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‎_posts/.obsidian/core-plugins.json

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‎_posts/.obsidian/graph.json

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"repelStrength": 20,
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"linkStrength": 1,
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"linkDistance": 158,
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‎_posts/Math/2022-01-02-optimization.md

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- 无约束优化问题可以是全局优化的，也可以是局部优化的
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- 有约束优化问题也可以是全局优化的，也可以是局部优化的
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- <u>最小二乘问题是凸优化问题的一个特例</u>
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- <u>线性规划问题是凸优化问题的一个特例</u>
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---
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@@ -69,7 +67,7 @@ F(x) 称为目标函数，或者代价函数。
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$$
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\begin{align}
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& \textrm{Given }F：\mathbf{R} ^{n} \mapsto \mathbf{R} \\
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& \textrm{Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(x)\}. \\
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& \textrm{Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(\mathbf x)\}. \\
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\end{align}
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$$
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$$
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\begin{align}
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& \textrm{Given }F：\mathbf{R} ^{n} \mapsto \mathbf{R} \\
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& \textrm{Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(x)\}. \\
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& \textrm{Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(\mathbf x)\}. \\
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& \textrm{subject to } f_i(x) \leq b_i, i = 1,...,m.
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\end{align}
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$$
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$$
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\begin{align}
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& \textrm{Given }F：\mathbf{R} ^{n} \mapsto \mathbf{R}. \\
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& \textrm{ Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(x)\}.
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& \textrm{ Find } \mathbf{x}^+ = \textrm {argmin}_\mathbf{x} \{F(\mathbf x)\}.
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\end{align}
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$$
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##### 1.6 非线性优化
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如果优化问题不是线性的，就称为非线性规划。
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非线性规划问题的研究主要关注在局部最优化问题的求解上。
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如果优化问题不是线性的，就称为非线性优化。
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##### 1.7 凸优化问题
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$$
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\begin{align}
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& \textrm{Given }F：\mathbf{R} ^{n} \mapsto \mathbf{R} \\
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& \textrm{Find } \mathbf{x}^+ = \text {argmin}_\mathbf{x} \{F(x)\}. \\
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& \textrm{Find } \mathbf{x}^+ = \text {argmin}_\mathbf{x} \{F(\mathbf x)\}. \\
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& \textrm{subject to } f_i(x) \leq b_i, i = 1,...,m.
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\end{align}
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$$
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比较线性函数和凸函数，可以发现凸函数仅仅需要在 $\alpha$ 和 $\beta$ 取特定数值的情况下满足不等式，而线性需要严格满足等式。
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- 可见 <u>线性规划问题是凸优化问题的一个特例</u>，且线性规划是广泛应用的一类凸优化问题。
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- 可见 <u>线性优化问题是凸优化问题的一个特例</u>，且是广泛应用的一类凸优化问题。
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- <u>线性函数一定是是凸函数</u>。
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- <u>非线性函数可能是凸函数，也可能是非凸的</u>。
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- 凸优化问题的求解已经有了非常成熟的解法，所以本文主要关注于凸优化。
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[2022-01-04-最小二乘](Math/2022-01-04-最小二乘.md)
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线性最小二乘
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非线性最小二乘
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## 2. 凸集
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### 2.1 仿射集合和凸集

‎_posts/Robotics/2021-05-16-Bayesian-filter.md

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1. <u>-> 2. -> 3.</u> <u>-> 2. -> 3.</u> <u>-> 2. -> 3.</u> <u>-> 2. -> 3.</u> 不断进行下去
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<img src="/home/trifo/code/sync/DevelopmentNotes/img/Screenshot from 2021-09-07 11-32-03.png" alt="Screenshot from 2021-09-07 11-32-03" style="zoom:33%;" />
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![](img/Screenshot%20from%202021-09-07%2011-32-03.png)
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‎_posts/Robotics/Geometry/2021-06-01-3dpose.md

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### 姿态表达
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- 欧拉角 [2021-06-02-EulerAngles](YuYuCong.github.io/_posts/Robotics/Geometry/2021-06-02-EulerAngles.md)
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- 旋转矩阵 [2021-06-03-RotateMatrix](YuYuCong.github.io/_posts/Robotics/Geometry/2021-06-03-RotateMatrix.md)
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- 四元数 [2021-06-05-Quaternion](YuYuCong.github.io/_posts/Robotics/Geometry/2021-06-05-Quaternion.md)
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- 轴角 [2021-06-04-AngleAxis](YuYuCong.github.io/_posts/Robotics/Geometry/2021-06-04-AngleAxis.md)
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- 欧拉角 [2021-06-02-EulerAngles](Robotics/Geometry/2021-06-02-EulerAngles.md)
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- 旋转矩阵 [2021-06-03-RotateMatrix](Robotics/Geometry/2021-06-03-RotateMatrix.md)
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- 四元数 [2021-06-05-Quaternion](Robotics/Geometry/2021-06-05-Quaternion.md)
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- 轴角 [2021-06-04-AngleAxis](Robotics/Geometry/2021-06-04-AngleAxis.md)
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- SO3 todo(congyu)
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‎_posts/Robotics/Geometry/2021-06-05-Quaternion.md

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四元数微分
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![|200](_backup/post-robotics-quaternion-diff.png)
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![|200](img/in-post/post-geometry/post-robotics-quaternion-diff.png)
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$$
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\begin{equation}

