一文洞悉Python必备50种算法！资深大牛至少得掌握25种！

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407792215" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;">

image
完整代码加群：683380553 获取！
<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

一、环境需求

二、怎样使用

三、本地化

3.1扩展卡尔曼滤波本地化

3.2无损卡尔曼滤波本地化

3.3粒子滤波本地化

3.4直方图滤波本地化

四、映射

4.1高斯网格映射

4.2光线投射网格映射

4.3k均值物体聚类

4.4圆形拟合物体形状识别

五、SLAM

5.1迭代最近点匹配

5.2EKF SLAM

5.3FastSLAM 1.0

5.4FastSLAM 2.0

5.5基于图的SLAM

六、路径规划

6.1动态窗口方式

6.2基于网格的搜索

迪杰斯特拉算法

A*算法

势场算法

6.3模型预测路径生成

路径优化示例

查找表生成示例

6.4状态晶格规划

均匀极性采样（Uniform polar sampling）

偏差极性采样（Biased polar sampling）

路线采样（Lane sampling）

6.5随机路径图（PRM）规划

6.6Voronoi路径图规划

6.7快速搜索随机树（RRT）

基本RRT

RRT*

基于Dubins路径的RRT

基于Dubins路径的RRT*

基于reeds-shepp路径的RRT*

Informed RRT*

批量Informed RRT*

闭合回路RRT*

LQR-RRT*

6.8三次样条规划

6.9B样条规划

6.10Eta^3样条路径规划

6.11贝济埃路径规划

6.12五次多项式规划

6.13Dubins路径规划

6.14Reeds Shepp路径规划

6.15基于LQR的路径规划

6.16Frenet Frame中的最优路径

七、路径跟踪

7.1姿势控制跟踪

7.2纯追迹跟踪

7.3史坦利控制

7.4后轮反馈控制

7.5线性二次regulator（LQR）转向控制

7.6线性二次regulator（LQR）转向和速度控制

7.7模型预测速度和转向控制

八、项目支持

一、环境需求

Python 3.6.x

numpy

scipy

matplotlib

pandas

cvxpy 0.4.x

二、怎样使用

安装必要的库；

克隆本代码仓库；

执行每个目录下的python脚本；

如果你喜欢，则收藏本代码库：）

三、本地化

3.1 扩展卡尔曼滤波本地化

私信小编001 获取源文件以及PDF！

该算法利用扩展卡尔曼滤波器（Extended Kalman Filter, EKF）实现传感器混合本地化。

蓝线为真实路径，黑线为导航推测路径（dead reckoning trajectory），绿点为位置观测（如GPS），红线为EKF估算的路径。

红色椭圆为EKF估算的协方差。

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

3.2 无损卡尔曼滤波本地化

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814538" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

该算法利用无损卡尔曼滤波器（Unscented Kalman Filter, UKF）实现传感器混合本地化。

线和点的含义与EKF模拟的例子相同。

相关阅读：

利用无差别训练过的无损卡尔曼滤波进行机器人移动本地化

https://www.researchgate.net/publication/267963417_Discriminatively_Trained_Unscented_Kalman_Filter_for_Mobile_Robot_Localization

3.3 粒子滤波本地化

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814541" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

该算法利用粒子滤波器（Particle Filter, PF）实现传感器混合本地化。

蓝线为真实路径，黑线为导航推测路径（dead reckoning trajectory），绿点为位置观测（如GPS），红线为PF估算的路径。

该算法假设机器人能够测量与地标（RFID）之间的距离。

PF本地化会用到该测量结果。

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

3.4 直方图滤波本地化

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814543" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

该算法是利用直方图滤波器（Histogram filter）实现二维本地化的例子。

红十字是实际位置，黑点是RFID的位置。

蓝色格子是直方图滤波器的概率位置。

在该模拟中，x，y是未知数，yaw已知。

滤波器整合了速度输入和从RFID获得距离观测数据进行本地化。

不需要初始位置。

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

四、映射

4.1 高斯网格映射

本算法是二维高斯网格映射（Gaussian grid mapping）的例子。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814545" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

