Normalized Sense Function
In this notebook, let’s go over the steps a robot takes to help localize itself from an initial, uniform distribution to sensing and updating that distribution and finally normalizing that distribution.
- The robot starts off knowing nothing; the robot is equally likely to be anywhere and so
pis a uniform distribution. - Then the robot senses a grid color: red or green, and updates this distribution
paccording to the values of pHit and pMiss. - We normalize
psuch that its components sum to 1.
<img src=’images/robot_sensing.png’ width=50% height=50% />
# importing resources
import matplotlib.pyplot as plt
import numpy as np
A helper function for visualizing a distribution.
def display_map(grid, bar_width=1):
if(len(grid) > 0):
x_labels = range(len(grid))
plt.bar(x_labels, height=grid, width=bar_width, color='b')
plt.xlabel('Grid Cell')
plt.ylabel('Probability')
plt.ylim(0, 1) # range of 0-1 for probability values
plt.title('Probability of the robot being at each cell in the grid')
plt.xticks(np.arange(min(x_labels), max(x_labels)+1, 1))
plt.show()
else:
print('Grid is empty')
QUIZ: Modify your code so that it normalizes the output for the sense function.
This means that the entries in q should sum to one.
Note that pHit refers to the probability that the robot correctly senses the color of the square it is on, so if a robot senses red and is on a red square, we’ll multiply the current location probability (0.2) with pHit. Same goes for if a robot senses green and is on a green square.
# given initial variables
p=[0.2, 0.2, 0.2, 0.2, 0.2]
# the color of each grid cell in the 1D world
world=['green', 'red', 'red', 'green', 'green']
# Z, the sensor reading ('red' or 'green')
Z = 'red'
pHit = 0.6
pMiss = 0.2
## Complete this function
def sense(p, Z):
''' Takes in a current probability distribution, p, and a sensor reading, Z.
Returns a *normalized* distribution after the sensor measurement has been made, q.
This should be accurate whether Z is 'red' or 'green'. '''
q=[]
##TODO: normalize q
# loop through all grid cells
for i in range(len(p)):
# check if the sensor reading is equal to the color of the grid cell
# if so, hit = 1
# if not, hit = 0
hit = (Z == world[i])
q.append(p[i] * (hit * pHit + (1-hit) * pMiss))
return q
q = sense(p,Z)
print(q)
display_map(q)
