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视频来自---斯坦福大学工程技术

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专业开发中心

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好吧 我们开始

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欢迎参加机器人技术入门讲座-2008

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嗯 大家新年快乐

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在“机器人技术入门”课程中，我们会涉及

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一些机器人技术的基础--也就是说 我们会以

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多种数学模型来表达

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机器人系统

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其实你们刚刚在课堂里已经见过这些了

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你们刚才看到的是

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我们对一个仿人机器人系统的模拟

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以及这个模型的控制。

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如果你想要建立一个机器人模型

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来进行模拟，你必须建立一个

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这个系统的运动学表达

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还需要能够驱动这个系统，也就需要

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进入到电机层来确定使系统正确运动的转矩

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以及驱动力

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那么，咱们回到这个...

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我觉得这个很有趣

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嗯，这是一个你要去控制的机器人

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那么问题来了：我们应该用什么方法

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控制这条手臂从这个位置移动到另一个位置

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如果你考虑这个问题，会发现控制这个机器人

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有许多方法

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首先，你要知道当前机器人的位置，那么

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要知道位置你就需要一些传感器

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那么，要知道机器人的位置

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你会需要哪些传感器呢？

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有什么建议吗？

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GPS

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GPS？

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好吧

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那你用GPS能测量到几个参数呢？

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（我觉得可以啊）

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没问题没问题

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咱们可以试想一下

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几个参数--

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用GPS都能确定什么呢？

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（也许XY坐标吧）

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对，你能确定GPS本身定位的

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X和Y坐标坐标，对吗？

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但是，有多少个自由度--

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与多少个体在运动？

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比如我从这里移动到这里，多少个体在运动？

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你要在机器人上

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安装几台GPS呢？

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（呵呵哒）要是有47个自由度你就得装47个GPS

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那怎么行呢

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太昂贵了

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再来个建议

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我们需要点别的传感器

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（试试编码器）

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编码器！对啊，编码器

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那么编码器只测量

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一个自由度，只测量角度

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那我们有47个自由度

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需要多少编码器呢？

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四十七个

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这样可以提供相对位置，但是我们没法知道

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这个设备在这里或者那里，对吗？

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所以你需要一个GPS来定位某一个体

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然后基于这个体定位所有--

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还有没有其他--

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(Differential navigation 差动导航)

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对啊，在已知初始位置基础上进行积分或者使用--

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（视觉系统）

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视觉系统来定位至少一个或两个体

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然后你就知道机器人的位置，进而知道

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机器人运动的相对位置、速度

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所以一旦我们定位了机器人整体，我们就要找到一种方法

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来描述机器人各个体的位置。

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比如右手在哪里？

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左手在哪里？

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这里--你需要--

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这里你需要哪些信息？

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你需要了解所有刚体之间的位置关系

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然后一旦机器人站在那，你才能知道

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位置--比如手臂如何定位，手如何定位

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头如何定位

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然后需要一点来自于...学科的--

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（可以用陀螺仪）哦，我现在先不讨论传感器

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假设我们已经知道这些信息了，但我们需要确定一个....

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（一个模型）

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一个模型，运动学模型

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首先我们需要运动关系

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而且当系统运行起来，就会产生动力，对吗？

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所以你还得确定惯性力

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你需要知道--

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比如你移动右手，突然间整个系统都开始运动了

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对不对？

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这些相互连接的刚体之间是有

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耦合关系的

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所以我们要确定动力关系

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一旦你建立了这些模型，你就要考虑

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如何控制机器人

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那么我们如何像这样控制机器人呢？

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比如怎样把这个体移动到这里呢？

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我们怎么做呢？

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这只手--我想移动到这个位置

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您说什么？

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（前正向、逆向运动学）

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哦，非常好！

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那么，正向运动关系提供你手的

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位置

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逆向运动关系提供你--

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已知的你希望手所在的位置

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你需要

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你应该能够据此求得各个关节角

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是的

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如果你求出来了，你就应该知道每一个关节

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的目标运动角度

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然后再控制这些关节到达恰当的

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关节位置，然后手臂就移动到那个状态了

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关节位置，然后手臂就移动到那个状态了

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那我们能对这个机器人进行逆运动学求解吗？

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不太容易

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对一个机械臂这种6自由度的机器人来说

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就已经很难了，何况对一个有这么多自由度的机器人--

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那么假设我要把它移动到这个位置--这里

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这个位置

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有无数种轨迹可以达到这个位置

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这个问题就有无穷无尽种解

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何况，一个真人是不会

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以这种方式运动的。

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我是说，你要移动你的手臂时，你会去进行

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逆运动学运算吗？

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会吗？不会的

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所以，我们会看到不同的方式--

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哦，我会晚一点再讲解这一点，现在呢--

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不太清楚，是不是大家现在对机器人的基本概念已经

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有所了解了

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这张图片--是一个工作机器人在一个

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制造厂的隔绝环境内，正在工作

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捡拾，捡拾然后放置，在两个位置间运动

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与人类没有任何互动。但机器人技术，经过这么多年

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已经蜕变了

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今天，机器人已经有很多运用领域了

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从协助对人的外科手术

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到协助搬运重物

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到娱乐机器人，到各种机器人，各种不同

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领域

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而真正让人对机器人技术痴迷的是：

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机器人已经愈来愈接近人类--

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我们现在使用机器人来搬运，举升

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来工作，通过触觉交互技术来拓展人类

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的双手

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你可以触摸虚拟物品或者真实的物品

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我不确定大家是不是都知道触觉(haptics)

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触觉来自于“觉”--一个希腊词汇

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指的是

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触摸的感觉

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从触觉中--

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比如这里是

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外科医生的手，手术正在进行中

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医生在病人体外操作，而机器人在

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体内运行，不用开膛破肚，我们只需要一个

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小小的切口

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通过这个小口把机器人探入，在体内

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进行手术

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术后恢复效果惊人

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住了几天院，病人就

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出院了

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借助触觉技术或者借助一个上位机的远程手术

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让我们可以控制--

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比如这有一个“身手异处”的外科医生，正在手术

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或者水下操作，或者与一个真实家庭环境

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或者工厂环境的交互

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机器人技术还有一个地方特别有趣

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由于机器人技术着眼于铰接的体系统，现在我们就可以

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使用各种模型，各种与机器人有关的技术

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对人类进行建模，或者创造一种

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人类的数字模型，我们一会儿会看到，

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这种模型可以模仿或者受控来复现运动捕捉设备捕捉到的人类运动行为。

