15、机器人视觉与三维感知构建技术详解

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最新推荐文章于 2025-12-03 12:47:43 发布

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分类专栏：机器人认知与导航探秘文章标签：机器人视觉三维感知坐标系统转换

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机器人视觉与三维感知构建技术详解

1. 坐标系统转换

在机器人的视觉系统中，将基于机器人的坐标系统转换为全局坐标系统是一项重要的任务。通过建立基于车辆的坐标系统与以对象为中心的坐标系统之间的关系，就能够实现从机器人坐标系统到全局表示的转换，这可以通过以下两个步骤完成：
1. 平移操作 ：首先，将基于机器人的坐标系统按照平移向量 (xv, yv, zv) 进行平移，使得新系统的原点与全局坐标系统的原点重合。这一过程可以用方程 (13.14) 表示。平移完成后，会进行一系列的旋转操作，以使两个坐标系统对齐。
2. 绕 Zv′ 轴旋转 φ2 ：通过将 Xv′ - Yv′ 平面绕 Zv′ 轴旋转 φ2 角度来完成这一旋转操作，其中 φ2 是 Yv′ 轴与 Y0 轴之间的夹角。这里假设两个坐标系统的 Z 轴是重合的（可将地面视为 X0 - Y0 平面），从而得到如下关系：

(13.14)
⎛ X'v ⎞   ⎛ Xv - x ⎞
⎜ Y'v ⎟ = ⎜ Yv - y ⎟
⎝ Z'v ⎠   ⎝ Zv - z ⎠

(13.15)
⎛ X0 ⎞   ⎛ cosφ2  -sinφ2  0 ⎞ ⎛ X'v - x ⎞
⎜ Y0 ⎟ = ⎜ sinφ2   cosφ2  0 ⎟ ⎜ Y'v - y ⎟
⎝ Z0 ⎠   ⎝    0       0    1 ⎠ ⎝ Z'v - z ⎠

通过结合方程 (13.13) 得到的相机与机器人坐标系统之间的关系，以及方程 (13.15) 得到的机器人与全局坐标系统之间的关系，就可以得到相机与以对象为中心的坐标系统之间的关系。

完成坐标系统的对齐后，通过对所有过程进行求和来进行透视投影，具体如下：
```plaintext
(13.16)
⎛ 1 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 -x0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ cosA -sinA 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ f 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 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0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞

其中， (x0, y0, z0) 表示相机坐标系统相对于用户定义坐标系统的位移向量， A 和 B 分别表示相机的水平旋转角和垂直旋转角， C 表示倾斜角（在我们的例子中为零）。从上述关系中，我们可以轻松推导出相机的透视矩阵 (T) ，其表示为 (13.17) ：

```plaintext
(13.17)
⎛ t11 t12 t13 t14 ⎞
⎜ t21 t22 t23 t24 ⎟
⎜ t31 t32 t33 t34 ⎟
⎝ t41 t42 t43 t44 ⎠
=
⎛ 1 0 0 -x0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ cosA -sinA 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ f 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ ⎛ 1 0 0 0 ⎞ 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