‎_posts/Robotics/Geometry/2021-06-10-Geometry-Convert.md

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![img](https://img-blog.csdnimg.cn/20191217160826969.png)
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- arctan和arcsin的结果是![[-\frac{\pi}{2},\frac{\pi}{2}]](https://private.codecogs.com/gif.latex?%5B-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5D)，这并不能覆盖所有朝向(对于![\theta](https://private.codecogs.com/gif.latex?%5Ctheta)角![[-\frac{\pi}{2},\frac{\pi}{2}]](https://private.codecogs.com/gif.latex?%5B-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5D)的取值范围已经满足)，因此需要用atan2来代替arctan。
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- arctan和arcsin的结果是
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$$[-\frac{\pi}{2},\frac{\pi}{2}]$$(https://private.codecogs.com/gif.latex?%5B-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5D)，这并不能覆盖所有朝向(对于![\theta](https://private.codecogs.com/gif.latex?%5Ctheta)角$$[\frac{\pi}{2},\frac{\pi}{2}]$$(https://private.codecogs.com/gif.latex?%5B-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%5D)的取值范围已经满足)，因此需要用atan2来代替arctan。
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- 符号约定 q0q1q2q3 qwqxqyqz
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![img](https://img-blog.csdnimg.cn/20191217160923942.png)

‎_posts/c++/4.stl/2020-10-12-shared-ptr.md

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layout: post
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title: "Smart Pointer"
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description: "Smart Pointer"
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categories: [c++]
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tags: [c++,shared_ptr]
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title: Smart Pointer
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description: Smart Pointer
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categories:
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- c++
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tags:
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- shared_ptr
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- cpp
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- cplusplus
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‎_posts/c++/DesignPattern/BehaviorTree/2021-01-26-BehaviorTree.md

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layout: post
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title: "BehaviorTree(行为树)入门"
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subtitle: "使用行为树模式，让机器人实现复杂任务决策"
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categories: [Design-Pattern]
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tags: [BehaviorTree, Design-Pattern, c++, state-machine, ros]
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header-img: "img/in-post/post-cpp/bg_behavior_tree.drawio.png"
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title: BehaviorTree(行为树)入门
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subtitle: 使用行为树模式，让机器人实现复杂任务决策
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categories:
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- Design-Pattern
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tags:
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- BehaviorTree
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- Design-Pattern
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- state-machine
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- ros
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header-img: img/in-post/post-cpp/bg_behavior_tree.drawio.png
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date: 2021.01.26
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‎_posts/c++/GoogleTest/2020-08-10-Google_Test.md

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layout: post
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title: "Google Test使用方法总结"
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description: "写代码不测试，bug满天飞。"
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categories: [c++]
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tags: [c++,gtest,unit-test]
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title: Google Test使用方法总结
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description: 写代码不测试，bug满天飞。
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categories:
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- c++
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tags:
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- gtest
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- unit-test
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- cpp
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- cplusplus
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redirect_from:
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‎_posts/c++/GoogleTest/2020-08-17-GFlags.md

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layout: post
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title: "GFlags使用方法教程"
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title: GFlags使用方法教程
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subtitle: "GFlags: 方便的使用c++命令行参数"
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categories: [c++]
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tags: [c++, gflags]
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header-img: "img/in-post/"
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categories:
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- c++
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tags:
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- gflags
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- cpp
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- cplusplus
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header-img: img/in-post/
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date: 2020.08.17
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---

‎_posts/c++/GoogleTest/2020-08-18-GLog.md

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title: "GLog 使用方法与技巧"
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subtitle: "GLog:简单易用的c++日志库"
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categories: [c++]
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tags: [c++, glog]
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header-img: "img/in-post/"
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title: GLog 使用方法与技巧
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subtitle: GLog:简单易用的c++日志库
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categories:
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- c++
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tags:
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- glog
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- cplusplus
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- cpp
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header-img: img/in-post/
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‎_posts/c++/GoogleTest/2022-09-09-config.md

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title: "如何设计易用的c++参数配置文件？"
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subtitle: "Yaml vs. json，还是自己尝试设计一个吧"
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categories: [c++]
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tags: [c++,json]
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header-img: "img/in-post/"
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title: 如何设计易用的c++参数配置文件？
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subtitle: Yaml vs. json，还是自己尝试设计一个吧
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categories:
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- c++
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tags:
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- json
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- cpp
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- cplusplus
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header-img: img/in-post/
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‎_posts/c++/boost/2020-09-25-boost filesystem.md

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title: "Boost filesystem"
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description: "boost filesystem"
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categories: [c++]
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tags: [boost,c++]
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title: Boost filesystem
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description: boost filesystem
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categories:
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- c++
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tags:
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- boost
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- cpp
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- cplusplus
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<h4>Reference</h4>
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- http://zh.highscore.de/cpp/boost/filesystem.html
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- [http://zh.highscore.de/cpp/boost/filesystem.html](http://zh.highscore.de/cpp/boost/filesystem.html)
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- boost filesystem [https://www.boost.org/doc/libs/1_79_0/libs/filesystem/doc/index.htm](https://www.boost.org/doc/libs/1_79_0/libs/filesystem/doc/index.htm)
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‎_posts/c++/coding-style/2020-07-27-coding-style.md

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tags: [c++]
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header-img: "img/in-post/post-cpp/bg_code_style.png"
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title: c++ coding style
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subtitle: c++代码风格规范，以及一些良好的代码习惯建议
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categories:
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- c++
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tags:
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- cpp
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- cplusplus
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header-img: img/in-post/post-cpp/bg_code_style.png
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> 本文主要记录c++ coding style相关的一些笔记，以及一些常用的代码建议与小技巧。尽力将自己写的代码视作一件艺术品，是技术与艺术的结合体。
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}
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```
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在CmakeList中禁止写出 float-equal 的代码

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