diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 91cb81d..53d0820 100644 --- a/.github/workflows/ci.yml +++ b/.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 diff --git a/.gitignore b/.gitignore index 836a057..deba3e0 100644 --- a/.gitignore +++ b/.gitignore @@ -40,4 +40,5 @@ # Custom rules (everything added below won't be overriden by 'Generate .gitignore File' if you use 'Update' option) -site/ \ No newline at end of file +site/ +.cache/ diff --git a/docs/.pages b/docs/.pages new file mode 100644 index 0000000..299a36f --- /dev/null +++ b/docs/.pages @@ -0,0 +1,4 @@ +nav: + - Home: index.md + - Blog: blog + - RSS: feed_rss_created.xml \ No newline at end of file diff --git a/docs/blog/index.md b/docs/blog/index.md new file mode 100644 index 0000000..c58f16c --- /dev/null +++ b/docs/blog/index.md @@ -0,0 +1,2 @@ +# Blog + diff --git "a/docs/blog/posts/\350\277\221\344\274\274\351\225\277\346\226\271\345\275\242\347\232\204\346\234\272\345\231\250\344\272\272\347\242\260\346\222\236\346\243\200\346\265\213\344\274\230\345\214\226.md" "b/docs/blog/posts/\350\277\221\344\274\274\351\225\277\346\226\271\345\275\242\347\232\204\346\234\272\345\231\250\344\272\272\347\242\260\346\222\236\346\243\200\346\265\213\344\274\230\345\214\226.md" new file mode 100644 index 0000000..7c1d69f --- /dev/null +++ "b/docs/blog/posts/\350\277\221\344\274\274\351\225\277\346\226\271\345\275\242\347\232\204\346\234\272\345\231\250\344\272\272\347\242\260\346\222\236\346\243\200\346\265\213\344\274\230\345\214\226.md" @@ -0,0 +1,164 @@ +--- +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%** + + + +### 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" \ No newline at end of file diff --git a/docs/index.md b/docs/index.md index 125e876..a7b6127 100644 --- a/docs/index.md +++ b/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 -## Commands - -* `mkdocs new [dir-name]` - Create a new project. -* `mkdocs serve` - Start the live-reloading docs server. -* `mkdocs build` - Build the documentation site. -* `mkdocs -h` - Print help message and exit. - -## Project layout - - mkdocs.yml # The configuration file. - docs/ - index.md # The documentation homepage. - ... # Other markdown pages, images and other files. - -I'm Wz + 思绪来得快去得也快，偶尔会在这里停留 -- 云风 \ No newline at end of file diff --git a/mkdocs.yml b/mkdocs.yml index 630785d..d4ea46b 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -1,4 +1,74 @@ -site_name: My site -site_url: https://mydomain.org/mysite +site_description: Aglargil's Blog +site_name: Aglargil's Blog +site_url: https://aglargil.github.io/ + +repo_url: https://github.com/Aglargil/Aglargil.github.io +repo_name: Aglargil/Aglargil.github.io + theme: name: material + custom_dir: overrides + features: + - content.code.copy + - content.code.select + - content.code.annotate + - navigation.instant + - navigation.tabs + - navigation.path + - navigation.top + - navigation.indexes + - toc.follow + language: zh + palette: + # Palette toggle for automatic mode + - media: "(prefers-color-scheme)" + toggle: + icon: material/brightness-auto + name: Switch to light mode + + # Palette toggle for light mode + - media: "(prefers-color-scheme: light)" + scheme: default + toggle: + icon: material/brightness-7 + name: Switch to dark mode + + # Palette toggle for dark mode + - media: "(prefers-color-scheme: dark)" + scheme: slate + toggle: + icon: material/brightness-4 + name: Switch to system preference + +plugins: + - awesome-pages + - blog + - glightbox + - rss: + match_path: blog/posts/.* + abstract_chars_count: -1 + date_from_meta: + as_creation: date.created + as_update: date.updated + categories: + - categories + - tags + - search + +markdown_extensions: + - pymdownx.highlight: + anchor_linenums: true + line_spans: __span + pygments_lang_class: true + - pymdownx.inlinehilite + - pymdownx.snippets + - pymdownx.superfences + - pymdownx.details + - admonition + - attr_list + - md_in_html + - def_list + - pymdownx.tasklist: + custom_checkbox: true + +copyright: 版权所有 diff --git a/overrides/partials/comments.html b/overrides/partials/comments.html new file mode 100644 index 0000000..c8e88f5 --- /dev/null +++ b/overrides/partials/comments.html @@ -0,0 +1,17 @@ + +