2D反向运动学实施 [英] 2D Inverse Kinematics Implementation
问题描述
我想实现在2D臂反向运动（由三个坚持与关节）。我能够最低臂旋转到所需位置。现在，我有一些问题：
I am trying to implement Inverse Kinematics on a 2D arm(made up of three sticks with joints). I am able to rotate the lowest arm to the desired position. Now, I have some questions:
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我怎样才能让非常久远第三上臂举使手臂的终点到达所需的点。我是否需要使用旋转矩阵为，如果是有人可以给我一些例子或帮助，有没有其他的possibl，E的方式来做到这一点没有旋转矩阵???
How can I make the upper arm move alongwith the third so the end point of the arm reaches the desired point. Do I need to use the rotation matrices for both and if yes can someone give me some example or an help and is there any other possibl;e way to do this without rotation matrices???
最低仅ARM沿一个方向移动。我试了谷歌，他们说，两个向量的积给方向的手臂，但是这是为3D。我使用的2D和跨产品的两个向量2D给出一个标量。所以，我怎么能确定其方向???
The lowest arm only moves in one direction. I tried google it, they are saying that cross product of two vectors give the direction for the arm but this is for 3D. I am using 2D and cross product of two 2D vectors give a scalar. So, how can I determine its direction???
PLZ人任何帮助，将AP preciated ....
Plz guys any help would be appreciated....
在此先感谢
维克拉姆
Thanks in advance Vikram
推荐答案
我给它一个镜头，但因为我的机器人在过去的二十年中，采取与一粒盐。
I'll give it a shot, but since my Robotics are two decades in the past, take it with a grain of salt.
我学到它的方式，每一个关节由自己的旋转矩阵描述，相对于当前位置和方向确定。整条手臂的终点的坐标，然后通过旋转矩阵相结合来计算。
The way I learned it, every joint was described by its own rotation matrix, defined relative to its current position and orientation. The coordinate of the whole arm's endpoint was then calculated by combining the rotation matrices together.
这正是实现你正在寻找的效果：你可以只移动一个关节（改变其方向），以及其他所有的关节自动执行
This achieved exactly the effect you are looking for: you could move only one joint (change its orientation), and all the other joints followed automatically.
您不会有让周围多少机会矩阵在这里 - 事实上，如果你使用齐次坐标，所有联名计算（旋转以及转换）可以用矩阵乘法模型。的优点在于，在完整臂位置然后可以与单个矩阵（加上臂的原点）进行说明。
You won't have much chance in getting around matrices here - in fact, if you use homogeneous coordinates, all joint calculations (rotations as well as translations) can be modeled with matrix multiplications. The advantage is that the full arm position can then be described with a single matrix (plus the arm's origin).
通过这个转换矩阵，可以解决逆运动学问题：既然变换矩阵元素将取决于关节的角度，你可以把整个计算'终点=起点点¯x转型作为方程组，与起点和端点已知的，就可以解决这个系统来确定未知的角度。这里的困难在于，该公式可能不解决的，或者说有多种解决方案。
With this transformation matrix, you can tackle the inverse kinematic problem: since the transformation matrix' elements will depend on the angles of the joints, you can treat the whole calculation 'endpoint = startpoint x transformation' as a system of equations, and with startpoint and endpoint known, you can solve this system to determine the unknown angles. The difficulty herein lies that the equation may not be solvable, or that there are multiple solutions.
我不明白你的第二个问题，虽然 - 什么是你寻找
I don't quite understand your second question, though - what are you looking for?
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