4.2 光线投射网格映射

本算法是二维光线投射网格映射（Ray casting grid map）的例子。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814546" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

4.3 k均值物体聚类

本算法是使用k均值算法进行二维物体聚类的例子。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814548" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

4.4 圆形拟合物体形状识别

本算法是使用圆形拟合进行物体形状识别的例子。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814550" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

蓝圈是实际的物体形状。

红叉是通过距离传感器观测到的点。

红圈是使用圆形拟合估计的物体形状。

五、SLAM

同时本地化和映射（Simultaneous Localization and Mapping，SLAM）的例子。

5.1 迭代最近点匹配

本算法是使用单值解构进行二维迭代最近点（Iterative Closest Point，ICP）匹配的例子。

它能计算从一些点到另一些点的旋转矩阵和平移矩阵。相关阅读：

机器人运动介绍：迭代最近点算法

https://cs.gmu.edu/~kosecka/cs685/cs685-icp.pdf

5.2 EKF SLAM

这是基于扩展卡尔曼滤波的SLAM示例。

蓝线是真实路径，黑线是导航推测路径，红线是EKF SLAM估计的路径。

绿叉是估计的地标。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814553" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

5.3 FastSLAM 1.0

这是用FastSLAM 1.0进行基于特征的SLAM的示例。

蓝线是实际路径，黑线是导航推测，红线是FastSLAM的推测路径。

红点是FastSLAM中的粒子。

黑点是地标，蓝叉是FastLSAM估算的地标位置。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814555" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

5.4 FastSLAM 2.0

这是用FastSLAM 2.0进行基于特征的SLAM的示例。

动画的含义与FastSLAM 1.0的情况相同。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814556" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

相关阅读：

概率机器人学

http://www.probabilistic-robotics.org/

Tim Bailey的SLAM模拟

http://www-personal.acfr.usyd.edu.au/tbailey/software/slam_simulations.htm

5.5 基于图的SLAM

这是基于图的SLAM的示例。

蓝线是实际路径。

黑线是导航推测路径。

红线是基于图的SLAM估算的路径。

黑星是地标，用于生成图的边。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814558" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

相关阅读：

基于图的SLAM入门

http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf

六、路径规划

6.1 动态窗口方式

这是使用动态窗口方式（Dynamic Window Approach）进行二维导航的示例代码。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814560" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

相关阅读：

用动态窗口方式避免碰撞

https://www.ri.cmu.edu/pub_files/pub1/fox_dieter_1997_1/fox_dieter_1997_1.pdf

6.2 基于网格的搜索

迪杰斯特拉算法

这是利用迪杰斯特拉（Dijkstra）算法实现的基于二维网格的最短路径规划。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814563" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

动画中青色点为搜索过的节点。

A算法*

下面是使用A星算法进行基于二维网格的最短路径规划。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814565" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

<input class="pgc-img-caption-ipt" placeholder="图片描述(最多50字)" value="" style="box-sizing: border-box; outline: 0px; color: rgb(102, 102, 102); position: absolute; left: 187.5px; transform: translateX(-50%); padding: 6px 7px; max-width: 100%; width: 375px; text-align: center; cursor: text; font-size: 12px; line-height: 1.5; background-color: rgb(255, 255, 255); background-image: none; border: 0px solid rgb(217, 217, 217); border-radius: 4px; transition: all 0.2s cubic-bezier(0.645, 0.045, 0.355, 1);"></tt-image>

动画中青色点为搜索过的节点。

启发算法为二维欧几里得距离。

势场算法

下面是使用势场算法进行基于二维网格的路径规划。

<tt-image data-tteditor-tag="tteditorTag" contenteditable="false" class="syl1553407814567" data-render-status="finished" data-syl-blot="image" style="box-sizing: border-box; cursor: text; color: rgb(34, 34, 34); font-family: "PingFang SC", "Hiragino Sans GB", "Microsoft YaHei", "WenQuanYi Micro Hei", "Helvetica Neue", Arial, sans-serif; font-size: 16px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: block;"> image

</tt-image>