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http://blog.donews.com/wanderpoet/archive/2005/07/04/453608.aspx
看到一篇关于Gimbal Lock的E文,解释得挺清楚的,翻译如下:

Gimbal Lock

。。。
Maybe it's a bit difficult to understand. OK, let me show you a real sence.

可能有点不好理解。让我们看个现实中的场景。

Say that we have a telescope and a tripod to put the telescope on. The tripod is put on the ground. The top of the tripod holding the telescope is leveled with the horizon (reference plane) so that a vertical rotation axis (we call it X axis) is perfectly vertical to the ground plane. The telescope can then be rotated around 360 degrees in X axis so that it can scan the horizon in all the directions of the compass. Zero degrees azimuth is usually set toward a heading of true north. A second horizontal axis parallel to the ground plane (we call it Y axis), enables the telescope to be rotated in elevation upward or downward from the horizon. The horizon is usually set at zero degrees and the telescope can be rotated +90 degrees upward in elevation so that it is looking straight up toward the zenith or rotated -90 degrees downward so that it is looking vertically at the ground plane.

假如我们有一个望远镜和一个用来放望远镜的三脚架,(我们将)三脚架放在地面上,使支撑望远镜的三脚架的顶部是平行于地平面(参考平面)的,以便使得竖向的旋转轴(记为x轴)是完全地垂直于地平面的。现在,我们就可以将望远镜饶x轴旋转360度,从而观察(以望远镜为中心的)水平包围圈的所有方向。通常将正北朝向方位角度记为0度方位角。第二个坐标轴,即平行于地平面的横向的坐标轴(记为y轴)使得望远镜可以饶着它上下旋转,通常将地平面朝向的仰角记为0度,这样,望远镜可以向上仰+90度指向天顶,或者向下-90度指向脚底。

OK, that's all we needed. every point in the sky (and the ground) can be referenced by only ONE unique pair of X and Y readings. For example an X of 90 degrees and Y of 45 degrees specifies a point exactly due east of the telescope and in a skyward direction half way up toward the zenith.

好了,万事俱备。现在,天空中(包括地面上)的每个点只需要唯一的一对x和y度数就可以确定。比如x=90度,y=45度指向的点是位于正东方向的半天空上。

Now let me show you how the gimal lock occurred. We detect a high flying aircraft, near the horizon, due east from the telescope (X = 90 degrees, Y = 10 degrees) and we follow it (track it) as it comes directly toward us. The X angle stays at 90 degrees and the Y angle slowly increases. As the aircraft comes closer the Y angle increases more rapidly and just as the aircraft reaches an Y of 90 degrees (exactly overhead), it makes a sharp turn due south. We find that we cannot quickly move the telescope toward the south because the Y angle is exactly +90 degrees so we loose sight (loose track) of the aircraft . We have GIMBAL LOCK!

现在,看看万向节死锁是怎么发生的。一次,我们探测到有一个飞行器贴地飞行,位于望远镜的正东方向(x=90度,y=10度),朝着我们直飞过来,我们跟踪它。飞行器飞行方向是保持x轴角度90度不变,而y向的角度在慢慢增大。随着飞行器的临近,y轴角增长的越来越快且当y向的角度达到90度时(即将超越),突然它急转弯朝南飞去。这时,我们发现我们不能将望远镜朝向南方,因为此时y向已经是90度,造成我们失去跟踪目标。这就是万向节死锁!

(译注:为什么说不能将望远镜朝向南方呢,让我们看看坐标变化,从开始的(x=90度,y=10度)到(x=90度,y=90度),这个过程没有问题,望远镜慢慢转动跟踪飞行器。当飞行器到达(x=90度,y=90度)后,坐标突然变成(x=180度,y=90度)(因为朝南),x由90突变成180度,所以望远镜需要饶垂直轴向x轴旋转180-90=90度以便追上飞行器,但此时,望远镜已经是平行于x轴,我们知道饶平行于自身的中轴线的的旋转改变不了朝向,就象拧螺丝一样,螺丝头的指向不变。所以望远镜的指向还是天顶。而后由于飞行器飞远,坐标变成(x=180度,y<90度)时,y向角减小,望远镜只能又转回到正东指向,望'器'兴叹。这说明用x,y旋转角(又称欧拉角)来定向物体有时并不能按照你想像的那样工作,象上面的例子中从(x=90度,y=10度)到(x=90度,y=90度),坐标值的变化和飞行器空间的位置变化一一对应,但是从(x=90度,y=90度)到(x=180度,y=90度),再到(x=180度,y<90度)这个变化,飞行器位置是连续的变化,但坐标值的变化却不是连续的(从90突变到180),其原因在于(x=90度,y=90度)和(x=180度,y=90度)甚至和(x=任意度,y=90度)这些不同的坐标值对应空间同一个位置,这种多个坐标值对应同一个位置的不一致性是造成死锁的根源。【感谢zeroyear, fatfatson 等的深层解释,原先解释的不够清晰,故修改如上。原文:按照欧拉角旋转确实可以正确地定向,但从(x=90度,y=90度)到(x=180度,y=90度),再到(x=180度,y<90度),按照欧拉角旋转后的定向并非正确】)

It's a example of 2D coordinate frame. It's very similar in 3D frame. We say that you have a vector which is parellel to the X axis. And we rotate it around  Y axis so that the vector is parellel to the Z axis. Then we find that any rotations around  Z axis will have no effect on the vector. We say that we have a GIMBAL LOCK

上面是2维坐标系中的例子,同样,对于3维的也一样。比如有一个平行于x轴的向量,我们先将它饶y旋转直到它平行于z轴,这时,我们会发现任何饶z的旋转都改变不了向量的方向,即万向节死锁。

(译注:3维的万向节死锁情况分析见:http://www.cnblogs.com/soroman/archive/2008/03/24/1118996.html)

 

 


posted on 2006-10-11 13:14  SoRoMan  阅读(15740)  评论(39编辑  收藏  举报
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