ACRL-two-old.py


# coding: utf-8

# In[6]:

# get_ipython().magic(u'matplotlib inline')


# In[7]:

# import matplotlib.pyplot as plt
import numpy as np
import time
import math
from collections import Counter
from tqdm import tqdm
from joblib import Parallel, delayed
import multiprocessing
import sys

import tiles

num_cores = multiprocessing.cpu_count()
print("numCores = " + str(num_cores))

# In[8]:

# plt.xkcd()  # Yes...

tmax = 3000

phase1maxT = 300000
phase2maxT = phase1maxT + 300000

t = tmax*np.linspace(0, 1, tmax, endpoint=False)

# Define the target angles
targetAngles = np.zeros((tmax,2))
for i in range(0, tmax, 4000): 
    targetAngles[i:i+1000,0] = 0.5
    targetAngles[i+1000:i+2000,0] = 1
    targetAngles[i+2000:i+3000,0] = 1.5
    targetAngles[i+3000:i+4000,0] = 1
    targetAngles[i:i+1000,1] = -3
    targetAngles[i+1000:i+2000,1] = -1.5
    targetAngles[i+2000:i+3000,1] = 0
    targetAngles[i+3000:i+4000,1] = -1.5
    
angleMins = np.amin(targetAngles, 0)
angleMaxs = np.amax(targetAngles, 0)

# Two subplots, unpack the axes array immediately
# plt.figure(figsize=(40,40))
# f, ax1 = plt.subplots(1, 1, sharey=False)
# ax1.set_ylim(-4,2)
# ax1.plot(t, targetAngles)
# ax1.set_title('Target Joint Signals')

# In[ ]:

delay = 0

# Noise is defined by a random normal variable 
noise = np.random.normal(0,0.001,(tmax,2))
simEMG = np.zeros((tmax+delay,2))

for i in range(1,tmax):
    if targetAngles[i,0] == 1:
        simEMG[i + delay,0] = -1
        simEMG[i + delay,1] = 1
    elif targetAngles[i,0] < 1:
        simEMG[i + delay,0] = 0
        simEMG[i + delay,1] = 0        
    elif targetAngles[i,0] > 1:
        simEMG[i + delay,0] = 1
        simEMG[i + delay,1] = -1
        
simEMGdiff = simEMG[0:tmax, :] # + noise

emgMins = np.amin(simEMGdiff, 0)
emgMaxs = np.amax(simEMGdiff, 0)

# plt.figure(figsize=(40,40))
# f, ax2 = plt.subplots(1, 1, sharey=False)
# ax2.plot(t, simEMGdiff)
# ax2.set_ylim(-1.5, 1.5)
# ax2.set_title('Simulated Noisy EMG Signal')

# In[ ]:

# Implement a learning algorithm to try to fit the signal
numJoints = 1
numEMG = 1

jointAngle = np.zeros((tmax, numJoints))

# Initialize the state array for the trajectory
# Possible feedback from the simulated arm includes the angle
# (in radians) and angular velocity (in radians per second) of
# each joint, and the Cartesian position of the end effector.

# Initialize the continuous state space 
# composed of joint angles (thetaW,thetaE)
# and differential EMG signals (dS1,dS2)
# thetaW, thetaE, dS1, dS2
s = np.zeros(numJoints+numEMG)

# Grab the initial values of the state space
# TODO: make sure this is valuable
s = np.hstack((targetAngles[0, :numJoints], simEMG[0, :numEMG]))

# Standard deviation should cover the possible action set
maxAngVelInt_stdC = 1023

# Initialize the saved variables
reward = np.zeros(tmax)
delta = np.zeros(tmax)

agentMean = np.zeros((tmax,numJoints))
agentStd = np.zeros((tmax,numJoints))

# define the number of tilings
numTilings = 25 # 5 25

# this defines the resolution of the tiling
resolutions = np.array([5, 8, 12, 20]) # resolutions = np.array([5,8,12,20])

numFeatures = len(s)