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这种模型可以模仿或者受控来复现运动捕捉设备捕捉到的人类运动行为。

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这种模型可以模仿或者受控来复现运动捕捉设备捕捉到的人类运动行为。

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另外，使用我们正在开发的与

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真是物理世界的交互，我们将能够使用触觉设备

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来探求那些我们在曾经不能触摸的

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物理世界--举个例子，我们自身不可能下潜到

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原子尺度，但我们可以模拟原子世界，再通过

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触觉设备我们就可以探索这个世界

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也许机器人技术最让人兴奋的是

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模仿机器人，看上去像人类，而且

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行为举止与生物，动物或者人类相似

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这是几年前，我在日本

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有人认识这个地方吗？

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（大阪）

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他说是大阪

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（横滨）

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很对，但是你去过，你这是骗红！

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（蛤......蛤）所以这就是横滨，在横滨，当时是

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Robodex

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Robodex集合了千千万万的

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机器人爱好者来领略机器人技术的最新成就

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这是几年以前

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你在这能看到ASIMO--ASIMO事实上是

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HONDA即P2和P3机器人之后推出的

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最新产品

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除此之外，你可以看到，嗯，几乎是所有机器人大鳄，

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在仿人机器人上的成就

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有没有人看过...

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这个？

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你们见过这个机器人吗？

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这是SONY的机器人--

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我记得我这好像有个视频

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看看能不能放

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SONY机器人在一个运动板上保持平衡

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这可不容易

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你可以想象这种实时控制要求有多高

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还有动力学建模和所有有关的方面

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还有动力学建模和所有有关的方面

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这是几年前完成的

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其实，我们几年前把这个机器人弄来斯坦福过

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他们在这做过一次表演，当时看到它做出的舞蹈表演

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和性能表现的确挺激动人心的

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还有许多名目繁多的机器人，尤其是在亚洲--

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在日本和韩国--有很多仿人机器人

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AIST制造了一系列机器人：HRP，HRP-1，和-2

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00:12:50,810 --> 00:12:53,060
而且他们还在进一步给它增加更多功能

