Udacity Unit 4-19 Code (written by Sebastian Thrun)

gistfile1.py

# ----------
# User Instructions:
# 
# Implement the function optimum_policy2D() below.
#
# You are given a car in a grid with initial state
# init = [x-position, y-position, orientation]
# where x/y-position is its position in a given
# grid and orientation is 0-3 corresponding to 'up',
# 'left', 'down' or 'right'.
#
# Your task is to compute and return the car's optimal
# path to the position specified in `goal'; where
# the costs for each motion are as defined in `cost'.

# EXAMPLE INPUT:

# grid format:
#     0 = navigable space
#     1 = occupied space 
grid = [[1, 1, 1, 0, 0, 0],
        [1, 1, 1, 0, 1, 0],
        [0, 0, 0, 0, 0, 0],
        [1, 1, 1, 0, 1, 1],
        [1, 1, 1, 0, 1, 1]]
goal = [2, 0] # final position
init = [4, 3, 0] # first 2 elements are coordinates, third is direction
cost = [2, 1, 20] # the cost field has 3 values: right turn, no turn, left turn

# EXAMPLE OUTPUT:
# calling optimum_policy2D() should return the array
# 
# [[' ', ' ', ' ', 'R', '#', 'R'],
#  [' ', ' ', ' ', '#', ' ', '#'],
#  ['*', '#', '#', '#', '#', 'R'],
#  [' ', ' ', ' ', '#', ' ', ' '],
#  [' ', ' ', ' ', '#', ' ', ' ']]
#
# ----------


# there are four motion directions: up/left/down/right
# increasing the index in this array corresponds to
# a left turn. Decreasing is is a right turn.

forward = [[-1,  0], # go up
           [ 0, -1], # go left
           [ 1,  0], # go down
           [ 0,  1]] # do right
forward_name = ['up', 'left', 'down', 'right']

# the cost field has 3 values: right turn, no turn, left turn
action = [-1, 0, 1]
action_name = ['R', '#', 'L']


# ----------------------------------------
# modify code below
# ----------------------------------------

def optimum_policy2D():

	value = [[[999 for row in range(len(grid[0]))] for col in range(len(grid))],
			[[999 for row in range(len(grid[0]))] for col in range(len(grid))],
			[[999 for row in range(len(grid[0]))] for col in range(len(grid))],
			[[999 for row in range(len(grid[0]))] for col in range(len(grid))]]

	policy = [[[' ' for row in range(len(grid[0]))] for col in range(len(grid))],
			[[' ' for row in range(len(grid[0]))] for col in range(len(grid))],
			[[' ' for row in range(len(grid[0]))] for col in range(len(grid))],
			[[' ' for row in range(len(grid[0]))] for col in range(len(grid))]]

	policy2D = [[' ' for row in range(len(grid[0]))] for col in range(len(grid))]


	change = True
	while change:
		change = False
		# go through all grid cells and calculate values

		for x in range(len(grid)):
			for y in range(len(grid[0])):
				for orientation in range(4):
					if goal[0] == x and goal[1] == y: #GOAL
						if value[orientation][x][y] > 0:
							change = True
							value[orientation][x][y] = 0
							policy[orientation][x][y] = '*'
					elif grid[x][y] == 0:

						#calculate the three ways to propagate value
						for i in range(3):
							o2 = (orientation + action[i]) % 4
							x2 = x + forward[o2][0]
							y2 = y + forward[o2][1]

							if x2 >= 0 and x2 < len(grid) and y2 >= 0 and y2 < len(grid[0]) and grid[x2][y2] == 0:
								v2 = value[o2][x2][y2] + cost[i]
								if v2 < value[orientation][x][y]:
									value[orientation][x][y] = v2
									policy[orientation][x][y] = action_name[i]
									change = True
	x = init[0]
	y = init[1]
	orientation = init[2]


	policy2D[x][y] = policy[orientation][x][y]
	while policy[orientation][x][y] != '*':
		if policy[orientation][x][y] == '#':
			o2 = orientation
		elif policy[orientation][x][y] == 'R':
			o2 = (orientation - 1) % 4
		elif policy[orientation][x][y] == 'L':
			o2 = (orientation + 1) % 4
		x = x + forward[o2][0]
		y = y + forward[o2][1]
		orientation = o2
		policy2D[x][y] = policy[orientation][x][y]

								

	return policy2D 

print optimum_policy2D()