# Initialize the learning parameters
# m is the number of active features in the feature vector
m = numTilings * len(resolutions) + 1

gamma = 0.92 # 0.97
lambd = 0.3

# Different values for the 2013 paper
lambdw = 0.3
lambdv = lambdw # 0.7

alphaV = 0.1/m
alphaW = 0.01/m

alphaU = alphaW # 0.005/m # 0.01/m
alphaS = alphaW # 0.25*alphaU # 0.01/m #

# Actual length is the concatenation at different resolutions
# and the baseline feature
featVecLength = sum(np.power(resolutions, numFeatures)*numTilings)+1

# Initialize the weight vectors to zero 
# the should be as long as the feature vector x
elV = np.zeros(featVecLength)
v = np.zeros(featVecLength)

elU = np.zeros((featVecLength,numJoints))
elS = np.zeros((featVecLength,numJoints))
wU = np.zeros((featVecLength,numJoints))
wS = np.zeros((featVecLength,numJoints))

# This function converts the angular velocity from an integer in the range [-1023,1023]
# to an angular velocity in radians per second.
# The no-load speed of the motor is ~60RPM, which is around 6 radians per second
# rad/s = rot(RPM) 2*pi/60
# This should give a good simulation of the true robotic kinematics
def conAngIntToangVel(angInt):
    motorVel = 60
    angVel = motorVel * angInt / maxAngVelInt_stdC
    return angVel


def normsingle(val, oldmin, oldmax, newmin, newmax):
    return (((val - oldmin) * (newmax - newmin)) / (oldmax - oldmin)) + newmin


def normalize(state):
    # Normalize the state value given the maximum and minimum possible values
    # All components in s were normalized to the range [0, 1]
    # according to their minimum and maximum POSSIBLE VALUES!
    sMins = np.concatenate((angleMins[:numJoints], emgMins[:numEMG]))
    sMaxs = np.concatenate((angleMaxs[:numJoints], emgMaxs[:numEMG]))

    # define the normalization constant
    nct = 0.5

    return Parallel(n_jobs=num_cores)(delayed(normsingle)(state[j], sMins[j]-nct, sMaxs[j]+nct, 0, 1) for j in range(len(state)))


def getfeatvec(res, normS):

    scalednormS = [x * res for x in normS]

    # x is the active tiles in this featurization
    # This featurization should return a single binary feature vector
    # with exactly m features in x(s) active at any time
    # Binary feature vector has a length of 4636426 or
    # sum(np.power(np.array([5,8,12,20]),4)*25)+1
    x = np.zeros(np.power(res, numFeatures)*numTilings)

    tilesOut = tiles.tiles(numTilings, res, scalednormS)

    for idx, val in enumerate(tilesOut):
        # for each tile index put out by the tile coder
        # we need to flip a bit in the feature vector
        # this bit index is given by the value of the tile from the tile coder
        # the index this value was at, the resolution of the tile
        x[val + (res**2 * idx)] = 1

    return x


def featurize(s):

    normS = normalize(s)

    featvecs = Parallel(n_jobs=num_cores)(delayed(getfeatvec)(resolutions[res], normS) for res in range(len(resolutions)))

    # Concatenate the feature vectors and add
    # Single active baseline unit
    catfeat = np.hstack(featvecs)
    catfeat = np.hstack((0, catfeat))

    print catfeat[0]

    print len(catfeat)

    print sum(np.power(np.array(resolutions), numFeatures)*numTilings)+1

    # For each resolution the features are needed 
    for res in np.nditer(resolutions):

        # Tilecoding hash table
        # ctu = tiles.CollisionTable(32, 'super safe')
        # ctu = tiles.CollisionTable(4096, 'unsafe')
        # cts = tiles.CollisionTable(4096, 'safe')
        # ctss = tiles.CollisionTable(4096, 'super safe')

        resVec = np.zeros(np.power(res, numFeatures)*numTilings)
        # resVecHash = np.zeros(4096)
 
        # Get the indexes of the tiles
        tilesOut = tiles.tiles(numTilings, res, normS*res)
        print tilesOut

#         print tilesOut 
        
        # tilesOutHash = tiles.tiles(numTilings, ctu, normS*res)
#         print tilesOutHash
        
        # resVecHash[tilesOutHash] = 1
        # print resVecHash
        
        # For each tile index flip a feature in the feature vector
        # for tileIndex in range(len(tilesOut)):
        #     resVec[tilesOut[tileIndex] + (res**2 * tileIndex)] = 1
            
