localization_program.py

# 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
from copy import deepcopy
def sense(p, Z, sensor_right, colors):
    q = deepcopy( p )
    for y in range( len(colors) ):
        for x in range( len(colors[0]) ):
            hit = (Z == colors[y][x])
            q[y][x] = p[y][x] * (hit * sensor_right + (1-hit) * (1-sensor_right) )

    s = sum( [sum(row) for row in q] )

    for y in range( len(colors) ):
        for x in range( len(colors[0]) ):
            q[y][x] = q[y][x] / s
    return q

def move( p, U, p_move, colors):
    q = deepcopy( p )

    for y in range( len(colors) ):
        for x in range( len(colors[0]) ):
            q[y][x] = p_move * p[ (y - U[0])% len(colors) ][ (x - U[1])% len(colors[0]) ]
            q[y][x] = q[y][x] + (1-p_move) * p[y ][ x ]

    return q

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))]

    for measurement, motion in zip( measurements, motions ):
        p = move( p, motion, p_move, colors)
        p = sense( p, measurement, sensor_right, colors )
    return p

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)
show(p) # displays your answer