224
00:12:52,850 --> 00:13:00,780
而且他们还在进一步给它增加更多功能

225
00:13:00,800 --> 00:13:03,890
有一个有意思的表演

226
00:13:03,910 --> 00:13:09,510
我们在名古屋附近拍的，当时是爱知县世博会

227
00:13:09,530 --> 00:13:15,650
他们在那展出了好几个项目

228
00:13:15,670 --> 00:13:21,319
有些是一些研究机构和企业

229
00:13:21,340 --> 00:13:24,890
联合建造的

230
00:13:24,910 --> 00:13:28,020
这是个舞蹈机器人

231
00:13:28,040 --> 00:13:34,920
这是那个HRP机器人

232
00:13:34,940 --> 00:13:37,480
HRP的步行演示

233
00:13:37,500 --> 00:13:41,060
步行功能已经被人们很好的掌握了

234
00:13:41,080 --> 00:13:46,180
但问题是：你怎样移动到一个位置

235
00:13:46,200 --> 00:13:50,470
取得一个物体并且和这个真实物的理世界进行互动

236
00:13:50,490 --> 00:13:51,550
这更有挑战性

237
00:13:51,570 --> 00:13:54,330
你可以看到这个滑动和触摸功能还不是很完备

238
00:13:54,350 --> 00:14:02,230
但这已经给我们指出了一个未来的研究方向

239
00:14:02,250 --> 00:14:05,020
这是一个有趣的设备

240
00:14:05,040 --> 00:14:07,480
来自早稻田大学

241
00:14:07,500 --> 00:14:11,320
他有更多的自由度--

242
00:14:11,340 --> 00:14:18,300
那么，另一个问题来了

243
00:14:18,320 --> 00:14:22,210
你在髋关节上有一个附加的自由度

244
00:14:22,230 --> 00:14:26,910
这样运动起来就更像人类了

245
00:14:26,930 --> 00:14:29,219
咱们看一个我最喜欢的

246
00:14:29,240 --> 00:14:36,700
这是一个仿人的，作动器也是仿人的

247
00:14:36,720 --> 00:14:41,240
使用的是人造肌肉来发起运动

248
00:14:41,260 --> 00:14:44,220
但是很显然，人造肌肉还有很多问题

249
00:14:44,240 --> 00:14:48,250
因为它的动态响应还非常滞后，而且所提供的动力也还不够

250
00:14:48,270 --> 00:14:51,699
因为它的动态响应还非常滞后，而且所提供的动力也还不够

251
00:14:51,720 --> 00:14:54,050
但是我们以后也会谈到这个问题

252
00:14:54,070 --> 00:15:24,070
那好，谁跟我说说你们对这个有什么感觉

253
00:15:25,010 --> 00:15:27,220
谁想说说？

254
00:15:27,240 --> 00:15:29,420
你怎么想？

255
00:15:29,440 --> 00:15:32,440
我们需要机器人完美复刻人类的外貌吗？

256
00:15:32,010 --> 00:15:33,010
我们需要机器人完美复刻人类的外貌吗？

257
00:15:33,010 --> 00:15:38,960
还是说我们只需要针对某些功能开发机器人？

258
00:15:38,980 --> 00:15:43,450
比如我们是伐木工，我们是不是只需要开发一个伐木机器人呢？

259
00:15:43,470 --> 00:15:44,840
比如我们是伐木工，我们是不是只需要开发一个伐木机器人呢？

260
00:15:44,860 --> 00:15:48,670
如果机器人要在人类社会中工作，那机器人是不是只需要

261
00:15:48,690 --> 00:15:53,140
两只手臂、移动能力、视觉能力

262
00:15:53,160 --> 00:15:56,240
两只手臂、移动能力、视觉能力

263
00:15:56,260 --> 00:16:00,740
思考一下这些问题挺有意思的：

264
00:16:00,760 --> 00:16:07,290
我们到底是需要 机器 “人”？ 还是 “机器” 人

265
00:16:07,310 --> 00:16:12,209
我们需要的是与所处环境进行最有效交互的“机器”吗？

266
00:16:12,230 --> 00:16:15,100
我们需要的是与所处环境进行最有效交互的“机器”吗？

267
00:16:15,120 --> 00:16:16,370
最后一个，我觉得是--

268
00:16:15,570 --> 00:16:25,950
是的，这是一个非常有趣的例子

269
00:16:25,970 --> 00:16:30,150
借助外骨骼，我们能多大程度上扩展人类的能力

270
00:16:30,170 --> 00:16:33,939
你穿戴好这个，你就变成了超人了

271
00:16:33,960 --> 00:16:37,390
你能搬很重的东西

272
00:16:37,410 --> 00:16:43,100
他们在这展示的是，我相信有60公斤

273
00:16:43,120 --> 00:16:47,030
人根本感觉不到任何重量，因为载荷都被外骨骼系统承担了

274
00:16:47,050 --> 00:16:52,430
人根本感觉不到任何重量，因为载荷都被外骨骼系统承担了

275
00:16:52,450 --> 00:16:56,300
还有一个有意思的视频，来自东京工大

276
00:16:56,320 --> 00:17:02,500
一款游动机器人

277
00:17:02,520 --> 00:17:05,660
能肯定的是这个机器人是防水的

278
00:17:05,680 --> 00:17:15,069
总而言之，机器人技术越来越向仿人方向发展

279
00:17:15,089 --> 00:17:16,230
总而言之，机器人技术越来越向仿人方向发展

280
00:17:16,250 --> 00:17:21,400
我们也看到了，机器人也渐渐走近人们的生活

281
00:17:21,420 --> 00:17:27,760
我们

282
00:17:27,780 --> 00:17:32,190


283
00:17:32,210 --> 00:17:33,210


284
00:17:33,210 --> 00:17:38,920


285
00:17:38,940 --> 00:17:41,990


286
00:17:42,010 --> 00:17:46,320


287
00:17:46,340 --> 00:17:48,320


288
00:17:48,340 --> 00:17:51,750


289
00:17:51,770 --> 00:17:55,530


290
00:17:55,550 --> 00:17:56,550


291
00:17:56,550 --> 00:18:00,560


292
00:18:00,580 --> 00:18:05,850


293
00:18:05,870 --> 00:18:12,629


294
00:18:12,650 --> 00:18:13,650


295
00:18:13,650 --> 00:18:18,170


296
00:18:18,190 --> 00:18:24,320


297
00:18:24,340 --> 00:18:29,439


298
00:18:29,460 --> 00:18:30,460


299
00:18:30,460 --> 00:18:34,690


300
00:18:34,710 --> 00:18:36,010


301
00:18:36,030 --> 00:18:39,790


302
00:18:39,810 --> 00:18:41,720


303
00:18:41,740 --> 00:18:44,900


304
00:18:44,920 --> 00:18:48,510


305
00:18:48,530 --> 00:18:53,290


306
00:18:53,310 --> 00:18:58,270


307
00:18:58,290 --> 00:19:01,580


308
00:19:01,600 --> 00:19:03,719


309
00:19:03,740 --> 00:19:11,410


310
00:19:11,430 --> 00:19:13,950


311
00:19:13,970 --> 00:19:15,590


312
00:19:15,610 --> 00:19:20,620


313
00:19:20,640 --> 00:19:21,640


314
00:19:21,640 --> 00:19:22,640


315
00:19:21,950 --> 00:19:24,240


316
00:19:24,260 --> 00:19:27,010


317
00:19:26,900 --> 00:19:29,230


318
00:19:29,250 --> 00:19:32,300


319
00:19:32,320 --> 00:19:38,520


320
00:19:38,540 --> 00:19:43,590


321
00:19:43,610 --> 00:19:48,629


322
00:19:48,650 --> 00:19:49,970


323
00:19:49,990 --> 00:19:52,410


