台大机器人学——林沛群
![](https://pic3.zhimg.com/80/v2-daae155ddcb09ce70f8eb1a0b2d4767e_720w.jpg)
进一步精准找到两个frame之间的变换关系(Transformation Matrix的量化表达式什么)
要如何借由DH表达法中的4个参数,求得Transformation Matrix?
![](https://pic3.zhimg.com/80/v2-dd4cb9f0d784a40656794475ff070656_720w.jpg)
![](https://www.guyuehome.com//Uploads/Editor/202109/20210903_54665.png)
![](https://pic3.zhimg.com/80/v2-aa74fb3c0f340a0163166c848eaac5ca_720w.jpg)
- 其中,按照mapping后乘思想,可列出:
![](https://pic3.zhimg.com/80/v2-86f3705f7fd4d3d8296461fb04d55ade_720w.jpg)
- 继续拆解:
![](https://pic1.zhimg.com/80/v2-a579ecfcff8a405524220dd8a6553b50_720w.jpg)
- Thus:
![](https://pic1.zhimg.com/80/v2-a01ee2f53b8a414bd661c3308463312c_720w.jpg)
- 有了i与i-1的frame的转换关系后,连续的link transformations也很好求:
![](https://pic1.zhimg.com/80/v2-0a8494832fe3aef9b0f7fd1f4e2f8c38_720w.jpg)
Frame{n}相对于Frame{0}的空间集合关系清楚,且量化的定义在Frame{n}下表达的向量可以转回到Frame{0}下来定义表达(对地)。
Example1:
上面的详细推导过程:
![](https://pic4.zhimg.com/80/v2-1dbaa434285c90e91c0b2bb3dac6ea27_720w.jpg)
Example 2: A RRR Manipulator
![](https://pic4.zhimg.com/80/v2-f4a8f8deb9b851f66ed21844c81780e3_720w.jpg)
Example 3: A RPR Manipulator
![](https://pic3.zhimg.com/80/v2-14b731e0bd2889e2f815e41c64be6496_720w.jpg)
注意,当Z轴相交,即
的时候,有很多定义方式:
有两个选择
有两个选择
- 单纯的两轴相交,就有4种选择,不是唯一解...
![](https://pic4.zhimg.com/80/v2-75fd82629190e9bcf3096a1fe78ea25f_720w.jpg)
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