        # x = np.append(x, resVec)

    return catfeat

def getReward(newAngles,timeStep):
    # Define the reward function of the system
    # A positive reward of rt = 1.0 was
    # delivered when θw and θe were both within 0.1 radians of
    # their target angles. A reward of rt = −0.5 was delivered
    # in all other cases, in essence penalizing the learning system
    # when the arm’s posture differed from the target posture.

    target = targetAngles[timeStep,range(numJoints)]    
    absAngleError = np.abs(newAngles-target)
    
    if all(absAngleError < 0.1):
        r = 0.1
    else:
        r = -0.5

    return r

def perform(vel,s,timeStep):
    # take the action and observe the new state and the reward 
    # new state is defined by the new joint angle
    # which is defined by the old joint angle and the new angular velocity
    # which is applied for that time step and the
    # emg signal at that time index 
    
    # Calculate the new angular state of the joint
    # old angle + angular velocity * time (in this case time = 5ms, the period of action selection)
    # this limits the amount of motion of the joint possible in each action selection

    # Define the new state space with the new angle and the emg information from the next step    
    newAngles = np.zeros(numJoints)
    newAngles[:] = np.clip((s[:numJoints] + (vel[:] * 0.005)), 0, math.pi)
  
    s = np.hstack((newAngles, simEMGdiff[timeStep, range(numEMG)]))
    
    # Get the reward for the new angle
    r = getReward(newAngles,timeStep)
    
    return r, s

# process the training samples that are given
for i in tqdm(range(tmax)):
    
    jointAngle[i, :] = s[:numJoints]

    # Featurize the state
    x = featurize(s)
    
    a = np.zeros(numJoints)
    angVels = np.zeros(numJoints)
    
    # Calculate the mean and standard deviation of the action selection
    for j in range(numJoints):      
        agentMean[i,j] = np.dot(wU[:,j],x)
        agentStd[i,j] = max(1,np.exp(np.dot(wS[:,j],x) + np.log(maxAngVelInt_stdC)))

        # get the action from the normal distribution
        # angular velocity commands are sent to joints (simulated servos) 
        # as integers in the range [−maxAngVelInt_stdC, maxAngVelInt_stdC] 
        a[j] = round(np.random.normal(agentMean[i,j],agentStd[i,j])) 
    
        # If the action is outside the range, crop to the range
        if a[j] < -maxAngVelInt_stdC:
            a[j] = -maxAngVelInt_stdC
        elif a[j] > maxAngVelInt_stdC:
            a[j] = maxAngVelInt_stdC
        
        # Convert the action to an angular velocity
        angVels[j] = conAngIntToangVel(a[j])

    # Take action a and observe the reward, r, and the new state, s
    reward[i],s = perform(angVels,s,i)

    if numJoints > 1:
        # Initially, parameter vectors for the wrist and elbow joints
        # were each trained in isolation for 100k time steps;
        if i < phase1maxT:
            # set joint 2 to desired position
            s[1] = targetAngles[i,1]

        elif i < phase2maxT:
            # set joint 1 to desired position
            s[0] = targetAngles[i,0]

    # Featurize the new state
    newX = featurize(s)

    # Calculate the TD Error based on the old state and the new state
    delta[i] = reward[i] + (gamma * np.dot(v,newX)) - np.dot(v,x)
    
    # Critic's eligibility traces 
    # Updated eligibility trace from the 2013 paper
    # replacing eligibility traces in the critic used to accelerate learning
    elV = (lambdv * elV) + x
    elV = np.minimum(np.ones(featVecLength),elV)