324
00:19:52,430 --> 00:19:54,040


325
00:19:54,060 --> 00:19:57,790


326
00:19:57,810 --> 00:20:01,419


327
00:20:01,440 --> 00:20:04,250


328
00:20:04,270 --> 00:20:06,020


329
00:20:04,980 --> 00:20:08,480


330
00:20:06,240 --> 00:20:19,870


331
00:20:19,890 --> 00:20:25,300


332
00:20:25,320 --> 00:20:28,030


333
00:20:28,050 --> 00:20:31,020


334
00:20:31,040 --> 00:20:38,710


335
00:20:38,730 --> 00:20:40,920


336
00:20:40,940 --> 00:20:45,430


337
00:20:45,450 --> 00:20:51,270


338
00:20:51,290 --> 00:20:52,710


339
00:20:52,730 --> 00:20:55,570


340
00:20:55,590 --> 00:20:57,159


341
00:20:57,180 --> 00:21:00,570


342
00:21:00,590 --> 00:21:02,970


343
00:21:02,990 --> 00:21:08,580


344
00:21:08,600 --> 00:21:10,919


345
00:21:10,940 --> 00:21:14,510


346
00:21:14,530 --> 00:21:15,530


347
00:21:15,530 --> 00:21:18,950


348
00:21:18,970 --> 00:21:21,860


349
00:21:21,880 --> 00:21:25,300


350
00:21:25,320 --> 00:21:30,790


351
00:21:30,810 --> 00:21:34,100


352
00:21:34,120 --> 00:21:38,669


353
00:21:38,690 --> 00:21:46,040


354
00:21:46,060 --> 00:21:52,950


355
00:21:52,970 --> 00:21:53,970


356
00:21:53,970 --> 00:21:56,970


357
00:21:56,770 --> 00:21:58,250


358
00:21:58,270 --> 00:22:02,760


359
00:22:02,780 --> 00:22:06,660


360
00:22:06,680 --> 00:22:08,160


361
00:22:08,180 --> 00:22:11,880


362
00:22:11,900 --> 00:22:12,900


363
00:22:12,900 --> 00:22:20,800


364
00:22:20,820 --> 00:22:21,820


365
00:22:21,820 --> 00:22:25,080


366
00:22:25,100 --> 00:22:28,240


367
00:22:28,260 --> 00:22:34,340


368
00:22:34,360 --> 00:22:37,179


369
00:22:37,200 --> 00:22:38,200


370
00:22:38,200 --> 00:22:41,040


371
00:22:41,060 --> 00:22:44,480


372
00:22:44,500 --> 00:22:52,270


373
00:22:52,290 --> 00:22:55,510


374
00:22:55,530 --> 00:22:56,530


375
00:22:56,530 --> 00:22:59,379


376
00:22:59,400 --> 00:23:02,730


377
00:23:02,750 --> 00:23:03,750


378
00:23:03,750 --> 00:23:07,370


379
00:23:07,390 --> 00:23:10,660


380
00:23:10,680 --> 00:23:13,280


381
00:23:13,300 --> 00:23:17,659


382
00:23:17,680 --> 00:23:18,680


383
00:23:18,680 --> 00:23:23,200


384
00:23:23,220 --> 00:23:27,180


385
00:23:27,200 --> 00:23:31,340


386
00:23:31,360 --> 00:23:32,899


387
00:23:32,920 --> 00:23:37,190


388
00:23:37,210 --> 00:23:40,900


389
00:23:40,920 --> 00:23:45,810


390
00:23:45,830 --> 00:23:52,179


391
00:23:52,200 --> 00:23:55,310


392
00:23:55,330 --> 00:24:00,770


393
00:24:00,790 --> 00:24:04,320


394
00:24:04,340 --> 00:24:05,340


395
00:24:05,340 --> 00:24:07,500


396
00:24:07,520 --> 00:24:10,110


397
00:24:10,130 --> 00:24:12,700


398
00:24:12,720 --> 00:24:14,200


399
00:24:14,220 --> 00:24:15,220


400
00:24:15,220 --> 00:24:19,600


401
00:24:19,620 --> 00:24:26,780


402
00:24:26,800 --> 00:24:29,440


403
00:24:29,460 --> 00:24:31,620


404
00:24:31,640 --> 00:24:34,390


405
00:24:34,230 --> 00:24:35,490


406
00:24:35,510 --> 00:24:38,560


407
00:24:38,580 --> 00:24:39,580


408
00:24:39,580 --> 00:24:41,260


409
00:24:41,280 --> 00:24:44,460


410
00:24:44,480 --> 00:24:46,280


411
00:24:46,300 --> 00:24:48,800


412
00:24:48,170 --> 00:24:49,170


413
00:24:49,170 --> 00:24:52,530


414
00:24:52,550 --> 00:24:55,470


415
00:24:55,490 --> 00:25:00,220


416
00:25:00,240 --> 00:25:04,130


417
00:25:04,150 --> 00:25:07,340


418
00:25:07,360 --> 00:25:11,159


419
00:25:11,180 --> 00:25:14,540


420
00:25:14,560 --> 00:25:17,950


421
00:25:17,970 --> 00:25:18,970


422
00:25:18,970 --> 00:25:23,930


423
00:25:23,950 --> 00:25:30,150


424
00:25:30,170 --> 00:25:33,280


425
00:25:33,300 --> 00:25:37,870


426
00:25:37,890 --> 00:25:39,540


427
00:25:39,560 --> 00:25:44,550


428
00:25:44,570 --> 00:25:49,590


429
00:25:49,610 --> 00:25:53,240


430
00:25:53,260 --> 00:25:57,000


431
00:25:57,020 --> 00:26:01,030


432
00:26:01,050 --> 00:26:04,129


433
00:26:04,150 --> 00:26:08,250


434
00:26:08,270 --> 00:26:12,330


435
00:26:12,350 --> 00:26:15,750


436
00:26:15,770 --> 00:26:17,810


437
00:26:17,830 --> 00:26:25,520


438
00:26:25,540 --> 00:26:30,090


439
00:26:30,110 --> 00:26:34,729


440
00:26:34,750 --> 00:26:35,750


441
00:26:35,750 --> 00:26:40,130


442
00:26:40,150 --> 00:26:43,770


443
00:26:43,790 --> 00:26:44,909


444
00:26:44,930 --> 00:26:49,200


445
00:26:49,220 --> 00:26:54,880


446
00:26:54,900 --> 00:26:57,880


447
00:26:57,900 --> 00:27:02,930


448
00:27:02,950 --> 00:27:09,240


