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Localization.py
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# The function localize takes the following arguments:
#
# colors:
# 2D list, each entry either 'R' (for red cell) or 'G' (for green cell)
#
# measurements:
# list of measurements taken by the robot, each entry either 'R' or 'G'
#
# motions:
# list of actions taken by the robot, each entry of the form [dy,dx],
# where dx refers to the change in the x-direction (positive meaning
# movement to the right) and dy refers to the change in the y-direction
# (positive meaning movement downward)
# NOTE: the *first* coordinate is change in y; the *second* coordinate is
# change in x
#
# sensor_right:
# float between 0 and 1, giving the probability that any given
# measurement is correct; the probability that the measurement is
# incorrect is 1-sensor_right
#
# p_move:
# float between 0 and 1, giving the probability that any given movement
# command takes place; the probability that the movement command fails
# (and the robot remains still) is 1-p_move; the robot will NOT overshoot
# its destination in this exercise
#
# The function should RETURN (not just show or print) a 2D list (of the same
# dimensions as colors) that gives the probabilities that the robot occupies
# each cell in the world.
#
# Compute the probabilities by assuming the robot initially has a uniform
# probability of being in any cell.
#
# Also assume that at each step, the robot:
# 1) first makes a movement,
# 2) then takes a measurement.
#
# Motion:
# [0,0] - stay
# [0,1] - right
# [0,-1] - left
# [1,0] - down
# [-1,0] - up
def localize(colors,measurements,motions,sensor_right,p_move):
# initializes p to a uniform distribution over a grid of the same dimensions as colors
pinit = 1.0 / float(len(colors)) / float(len(colors[0]))
p = [[pinit for row in range(len(colors[0]))] for col in range(len(colors))]
# >>> Insert your code here <<<
for i in range(len(measurements)):
p = move(p, motions[i], p_move, colors)
p = sense(p, measurements[i], sensor_right, colors)
return p
def sense(p, Z, pHit, colors):
pMiss = 1. - pHit
q = [[0 for row in range(len(colors[0]))] for col in range(len(colors))]
for x in range(len(p[0])):
for y in range(len(p)):
hit = (Z == colors[y][x])
q[y][x] = (p[y][x] * (hit * pHit + (1-hit) * pMiss))
s = sum(map(sum,q))
for x in range(len(q[0])):
for y in range(len(q)):
q[y][x] = q[y][x] / s
return q
def move(p, U, p_move, colors):
p_stay = 1. - p_move
q = [[0 for row in range(len(colors[0]))] for col in range(len(colors))]
for x in range(len(q[0])):
for y in range(len(q)):
s = p_move * p[(y-U[0]) % len(p)][(x-U[1]) % len(p[0])]
s += p_stay * p[y][x]
q[y][x] = s
return q
def show(p):
rows = ['[' + ','.join(map(lambda x: '{0:.5f}'.format(x),r)) + ']' for r in p]
print '[' + ',\n '.join(rows) + ']'
#############################################################
# For the following test case, your output should be
# [[0.01105, 0.02464, 0.06799, 0.04472, 0.02465],
# [0.00715, 0.01017, 0.08696, 0.07988, 0.00935],
# [0.00739, 0.00894, 0.11272, 0.35350, 0.04065],
# [0.00910, 0.00715, 0.01434, 0.04313, 0.03642]]
# (within a tolerance of +/- 0.001 for each entry)
colors = [['R','G','G','R','R'],
['R','R','G','R','R'],
['R','R','G','G','R'],
['R','R','R','R','R']]
measurements = ['G','G','G','G','G']
motions = [[0,0],[0,1],[1,0],[1,0],[0,1]]
p = localize(colors,measurements,motions,sensor_right = 0.7, p_move = 0.8)
correct_answer = (
[[0.01105, 0.02464, 0.06799, 0.04472, 0.02465],
[0.00715, 0.01017, 0.08696, 0.07988, 0.00935],
[0.00739, 0.00894, 0.11272, 0.35350, 0.04065],
[0.00910, 0.00715, 0.01434, 0.04313, 0.03642]])
print "Main problem:"
show(p) # displays your answer
show(correct_answer)
print "\n"
# test 1
colors = [['G', 'G', 'G'],
['G', 'R', 'G'],
['G', 'G', 'G']]
measurements = ['R']
motions = [[0,0]]
sensor_right = 1.0
p_move = 1.0
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 0.0]])
print "Test 1:"
show(p)
show(correct_answer)
print "\n"
# test 2
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R']
motions = [[0,0]]
sensor_right = 1.0
p_move = 1.0
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.0, 0.0, 0.0],
[0.0, 0.5, 0.5],
[0.0, 0.0, 0.0]])
print "Test 2:"
show(p)
show(correct_answer)
print "\n"
# test 3
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R']
motions = [[0,0]]
sensor_right = 0.8
p_move = 1.0
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.06666666666, 0.06666666666, 0.06666666666],
[0.06666666666, 0.26666666666, 0.26666666666],
[0.06666666666, 0.06666666666, 0.06666666666]])
print "Test 3:"
show(p)
show(correct_answer)
print "\n"
# test 4
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R', 'R']
motions = [[0,0], [0,1]]
sensor_right = 0.8
p_move = 1.0
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.03333333333, 0.03333333333, 0.03333333333],
[0.13333333333, 0.13333333333, 0.53333333333],
[0.03333333333, 0.03333333333, 0.03333333333]])
print "Test 4:"
show(p)
show(correct_answer)
print "\n"
# test 5
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R', 'R']
motions = [[0,0], [0,1]]
sensor_right = 1.0
p_move = 1.0
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.0, 0.0, 0.0],
[0.0, 0.0, 1.0],
[0.0, 0.0, 0.0]])
print "Test 5:"
show(p)
show(correct_answer)
print "\n"
# test 6
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R', 'R']
motions = [[0,0], [0,1]]
sensor_right = 0.8
p_move = 0.5
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.0289855072, 0.0289855072, 0.0289855072],
[0.0724637681, 0.2898550724, 0.4637681159],
[0.0289855072, 0.0289855072, 0.0289855072]])
print "Test 6:"
show(p)
show(correct_answer)
print "\n"
# test 7
colors = [['G', 'G', 'G'],
['G', 'R', 'R'],
['G', 'G', 'G']]
measurements = ['R', 'R']
motions = [[0,0], [0,1]]
sensor_right = 1.0
p_move = 0.5
p = localize(colors,measurements,motions,sensor_right,p_move)
correct_answer = (
[[0.0, 0.0, 0.0],
[0.0, 0.33333333, 0.66666666],
[0.0, 0.0, 0.0]])
print "Test 7:"
show(p)
show(correct_answer)
print "\n"