    # Critic's parameter vector
    v = v + (alphaV * delta[i] * elV)

    if numJoints > 1:
    # Initially, parameter vectors for the wrist and elbow joints
    # were each trained in isolation for 100k time steps;
        if i < phase1maxT:
            # learn parameter vectors for joint 1
            # set joint 2 to desired position
            elU[:,0] = lambdw * elU[:,0] + np.multiply((a[0] - agentMean[i,0]),x)
            wU[:,0] = wU[:,0] + alphaU * delta[i] * elU[:,0]
            elS[:,0] = lambdw * elS[:,0] + np.multiply(((np.power((a[0] - agentMean[i,0]),2) / np.power(agentStd[i,0],2)) - 1),x)
            wS[:,0] = wS[:,0] + alphaS * delta[i] * elS[:,0]

        elif i < phase2maxT:
            # learn parameter vectors for joint 2
            # set joint 1 to desired position
            elU[:,1] = lambdw * elU[:,1] + np.multiply((a[1] - agentMean[i,1]),x)
            wU[:,1] = wU[:,1] + alphaU * delta[i] * elU[:,1]
            elS[:,1] = lambdw * elS[:,1] + np.multiply(((np.power((a[1] - agentMean[i,1]),2) / np.power(agentStd[i,1],2)) - 1),x)
            wS[:,1] = wS[:,1] + alphaS * delta[i] * elS[:,1]
        
        else:  
            for j in range(numJoints):
                # Actors parameters (eligibiliy traces and weight vectors)
                elU[:,j] = lambdw * elU[:,j] + np.multiply((a[j] - agentMean[i,j]),x)
                wU[:,j] = wU[:,j] + alphaU * delta[i] * elU[:,j]
                elS[:,j] = lambdw * elS[:,j] + np.multiply(((np.power((a[j] - agentMean[i,j]),2) / np.power(agentStd[i,j],2)) - 1),x)
                wS[:,j] = wS[:,j] + alphaS * delta[i] * elS[:,j]
    else:  
        for j in range(numJoints):
            # Actors parameters (eligibiliy traces and weight vectors)
            elU[:,j] = lambdw * elU[:,j] + np.multiply((a[j] - agentMean[i,j]),x)
            wU[:,j] = wU[:,j] + alphaU * delta[i] * elU[:,j]
            elS[:,j] = lambdw * elS[:,j] + np.multiply(((np.power((a[j] - agentMean[i,j]),2) / np.power(agentStd[i,j],2)) - 1),x)
            wS[:,j] = wS[:,j] + alphaS * delta[i] * elS[:,j]
        
    if (i%5000 == 0):
        print 'Step: ' + str(i)
        print np.sum(reward)
        
        
#     print 'Joint Angle: ' + str(jointAngle[i,:]) + ' rads'
#     print 'Target Angle: ' + str(targetAngles[i,range(numJoints)]) + ' rads'
#     print 'Agent Mean: ' + str(agentMean[i,:])
#     print 'Agent Std: ' + str(agentStd[i,:])
#     print 'Action: ' + str(angVels) + ' rad/s, move ' + str(angVels*0.005) + ' rads'
#     print 'New Joint Angles: ' + str(s[range(numJoints)]) + ' rads'
#     print 'Reward: ' + str(reward[i])
#     print 'TD Error: ' + str(delta[i])
#     print '\n'


# In[ ]:

# Visualize the learning    
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, targetAngles[:,range(numJoints)])
# ax1.set_title('Target Angles')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, jointAngle)
# ax1.set_title('Learned Joint Angles')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, delta)
# ax1.set_title('TD Error')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, np.cumsum(reward))
# ax1.set_title('Cumulative Return')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, agentMean)
# ax1.set_title('Agent Mean')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t, agentStd)
# ax1.set_title('Agent Standard Deviation')


# ##### 

# In[ ]:

# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t[-30000:], jointAngle[-30000:])
# ax1.plot(t[-30000:], targetAngles[-30000:])
# ax1.set_title('Target and Learned Angles')
# ax1.set_ylim([0, 2])
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t[0:30000], agentMean[0:30000])
# ax1.set_title('Agent Mean')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t[0:30000], agentStd[0:30000])
# ax1.set_title('Agent Standard Deviation')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t[-30000:], agentMean[-30000:])
# ax1.set_title('Agent Mean')
#
# fig = plt.figure()
# ax1 = fig.add_subplot(111)
# ax1.plot(t[-30000:], agentStd[-30000:])
# ax1.set_title('Agent Standard Deviation')