449
00:27:09,260 --> 00:27:10,730


450
00:27:10,750 --> 00:27:11,750


451
00:27:10,930 --> 00:27:17,870


452
00:27:17,890 --> 00:27:22,150


453
00:27:22,170 --> 00:27:26,090


454
00:27:26,110 --> 00:27:30,520


455
00:27:30,540 --> 00:27:33,690


456
00:27:33,710 --> 00:27:39,730


457
00:27:39,750 --> 00:27:40,760


458
00:27:40,780 --> 00:27:43,950


459
00:27:43,970 --> 00:27:46,630


460
00:27:46,650 --> 00:27:47,650


461
00:27:47,650 --> 00:27:51,920


462
00:27:51,940 --> 00:27:55,880


463
00:27:55,900 --> 00:27:59,500


464
00:27:59,520 --> 00:28:01,639


465
00:28:01,660 --> 00:28:10,110


466
00:28:10,130 --> 00:28:15,870


467
00:28:15,890 --> 00:28:19,870


468
00:28:19,890 --> 00:28:24,710


469
00:28:24,730 --> 00:28:30,110


470
00:28:30,130 --> 00:28:33,100


471
00:28:33,120 --> 00:28:36,600


472
00:28:36,620 --> 00:28:38,929


473
00:28:38,950 --> 00:28:44,430


474
00:28:44,450 --> 00:28:45,720


475
00:28:45,740 --> 00:28:50,340


476
00:28:50,360 --> 00:28:53,510


477
00:28:53,530 --> 00:28:57,290


478
00:28:57,310 --> 00:29:00,169


479
00:29:00,190 --> 00:29:04,860


480
00:29:04,880 --> 00:29:09,010


481
00:29:09,030 --> 00:29:14,399


482
00:29:14,420 --> 00:29:16,320


483
00:29:16,340 --> 00:29:20,530


484
00:29:20,550 --> 00:29:23,620


485
00:29:23,640 --> 00:29:25,060


486
00:29:25,080 --> 00:29:29,060


487
00:29:29,080 --> 00:29:35,050


488
00:29:35,070 --> 00:29:39,760


489
00:29:39,780 --> 00:29:44,260


490
00:29:44,280 --> 00:29:46,790


491
00:29:46,810 --> 00:29:49,679


492
00:29:49,700 --> 00:29:54,290


493
00:29:54,310 --> 00:29:59,169


494
00:29:59,190 --> 00:30:05,250


495
00:30:05,270 --> 00:30:08,450


496
00:30:08,470 --> 00:30:11,620


497
00:30:11,640 --> 00:30:17,120


498
00:30:17,140 --> 00:30:18,220


499
00:30:18,240 --> 00:30:21,200


500
00:30:21,220 --> 00:30:25,360


501
00:30:25,380 --> 00:30:27,880


502
00:30:27,900 --> 00:30:32,400


503
00:30:32,420 --> 00:30:36,280


504
00:30:36,300 --> 00:30:41,879


505
00:30:41,900 --> 00:30:45,960


506
00:30:45,980 --> 00:30:48,200


507
00:30:48,220 --> 00:30:55,780


508
00:30:55,800 --> 00:31:00,970


509
00:31:00,990 --> 00:31:04,820


510
00:31:04,840 --> 00:31:08,929


511
00:31:08,950 --> 00:31:12,200


512
00:31:12,220 --> 00:31:16,900


513
00:31:16,920 --> 00:31:20,400


514
00:31:20,420 --> 00:31:26,170


515
00:31:26,190 --> 00:31:28,870


516
00:31:28,890 --> 00:31:34,070


517
00:31:34,090 --> 00:31:38,530


518
00:31:38,550 --> 00:31:39,860


519
00:31:39,880 --> 00:31:40,930


520
00:31:40,950 --> 00:31:44,930


521
00:31:44,950 --> 00:31:46,270


522
00:31:46,290 --> 00:31:50,760


523
00:31:50,780 --> 00:31:55,560


524
00:31:55,580 --> 00:31:57,199


525
00:31:57,220 --> 00:32:01,950


526
00:32:01,970 --> 00:32:03,570


527
00:32:03,590 --> 00:32:07,580


528
00:32:07,600 --> 00:32:12,020


529
00:32:12,040 --> 00:32:17,730


530
00:32:17,750 --> 00:32:21,480


531
00:32:21,500 --> 00:32:26,040


532
00:32:26,060 --> 00:32:30,260


533
00:32:30,280 --> 00:32:34,310


534
00:32:34,330 --> 00:32:36,860


535
00:32:36,880 --> 00:32:37,880


536
00:32:37,460 --> 00:32:41,640


537
00:32:41,660 --> 00:32:45,250


538
00:32:45,270 --> 00:32:50,830


539
00:32:50,850 --> 00:32:55,149


540
00:32:55,170 --> 00:32:59,920


541
00:32:59,940 --> 00:33:03,560


542
00:33:03,580 --> 00:33:07,169


543
00:33:07,190 --> 00:33:08,690


544
00:33:07,310 --> 00:33:08,310


545
00:33:08,310 --> 00:33:11,240


546
00:33:11,260 --> 00:33:16,250


547
00:33:16,270 --> 00:33:17,270


548
00:33:17,270 --> 00:33:22,280


549
00:33:22,300 --> 00:33:30,450


550
00:33:30,470 --> 00:33:33,980


551
00:33:34,000 --> 00:33:35,000


552
00:33:35,000 --> 00:33:38,150


553
00:33:38,170 --> 00:33:41,790


554
00:33:41,810 --> 00:33:47,370


555
00:33:47,390 --> 00:33:51,440


556
00:33:51,460 --> 00:33:53,820


557
00:33:53,840 --> 00:33:58,959


558
00:33:58,980 --> 00:34:01,020


559
00:34:01,040 --> 00:34:04,780


560
00:34:04,800 --> 00:34:07,710


561
00:34:07,730 --> 00:34:12,560


562
00:34:12,580 --> 00:34:16,569


563
00:34:16,590 --> 00:34:17,600


564
00:34:17,620 --> 00:34:19,929


565
00:34:19,949 --> 00:34:24,989


566
00:34:25,010 --> 00:34:29,699


567
00:34:29,719 --> 00:34:32,870


568
00:34:32,889 --> 00:34:34,330


569
00:34:34,350 --> 00:34:38,319


570
00:34:38,340 --> 00:34:42,219


571
00:34:42,239 --> 00:34:46,219


572
00:34:46,239 --> 00:34:49,489


573
00:34:49,429 --> 00:34:51,629


