi Sakai\u7684Python\u6e90\u7801\u5730\u5740\u5982\u4e0b\uff1a \nhttps:\/\/github.com\/AtsushiSakai\/ \n\u6700\u540e\uff0c\u5982\u6709\u9700\u8981\u6211matlab\u539f\u7801\u7684\u670b\u53cb\u53ef\u4ee5\u5728\u8bc4\u8bba\u533a\u7559\u4e0b\u90ae\u7bb1\uff0c\u6211\u770b\u5230\u540e\u4f1a\u53ca\u65f6\u56de\u590d\u3002 \n\u5f69\u86cb\uff1a\u8fd9\u7bc7\u6587\u7ae0\u7684\u516c\u5f0f\u5b9e\u5728\u662f\u592a\u591a\u4e86\uff0c\u624b\u90fd\u8981\u6572\u9ebb\u4e86TAT\u3002\n<\/p>\n","protected":false},"excerpt":{"rendered":"
2022-05-20 \u524d\u8a00\uff1a\u5bf9\u4e8e\u65e0\u4eba\u9a7e\u9a76\u8def\u5f84\u89c4 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,1],"tags":[],"class_list":["post-323","post","type-post","status-publish","format-standard","hentry","category-technology-frontier","category-home"],"views":3,"_links":{"self":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/323"}],"collection":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/comments?post=323"}],"version-history":[{"count":1,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/323\/revisions"}],"predecessor-version":[{"id":324,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/posts\/323\/revisions\/324"}],"wp:attachment":[{"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/media?parent=323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/categories?post=323"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/222.128.65.89:18086\/index.php\/wp-json\/wp\/v2\/tags?post=323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}