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    Mars Rover Rotations
    ::火星轮渡轮轮轮

    The lesson discussed how the NASA Curiosity rover team has to send movement instructions based on rigid motions a full day before seeing the rover execute the instructions. Rotations are one of the fundamental ways in which a robot moves. In the case of the Mars Curiosity rover, not only does the rover itself  use rotations to navigate, but it also has a claw which uses rotations to pick up samples. To do this, engineers must use complicated algorithms based on a strong understanding of rigid motion. 
    ::讨论的教训是,NASA Curiosity rover团队在看到越野车执行指令前整整一天,必须依据僵硬的动作发出移动指令。旋转是机器人移动的基本方法之一。对于火星好奇度旋转来说,不仅越野车自己使用旋转来导航,而且它还有一个用旋转来采集样本的爪子。为此,工程师必须使用基于对僵硬动作的深刻理解的复杂算法。

    lesson content
    A Mars Rover with Claw on the Front

    U se the interactive below to play the role of the Mars rover engineers. Input a short sequence of rotations to  collect the samples. The claw will then perform the same rotations in the opposite direction to pick up the sample. Much like the Mars rover team, you must put all instructions in before executing the movement.
    ::使用下面的交互作用来扮演火星漫游者工程师的角色。 输入一个简短的旋转序列来采集样本。 然后爪子将进行相同的旋转, 向相反的方向取出样本。 与火星漫游者团队一样, 您必须在执行移动前输入所有指令 。

    As challenging as you may find this , it is only two rotations. Imagine the complexity of programming many  dozens of such steps, all based on a view from a tiny camera (which is, of course, controlled using rotations of its own)! 
    ::尽管你可能发现这具有挑战性,但这只是两个旋转。 想象一下程序设计数十个这样的步骤的复杂性, 所有这些都是基于一个小型相机的视图( 当然,这是用自己的旋转来控制的 ) !

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. What challenges did you face ? Did you get better after a couple of tries? (Imagine having to wait 24 hours between attempts)
      ::你面对什么挑战?经过几次尝试后,你是否变得更好? (想象在尝试之间必须等待24小时)
    2. Did you figure out any strategies?
      ::你有想出任何策略吗?

     

    Sequences of  Rotations
    ::轮换顺序

    In the previous interactive,  you saw an example of a sequence of rotations. The driver inputs a sequence of rotations to pick up the sample and then a sequence of opposite rotations  is performed in the opposite direction to return to the starting position.  You know that rotations turn an image around a center of rotation with every point of the rotated image remaining the same distance from the center of rotation. There is no limit to the number of times an image can rotate. However, like with sequences of translations, no matter how many times an image is rotated there is always one equivalent rotation that could have been performed to move it from the starting location straight to the ending location. Every time you perform a rotation the letters assigned to the vertices in the new image will get an apostrophe, just like with translations. When  A B C   is rotated, the new image will be labeled A ′ B ′ C ′ .  If it is rotated a second time, the new image will be labeled A ″ B ″ C ″ .
    ::在先前的互动中,您可以看到一个旋转序列的示例。 驱动程序输入一个旋转序列以采集样本, 然后在相反方向进行一个相反的旋转序列, 返回起始位置。 您知道旋转的图像会将一个图像围绕旋转中心旋转, 旋转图像的每个点与旋转中心保持相同的距离。 一个图像可以旋转的次数没有限制。 但是, 与翻译序列一样, 无论一个图像旋转多少次, 总是可以进行一个等效的旋转, 将图像从起始位置直接移动到结尾位置。 每次您执行旋转时, 分配给新图像中脊椎的字母都会得到一个折号, 就像翻译一样 。 当 ABC 旋转时, 新图像将会被标为 A_B_C_ 。 如果第二次旋转, 新图像将会被标为 AB_\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 。

    The interactive below will allow you to perform a sequence of two rotations on the pre-image, try it a few times and see if you can figure out how to recreate the result of the two rotations in sequence by using only one rotation  of the pre-image. It is always possible to do so. Is there a trick, pattern, or formula that you can discover that allows you to predict the single rotation equivalent to the two in sequence?
    ::下面的互动将允许您在预图像上执行两个旋转序列的顺序, 尝试它几次, 并查看您能否通过仅使用预图像的一个旋转来找到两个旋转序列的结果 。 总是可以这样做 。 您能否发现一个把戏、 模式或公式, 使您可以预测与两个旋转序列相等的单个旋转 ?

     

     

     

     

     

    Rotational Roving
    ::旋转轮动

    Joining the NASA Mars rover team takes intelligence and skill that are the product of lots of practice. Us e your knowledge of rigid motion sequences to guide the Mars rover through the practice course below.   
    ::加入美国航天局火星漫游者团队需要大量实践产生的智慧和技能。使用你对僵硬运动序列的知识引导火星漫游者通过下面的练习课程。

     

     

     

     

    Discussion Question
    ::讨论问题

    What challenges did you encounter? How did you handle them?
    ::你遇到什么挑战?

        Summary
    ::摘要

    • Rotations are rigid motions, so an image and pre-image are congruent after a single rotation or a series of rotations.
      ::轮廓是僵硬的动作,所以图像和预视图像在一次轮换或一系列轮换之后是相同的。
    • A series of rotations can always be replicated by a single rotation.
      ::一连串的轮换总是可以通过单一的轮换来复制。
    • As with translations and reflections, each vertex of an image gains an apostrophe after each rotation in a series.
      ::与翻译和反射一样,图像的每个顶端在一系列的每次旋转后都会增加一个波纹。