574
00:34:51,650 --> 00:34:53,989


575
00:34:54,010 --> 00:34:57,120


576
00:34:57,139 --> 00:34:58,140


577
00:34:58,140 --> 00:35:00,759


578
00:35:00,780 --> 00:35:04,210


579
00:35:04,230 --> 00:35:05,420


580
00:35:05,440 --> 00:35:12,130


581
00:35:12,150 --> 00:35:13,150


582
00:35:13,150 --> 00:35:21,520


583
00:35:21,540 --> 00:35:26,870


584
00:35:26,890 --> 00:35:27,890


585
00:35:27,890 --> 00:35:28,890


586
00:35:28,610 --> 00:35:29,610


587
00:35:28,790 --> 00:35:32,900


588
00:35:32,920 --> 00:35:35,520


589
00:35:35,540 --> 00:35:40,320


590
00:35:40,340 --> 00:35:44,230


591
00:35:44,250 --> 00:35:48,420


592
00:35:48,440 --> 00:35:52,350


593
00:35:52,370 --> 00:35:54,330


594
00:35:54,350 --> 00:35:58,460


595
00:35:58,480 --> 00:36:01,790


596
00:36:01,810 --> 00:36:03,870


597
00:36:03,890 --> 00:36:10,520


598
00:36:10,540 --> 00:36:12,600


599
00:36:12,620 --> 00:36:16,790


600
00:36:16,810 --> 00:36:22,049


601
00:36:22,070 --> 00:36:24,630


602
00:36:24,650 --> 00:36:28,110


603
00:36:28,130 --> 00:36:29,350


604
00:36:29,370 --> 00:36:31,609


605
00:36:31,630 --> 00:36:35,020


606
00:36:35,040 --> 00:36:36,040


607
00:36:36,040 --> 00:36:37,759


608
00:36:37,780 --> 00:36:41,810


609
00:36:41,830 --> 00:36:47,950


610
00:36:47,970 --> 00:36:48,970


611
00:36:48,970 --> 00:36:52,140


612
00:36:52,160 --> 00:36:58,259


613
00:36:58,280 --> 00:36:59,280


614
00:36:59,280 --> 00:37:05,020


615
00:37:05,040 --> 00:37:08,040


616
00:37:07,930 --> 00:37:09,899


617
00:37:09,920 --> 00:37:11,970


618
00:37:11,990 --> 00:37:12,990


619
00:37:12,580 --> 00:37:16,660


620
00:37:16,680 --> 00:37:19,040


621
00:37:19,060 --> 00:37:23,570


622
00:37:23,590 --> 00:37:29,060


623
00:37:29,080 --> 00:37:30,390


624
00:37:30,410 --> 00:37:37,290


625
00:37:37,310 --> 00:37:41,660


626
00:37:41,680 --> 00:37:48,190


627
00:37:48,210 --> 00:37:49,940


628
00:37:49,960 --> 00:37:56,380


629
00:37:56,400 --> 00:38:01,780


630
00:38:01,800 --> 00:38:05,640


631
00:38:05,660 --> 00:38:08,899


632
00:38:08,920 --> 00:38:09,920


633
00:38:09,920 --> 00:38:15,730


634
00:38:15,750 --> 00:38:18,680


635
00:38:18,700 --> 00:38:22,080


636
00:38:22,100 --> 00:38:26,430


637
00:38:26,450 --> 00:38:28,790


638
00:38:28,810 --> 00:38:33,020


639
00:38:33,040 --> 00:38:34,240


640
00:38:34,260 --> 00:38:38,110


641
00:38:38,130 --> 00:38:42,520


642
00:38:42,540 --> 00:38:43,540


643
00:38:43,540 --> 00:38:46,940


644
00:38:46,960 --> 00:38:49,870


645
00:38:49,890 --> 00:38:54,230


646
00:38:54,250 --> 00:39:00,090


647
00:39:00,110 --> 00:39:06,290


648
00:39:06,310 --> 00:39:07,549


649
00:39:07,570 --> 00:39:11,250


650
00:39:11,270 --> 00:39:12,270


651
00:39:12,270 --> 00:39:20,110


652
00:39:20,130 --> 00:39:24,850


653
00:39:24,870 --> 00:39:27,650


654
00:39:27,670 --> 00:39:30,040


655
00:39:30,060 --> 00:39:33,950


656
00:39:33,970 --> 00:39:40,839


657
00:39:40,860 --> 00:39:45,880


658
00:39:45,900 --> 00:39:48,100


659
00:39:48,120 --> 00:39:53,700


660
00:39:53,720 --> 00:40:00,220


661
00:40:00,240 --> 00:40:01,799


662
00:40:01,820 --> 00:40:06,360


663
00:40:06,380 --> 00:40:30,890


664
00:40:30,900 --> 00:40:31,900


665
00:40:30,910 --> 00:40:33,410


666
00:40:31,900 --> 00:40:34,400


667
00:40:32,800 --> 00:40:35,300


668
00:40:33,700 --> 00:40:36,200


669
00:40:34,600 --> 00:40:36,600


670
00:40:35,320 --> 00:40:39,030


671
00:40:39,050 --> 00:40:40,050


672
00:40:40,050 --> 00:40:44,150


673
00:40:44,170 --> 00:40:45,170


674
00:40:45,170 --> 00:40:49,530


675
00:40:49,550 --> 00:40:50,550


676
00:40:50,550 --> 00:40:54,160


677
00:40:54,180 --> 00:40:57,870


678
00:40:57,890 --> 00:41:03,529


679
00:41:03,550 --> 00:41:07,890


680
00:41:07,910 --> 00:41:08,910


681
00:41:08,910 --> 00:41:12,560


682
00:41:12,580 --> 00:41:18,060


683
00:41:18,080 --> 00:41:22,150


684
00:41:22,170 --> 00:41:23,420


685
00:41:23,070 --> 00:41:27,100


686
00:41:27,120 --> 00:41:32,130


687
00:41:32,150 --> 00:41:37,800


688
00:41:37,820 --> 00:41:43,070


689
00:41:43,090 --> 00:41:46,780


690
00:41:46,800 --> 00:41:50,570


691
00:41:50,590 --> 00:41:57,040


692
00:41:57,060 --> 00:42:00,730


693
00:42:00,750 --> 00:42:03,480


694
00:42:03,500 --> 00:42:10,860


695
00:42:10,880 --> 00:42:14,890


696
00:42:14,910 --> 00:42:16,020


697
00:42:16,040 --> 00:42:20,150


698
00:42:20,170 --> 00:42:24,500


