From 90f5b775a9dd827bfb9d011221105bdeee50db27 Mon Sep 17 00:00:00 2001 From: qiwihui Date: Sun, 17 Mar 2019 22:09:11 +0800 Subject: [PATCH] =?UTF-8?q?fix:=20=E5=88=A0=E9=99=A4=E5=A4=9A=E4=BD=99?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- source/partI/chapter4/16.3.md | 16 ---------------- source/partI/chapter4/images/16.4.png | Bin 25118 -> 0 bytes source/partI/chapter4/images/16.5.png | Bin 37084 -> 0 bytes source/partI/chapter4/images/16.6.png | Bin 59403 -> 0 bytes source/partI/chapter4/images/16.7.png | Bin 91488 -> 0 bytes source/partI/chapter4/images/4.4.png | Bin 15326 -> 0 bytes source/partI/chapter4/images/4.5.png | Bin 26091 -> 0 bytes 7 files changed, 16 deletions(-) delete mode 100644 source/partI/chapter4/16.3.md delete mode 100644 source/partI/chapter4/images/16.4.png delete mode 100644 source/partI/chapter4/images/16.5.png delete mode 100644 source/partI/chapter4/images/16.6.png delete mode 100644 source/partI/chapter4/images/16.7.png delete mode 100644 source/partI/chapter4/images/4.4.png delete mode 100644 source/partI/chapter4/images/4.5.png diff --git a/source/partI/chapter4/16.3.md b/source/partI/chapter4/16.3.md deleted file mode 100644 index 2cd3ba7..0000000 --- a/source/partI/chapter4/16.3.md +++ /dev/null @@ -1,16 +0,0 @@ -##16.3 体操机器人 -增强学习已经被应用在很多种类的物理控制任务中(例,一系列的机器人应用参考Connell和Mahadevan,1993)。一种这样的任务是*体操机器人*,一种两个关节,欠驱动的机器人,大致类似体操运动员在一个高杆上做摆动(如图 16.4)。第一个关节(对应于体操运动员的手)不能施加力矩,但是第二个关节(对应于体操运动员腕部的弯曲)可以。系统有四个连续状态变量:两个关节位置和两个关节速度。运动方程在图16.5中给出。这个系统已经被控制工程师广泛研究过(例,Spong,1997)。 -控制体操机器人的一个目的是在最短的时间内摆起机器人末端(“脚”)高于第一个关节大致一个连杆的距离。在这个任务中,加载到第二个关节的力矩受限于三个选择:固定大小的正力矩,同样大小的负力矩,或者没有力矩。在没有达到目标之前每一步的奖励都是-1,达到目标则结束该回合。没有折扣($\gamma=1$)。因此,任何状态,$s$,的最优值,$v_*(s)$是从$s$出发到达目标的最小时间(步数的整数值)。 -![RL](figures/16.4.png) -![RL](figures/16.5.png) -图16.5: 仿真体操机器人的运动方程。仿真的时间间隔为0.05秒,每四个时间间隔之后选择一次动作。第二个关节处施加的力矩由$\tau\in${+1,-1,0}来表示。关节位置没有约束,角速度有限制,$ \overset{\cdot}{\theta_1}\in[-4\pi,4\pi]$,$\overset{\cdot}{\theta_2}\in[-9\pi,9\pi]$。常量$m_1=m_2=1$(连杆的质量),$l_1=l_2=1$(连杆的长度),$l_c1=l_c2=0.5$(到质心的距离),$I_1=I_2=1$(连杆的转动惯量),$g=9.8$(重力)。 -Sutton(1996)提出了在线无模型的体操机器人起摆任务。虽然体操机器人是仿真的,仿真器并不能被智能体/控制器利用。训练和迭代就像是使用一个真的物理的体操机器人。每个回合从两个连杆都竖直向下处于自然状态开始。增强学习的智能体对机器人施加力矩知道目标达到。然后体操机器人恢复初始自然位置,新的回合开始。 -使用Sarsa($\lambda$)算法以及线性方程近似,代码和替换的轨迹如??页所示。有一个小的离散的动作集,很自然地每个动作会用到不同的tilings。下一个选择是用来表示状态的连续变量。一个聪明的设计者会用角度和第二个连杆的质心速度作为状态,这样做会使得解更加简洁并且能够泛化。但是因为这只是一个测试问题,直接用连杆的角度和和角速度:${\theta_1}$,$\overset{\cdot}{\theta_1}$,${\theta_2}$,$\overset{\cdot}{\theta_2}$。两个角度受限于机器人的物理活动范围(参照图16.5)并且角度自然受限于范围$[0,2\pi]$。因此,这个任务的状态空间是一个在四个维度上的有界矩形范围。 -这就出现了一个问题,用什么tilings?有很多种可能性,就如第九章中所讨论的。一种方法是用一个完整的网格,在每个维度上滑动四维空间,就会得到很多小的四维度的tiles。另外,也可以仅仅沿着一个维度滑动,形成超平面的条纹。在这种情况下,需要选择在哪个维度上滑动。当然所有的情形都需要选择滑块的宽度,每种tiling的数量,如果有多种tilings如何偏移。还可以沿着两个或者三个维度滑动得到其他的tilings。例如,如果希望两个连杆的速度交互的多些,那么就多一些tilings沿着这两个维度滑动。如果零附近速度值需要更加精确,那么就应该在这个空间滑动多些。 -Sutton用可以以多种简单的方式滑动的tilings。四个维度中的每一个都分为六个相等的区间。为角速度添加第七个区间如此一来tilings可以在所有的维度上被偏移随机的间隔分之一(参考第九章,“Ti了Coding”那一章)。所有的48个tilings,12个如上所述在所有四个维度上进行滑动,每个将空间分为$6\times7\times6\times7=1764$tiles。另外12个tilings沿着三个维度滑动(4个三维度集合中每个都有3个随机偏移的tilings)。最终每个动作总共有25000个tiles。数量很小,所以哈希没有必要。所有的tilings都被在所有相关维度上偏移了一个间隔随机分之一。 -学习算法剩余的参数是$\alpha=0.2/48$,$\lambda=0.9$,$\epsilon=0$,$\theta_0=0$。在这个任务中使用贪婪策略$(\varepsilon=0)$比较合理因为需要长序列的正确的动作。一个探索性的动作可能会导致整个很长序列的正确动作都无用。通过选择好的起始动作值(一个较低的0值)来达到探索的目的。如2.7节和例9.2所述,这使得智能体持续的得到负反馈不管初始得到什么奖励,从而驱使它尝试新的策略。 -![RL](figures/16.6.png) -![RL](figures/16.7.png) -图16.7 :体操机器人的一个典型的学习行为。每一组都是一系列连续的位置,细一点的线是开始的时候。箭头表明加载在关节上的力矩。 - -图16.6 展示了体操机器人任务和上面提到的学习算法的学习曲线。从单一运行曲线可以看到单一的回合有时候太长。这些回合,体操机器人通常只是来回摆动第二个关节,第一个关节只在竖直方向上改变一小点。虽然这种情况发生在很多步上,最终总是使得动作值变低。所有的运行过程最终都会得到这个问题的一个高效的策略,通常持续75步。图16.7是一个典型的最终解。起初体操机器人前后对称地移动几次,第二个连杆总是朝下。然后,一旦加载了足够的能量,第二个连杆向右上方摆起并且达到目标高度。 \ No newline at end of file diff --git a/source/partI/chapter4/images/16.4.png b/source/partI/chapter4/images/16.4.png 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