近似长方形的机器人碰撞检测优化

.github/workflows/ci.yml

@@ -26,4 +26,7 @@ jobs:
           restore-keys: |
             mkdocs-material-
       - run: pip install mkdocs-material 
+      - run: pip install mkdocs-glightbox
+      - run: pip install mkdocs-rss-plugin
+      - run: pip install mkdocs-awesome-pages-plugin
       - run: mkdocs gh-deploy --force

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 # Custom rules (everything added below won't be overriden by 'Generate .gitignore File' if you use 'Update' option)
 
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docs/.pages

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+  - Blog: blog
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docs/blog/index.md

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+# Blog
+

docs/blog/posts/近似长方形的机器人碰撞检测优化.md

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+---
+date:
+  created: 2024-07-23
+  updated: 2024-07-23
+categories:
+  - 机器人
+---
+
+# 近似长方形的机器人碰撞检测优化
+
+机器人是多边形，用12个圆形覆盖这个contour
+### 优化问题
+
+- 优化变量：12个圆形的x, y, r 
+- 目标函数：所有圆的并集（union_area）不属于 contour 部分的面积最小
+- 约束条件：
+    * bound: -1 < x < 1, -1 < y < 0, r > 0.05
+    * 所有圆的并集（union_area）和 contour的交集 (covered_area) 占 多边形的面积比大于**98%**
+
+<!-- more -->
+
+### 代码
+```python linenums="1"
+from scipy.optimize import minimize
+from shapely.geometry import Point, Polygon
+import matplotlib.pyplot as plt
+
+
+# 定义多边形
+polygon_coords = [
+    (0.177, 0),
+    (0.176, -0.0375),
+    (0.175, -0.075),
+    (0.165, -0.1125),
+    (0.155, -0.15),
+    (0.1335, -0.176),
+    (0.112, -0.202),
+    (0.06413, -0.202),
+    (0.01626, -0.202),
+    (-0.03161, -0.202),
+    (-0.07948, -0.202),
+    (-0.12735, -0.202),
+    (-0.17522, -0.202),
+    (-0.22309, -0.202),
+    (-0.27096, -0.202),
+    (-0.31883, -0.202),
+    (-0.3667, -0.202),
+    (-0.395, -0.1963),
+    (-0.4115, -0.1739),
+    (-0.428, -0.1515),
+    (-0.432925, -0.113625),
+    (-0.43785, -0.07575),
+    (-0.442775, -0.037875),
+    (-0.4477, 0),
+    (-0.442775, 0.037875),
+    (-0.43785, 0.07575),
+    (-0.432925, 0.113625),
+    (-0.428, 0.1515),
+    (-0.4115, 0.1739),
+    (-0.395, 0.1963),
+    (-0.3667, 0.202),
+    (-0.31883, 0.202),
+    (-0.27096, 0.202),
+    (-0.22309, 0.202),
+    (-0.17522, 0.202),
+    (-0.12735, 0.202),
+    (-0.07948, 0.202),
+    (-0.03161, 0.202),
+    (0.01626, 0.202),
+    (0.06413, 0.202),
+    (0.112, 0.202),
+    (0.1335, 0.176),
+    (0.155, 0.15),
+    (0.165, 0.1125),
+    (0.175, 0.075),
+    (0.176, 0.0375),
+    (0.177, 0),
+]
+polygon = Polygon(polygon_coords)
+polygon_area = polygon.area
+print("多边形面积：", polygon_area)
+
+# 圆的数量
+num_circles = 12  # 可以根据需要调整这个值
+
+# 初始化猜测
+xs = [-0.13, -0.13, -0.03, -0.03, -0.23, -0.23, 0.07, 0.07, -0.33, -0.33, -0.34, 0.07]
+ys = [0.1, -0.1, 0.1, -0.1, 0.1, -0.1, 0.1, -0.1, 0.1, -0.1, 0, 0]
+rs = [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.11, 0.11]
+initial_guess = xs + ys + rs
+
+# 边界条件
+x_bounds = [(-1, 1) for _ in range(num_circles)]
+y_bounds = [(-1, 1) for _ in range(num_circles)]
+r_bounds = [(0.05, None) for _ in range(num_circles)]
+bounds = x_bounds + y_bounds + r_bounds
+
+
+# 定义目标函数
+def objective(vars):
+    xs = vars[0:num_circles]
+    ys = vars[num_circles : 2 * num_circles]
+    rs = vars[2 * num_circles : 3 * num_circles]
+    circles = [Point(xs[i], ys[i]).buffer(rs[i]) for i in range(num_circles)]
+    union_area = circles[0]
+    sum_area = circles[0].area
+    for circle in circles[1:]:
+        sum_area += circle.area
+        union_area = union_area.union(circle)
+    return union_area.area - union_area.intersection(polygon).area
+
+
+def coverage_constraint(vars):
+    xs = vars[0:num_circles]
+    ys = vars[num_circles : 2 * num_circles]
+    rs = vars[2 * num_circles : 3 * num_circles]
+    circles = [Point(xs[i], ys[i]).buffer(rs[i]) for i in range(num_circles)]
+    union_area = circles[0]
+    for circle in circles[1:]:
+        union_area = union_area.union(circle)
+    covered_area = union_area.intersection(polygon).area
+    return covered_area - 0.98 * polygon_area
+
+
+# 约束条件
+constraints = [
+    {"type": "ineq", "fun": coverage_constraint},
+]
+
+
+# 执行优化
+result = minimize(
+    objective, initial_guess, method="SLSQP", bounds=bounds, constraints=constraints
+)
+
+# 解析结果
+xs = result.x[0:num_circles]
+ys = result.x[num_circles : 2 * num_circles]
+rs = result.x[2 * num_circles : 3 * num_circles]
+
+print("最优解：", result.fun)
+
+# 绘制结果
+fig, ax = plt.subplots()
+for x, y, r in zip(xs, ys, rs):
+    print("x: ", x, "y: ", y, "r: ", r)
+    circle = plt.Circle((x, y), r, color="blue", fill=True, alpha=0.3)
+    ax.add_patch(circle)
+
+x, y = polygon.exterior.xy
+ax.plot(x, y, "r")
+ax.set_xlim(-1, 1)
+ax.set_ylim(-1, 1)
+ax.set_aspect("equal")
+plt.show()
+
+```
+### 结果
+- 初始解
+![初始解](https://picgo-1257309505.cos.ap-guangzhou.myqcloud.com/image.png)
+- 最优解
+![最优解](https://picgo-1257309505.cos.ap-guangzhou.myqcloud.com/20240723155012.png)
+
+!!! note "初始解的选取很重要"

docs/index.md

@@ -1,19 +1,5 @@
-# Welcome to MkDocs
+# 欢迎来到AglarGil的个人博客
 
-For full documentation visit [mkdocs.org](https://www.mkdocs.org).
+!!! quote
 
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+    思绪来得快去得也快，偶尔会在这里停留 -- 云风

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