699
00:42:24,520 --> 00:42:27,990


700
00:42:28,010 --> 00:42:31,980


701
00:42:32,000 --> 00:42:33,660


702
00:42:33,680 --> 00:42:39,009


703
00:42:39,030 --> 00:42:41,370


704
00:42:41,390 --> 00:42:45,029


705
00:42:45,050 --> 00:42:47,800


706
00:42:47,230 --> 00:42:52,990


707
00:42:53,010 --> 00:42:55,780


708
00:42:55,800 --> 00:43:03,020


709
00:43:03,040 --> 00:43:07,830


710
00:43:07,850 --> 00:43:13,170


711
00:43:13,190 --> 00:43:18,970


712
00:43:18,990 --> 00:43:23,629


713
00:43:23,650 --> 00:43:27,480


714
00:43:27,500 --> 00:43:32,140


715
00:43:32,160 --> 00:43:35,359


716
00:43:35,380 --> 00:43:40,030


717
00:43:40,050 --> 00:43:41,450


718
00:43:41,470 --> 00:43:47,459


719
00:43:47,480 --> 00:43:52,500


720
00:43:52,520 --> 00:43:54,020


721
00:43:53,750 --> 00:43:56,590


722
00:43:56,610 --> 00:43:59,610


723
00:43:59,160 --> 00:44:02,600


724
00:44:02,620 --> 00:44:03,620


725
00:44:03,620 --> 00:44:06,670


726
00:44:06,690 --> 00:44:11,340


727
00:44:11,360 --> 00:44:13,260


728
00:44:13,280 --> 00:44:18,430


729
00:44:18,450 --> 00:44:19,450


730
00:44:19,450 --> 00:44:25,180


731
00:44:25,200 --> 00:44:28,169


732
00:44:28,190 --> 00:44:31,680


733
00:44:31,700 --> 00:44:33,450


734
00:44:33,470 --> 00:44:37,740


735
00:44:37,760 --> 00:44:40,450


736
00:44:40,470 --> 00:44:44,290


737
00:44:44,310 --> 00:44:49,560


738
00:44:49,580 --> 00:44:53,730


739
00:44:53,750 --> 00:44:58,970


740
00:44:58,990 --> 00:45:02,870


741
00:45:02,890 --> 00:45:06,230


742
00:45:06,250 --> 00:45:08,410


743
00:45:08,430 --> 00:45:12,690


744
00:45:12,710 --> 00:45:13,840


745
00:45:13,860 --> 00:45:15,810


746
00:45:15,830 --> 00:45:17,480


747
00:45:17,500 --> 00:45:21,260


748
00:45:21,280 --> 00:45:24,640


749
00:45:24,660 --> 00:45:30,629


750
00:45:30,650 --> 00:45:32,050


751
00:45:32,070 --> 00:45:33,690


752
00:45:33,710 --> 00:45:37,010


753
00:45:37,030 --> 00:45:42,230


754
00:45:42,250 --> 00:45:47,040


755
00:45:47,060 --> 00:45:58,390


756
00:45:58,410 --> 00:46:04,799


757
00:46:04,820 --> 00:46:11,670


758
00:46:11,690 --> 00:46:12,690


759
00:46:12,690 --> 00:46:14,180


760
00:46:14,200 --> 00:46:19,799


761
00:46:19,820 --> 00:46:23,320


762
00:46:23,340 --> 00:46:25,760


763
00:46:25,780 --> 00:46:31,850


764
00:46:31,870 --> 00:46:33,040


765
00:46:33,060 --> 00:46:38,720


766
00:46:38,740 --> 00:46:43,049


767
00:46:43,070 --> 00:46:46,370


768
00:46:46,390 --> 00:46:49,799


769
00:46:49,820 --> 00:46:54,880


770
00:46:54,900 --> 00:46:55,900


771
00:46:55,900 --> 00:46:58,880


772
00:46:58,900 --> 00:47:00,900


773
00:47:00,660 --> 00:47:04,730


774
00:47:04,750 --> 00:47:09,150


775
00:47:09,170 --> 00:47:11,680


776
00:47:11,700 --> 00:47:15,629


777
00:47:15,650 --> 00:47:18,150


778
00:47:17,250 --> 00:47:18,250


779
00:47:18,250 --> 00:47:23,750


780
00:47:23,770 --> 00:47:27,830


781
00:47:27,850 --> 00:47:31,049


782
00:47:31,070 --> 00:47:35,080


783
00:47:35,100 --> 00:47:39,370


784
00:47:39,390 --> 00:47:41,680


785
00:47:41,700 --> 00:47:44,339


786
00:47:44,360 --> 00:47:47,400


787
00:47:47,420 --> 00:47:55,190


788
00:47:55,210 --> 00:47:59,150


789
00:47:59,170 --> 00:48:01,920


790
00:48:01,940 --> 00:48:04,980


791
00:48:05,000 --> 00:48:06,230


792
00:48:06,250 --> 00:48:09,640


793
00:48:09,660 --> 00:48:14,290


794
00:48:14,310 --> 00:48:19,240


795
00:48:19,260 --> 00:48:20,260


796
00:48:20,260 --> 00:48:27,360


797
00:48:27,380 --> 00:48:28,380


798
00:48:28,380 --> 00:48:34,290


799
00:48:34,310 --> 00:48:39,150


800
00:48:39,170 --> 00:48:41,790


801
00:48:41,810 --> 00:48:45,740


802
00:48:45,760 --> 00:48:49,950


803
00:48:49,970 --> 00:48:54,490


804
00:48:54,510 --> 00:48:55,660


805
00:48:55,680 --> 00:49:01,279


806
00:49:01,300 --> 00:49:06,160


807
00:49:06,180 --> 00:49:09,180


808
00:49:09,060 --> 00:49:10,670


809
00:49:10,690 --> 00:49:12,300


810
00:49:12,320 --> 00:49:16,000


811
00:49:16,020 --> 00:49:21,880


812
00:49:21,900 --> 00:49:27,700


813
00:49:27,720 --> 00:49:31,859


814
00:49:31,880 --> 00:49:36,290


815
00:49:36,310 --> 00:49:41,870


816
00:49:41,890 --> 00:49:44,890


817
00:49:44,910 --> 00:49:51,490


818
00:49:51,510 --> 00:50:01,960


819
00:50:01,980 --> 00:50:02,980


820
00:50:02,980 --> 00:50:08,380


821
00:50:08,400 --> 00:50:11,450


822
00:50:11,470 --> 00:50:14,140


823
00:50:14,160 --> 00:50:17,730


824
00:50:17,750 --> 00:50:22,770


825
00:50:22,790 --> 00:50:27,810


826
00:50:27,830 --> 00:50:30,140


827
00:50:30,160 --> 00:50:35,560


828
00:50:35,580 --> 00:50:38,980


829
00:50:39,000 --> 00:50:42,980


830
00:50:43,000 --> 00:50:46,900


831
00:50:46,920 --> 00:50:48,480


832
00:50:48,500 --> 00:50:53,410


833
00:50:53,430 --> 00:50:54,960


834
00:50:54,980 --> 00:50:59,030


835
00:50:59,050 --> 00:51:00,800


836
00:51:00,820 --> 00:51:07,010


837
00:51:07,030 --> 00:51:10,500


838
00:51:10,520 --> 00:51:14,460


839
00:51:14,480 --> 00:51:18,740


840
00:51:18,760 --> 00:51:22,470


841
00:51:22,490 --> 00:51:25,950


842
00:51:25,970 --> 00:51:29,689


843
00:51:29,710 --> 00:51:36,810


844
00:51:36,830 --> 00:51:39,140


845
00:51:39,160 --> 00:51:40,730


846
00:51:40,750 --> 00:51:43,940


847
00:51:43,960 --> 00:51:45,490


848
00:51:45,510 --> 00:51:50,510


849
00:51:50,530 --> 00:51:52,250


850
00:51:52,270 --> 00:51:57,730


851
00:51:57,750 --> 00:52:02,500


852
00:52:02,520 --> 00:52:03,520


853
00:52:03,530 --> 00:52:08,260


854
00:52:08,280 --> 00:52:12,890


855
00:52:12,910 --> 00:52:18,230


856
00:52:18,250 --> 00:52:19,440


857
00:52:19,460 --> 00:52:24,970


858
00:52:24,990 --> 00:52:29,939


859
00:52:29,960 --> 00:52:40,070


860
00:52:40,090 --> 00:52:47,950


861
00:52:47,970 --> 00:52:50,500


862
00:52:50,520 --> 00:52:54,940


863
00:52:54,960 --> 00:53:01,380


864
00:53:01,400 --> 00:53:05,080


865
00:53:05,100 --> 00:53:06,980


866
00:53:07,000 --> 00:53:12,050


867
00:53:12,070 --> 00:53:14,930


868
00:53:14,950 --> 00:53:15,950


869
00:53:15,950 --> 00:53:20,490


870
00:53:20,510 --> 00:53:24,610


871
00:53:24,630 --> 00:53:28,830


872
00:53:28,850 --> 00:53:30,080


873
00:53:30,100 --> 00:53:33,279


874
00:53:33,300 --> 00:53:34,910


875
00:53:34,930 --> 00:53:39,740


876
00:53:39,760 --> 00:53:40,950


877
00:53:40,970 --> 00:53:44,220


878
00:53:44,220 --> 00:53:47,899


879
00:53:47,920 --> 00:53:51,030


880
00:53:51,050 --> 00:53:54,910


881
00:53:54,930 --> 00:53:57,680


882
00:53:57,700 --> 00:54:01,160


883
00:54:01,180 --> 00:54:04,359


884
00:54:04,380 --> 00:54:08,380


885
00:54:08,400 --> 00:54:11,150


886
00:54:10,910 --> 00:54:12,660


887
00:54:12,680 --> 00:54:17,620


888
00:54:17,640 --> 00:54:20,660


889
00:54:20,680 --> 00:54:21,680


890
00:54:21,680 --> 00:54:23,480


891
00:54:23,500 --> 00:54:24,920


892
00:54:24,940 --> 00:54:26,410


893
00:54:26,430 --> 00:54:28,180


894
00:54:27,980 --> 00:54:31,590


895
00:54:31,610 --> 00:54:38,600


896
00:54:38,620 --> 00:54:42,529


897
00:54:42,550 --> 00:54:45,320


898
00:54:45,340 --> 00:54:49,190


899
00:54:49,210 --> 00:54:50,990


900
00:54:51,010 --> 00:54:54,380


901
00:54:54,400 --> 00:54:58,540


902
00:54:58,560 --> 00:55:02,150


903
00:55:02,170 --> 00:55:08,290


904
00:55:08,310 --> 00:55:10,120


905
00:55:10,140 --> 00:55:11,140


906
00:55:11,140 --> 00:55:12,879


907
00:55:12,900 --> 00:55:15,400


908
00:55:15,350 --> 00:55:23,600


909
00:55:23,620 --> 00:55:30,630


910
00:55:30,650 --> 00:55:38,510


911
00:55:38,530 --> 00:55:42,330


912
00:55:42,350 --> 00:55:47,319


913
00:55:47,340 --> 00:55:51,970


914
00:55:51,990 --> 00:55:53,839


915
00:55:53,860 --> 00:55:58,300


916
00:55:58,320 --> 00:55:59,490


917
00:55:59,510 --> 00:56:00,510


918
00:55:59,600 --> 00:56:04,430


919
00:56:04,450 --> 00:56:07,390


920
00:56:07,410 --> 00:56:14,000


921
00:56:14,020 --> 00:56:16,530


922
00:56:16,550 --> 00:56:20,500


923
00:56:20,520 --> 00:56:27,140


924
00:56:27,160 --> 00:56:32,810


925
00:56:32,830 --> 00:56:37,130


926
00:56:37,150 --> 00:56:41,240


927
00:56:41,260 --> 00:56:42,510


928
00:56:42,130 --> 00:56:48,050


929
00:56:48,070 --> 00:56:52,150


930
00:56:52,170 --> 00:56:54,310


931
00:56:54,330 --> 00:56:55,830


932
00:56:55,630 --> 00:57:02,010


933
00:57:02,030 --> 00:57:04,290


934
00:57:04,310 --> 00:57:06,240


935
00:57:06,260 --> 00:57:10,300


936
00:57:10,320 --> 00:57:16,630


937
00:57:16,650 --> 00:57:20,330


938
00:57:20,350 --> 00:57:22,730


939
00:57:22,750 --> 00:57:27,070


940
00:57:27,090 --> 00:57:29,380


941
00:57:29,400 --> 00:57:31,640


942
00:57:31,660 --> 00:57:32,660


943
00:57:32,260 --> 00:57:33,260


944
00:57:32,350 --> 00:57:33,350


945
00:57:32,440 --> 00:57:39,440


946
00:57:39,460 --> 00:57:45,560


947
00:57:45,580 --> 00:57:47,330


948
00:57:46,120 --> 00:57:48,370