## Maze Solving Robot with Reinforcement Learning

28 Jul 2023

In this blog we will use the Value Iteration Algorithm to solve a maze and will implement the algorithm and simulate it with PyGame. This is what we will be making. You can find the code here Git Repo: https://github.com/akshayballal95/reinforcement_learning_maze.git

## Setting up the Project

Let us start by first creating a virtual environment using the following command

python -m venv venv

and activate it using the following command for windows

venv\Scripts\activate.bat

and for mac

source venv\bin\activate

Next, install the dependencies

pip install -r requirements.txt

## Creating the Maze Class

Create a new file called maze.py and import the libraries in it

import numpy as np
import random
from typing import Tuple

Next instantiate the Maze class and define an __init__ function

class Maze:
def __init__(
self, level, goal_pos: Tuple[int, int], MAZE_HEIGHT=600, MAZE_WIDTH=600, SIZE=25
):
self.goal = (23, 20)
self.number_of_tiles = SIZE
self.tile_size = MAZE_HEIGHT // self.number_of_tiles
self.walls = self.create_walls(level)
self.goal_pos = goal_pos
self.state = self.get_init_state(level)
self.maze = self.create_maze(level)

self.state_values = np.zeros((self.number_of_tiles, self.number_of_tiles))
self.policy_probs = np.full(
(self.number_of_tiles, self.number_of_tiles, 4), 0.25
)


The maze is created based on the level provided as input, and the goal position within the maze is specified by the goal_pos parameter. The class also contains attributes and methods related to solving the maze using reinforcement learning techniques.

• self.state_values : A NumPy array of size self.number_of_tiles x self.number_of_tiles filled with zeros. This array will be used to store the estimated values of each state during the reinforcement learning process.
• self.policy_probs : A NumPy array of size self.number_of_tiles x self.number_of_tiles x 4, where 4 represents the number of possible actions (up, down, left, right). Each entry in this array is initialized with 0.25, which means initially, each action is equally likely in each state. This array will be used to store the action probabilities for each state during the reinforcement learning process.

## Creating the Maze

   def create_maze(self, level):
maze = []
walls = []
for row in range(len(level)):
for col in range(len(level[row])):
if level[row][col] == " ":
maze.append((row, col))
elif level[row][col] == "X":
walls.append((row,col))
return maze, walls

def get_init_state(self, level):
for row in range(len(level)):
for col in range(len(level[row])):
if level[row][col] == "P":
return (row, col)

The provided code snippet contains two methods for the maze environment:

1. create_maze(self, level): This method takes the level parameter, which is a list of strings representing the maze layout. It iterates through each cell in the level and identifies the positions of maze tiles and walls based on the characters ” ” and “X”, respectively. It appends the positions of maze tiles as (row, col) tuples to the maze list and the positions of walls to the walls list. Finally, it returns a tuple containing two lists: the maze list with the positions of maze tiles and the walls list with the positions of walls.
2. get_init_state(self, level): This method also takes the level parameter, which represents the maze layout. It iterates through each cell in the level and searches for the character “P”. When it finds “P” in the maze, it immediately returns the position (row, col) of “P” as the initial state for the maze-solving process. The function stops searching once it finds “P” and returns the position as a tuple (row, col).

These two methods are used to set up the maze environment, define the initial state, and obtain the positions of walls and maze tiles for further processing and maze-solving algorithms.

## Take Steps and Compute Reward

def compute_reward(self, state: Tuple[int, int], action: int):
next_state = self._get_next_state(state, action)
return -float(state != self.goal_pos)

def step(self, action):
next_state = self._get_next_state(self.state, action)
reward = self.compute_reward(self.state, action)
done = next_state == self.goal
return next_state, reward, done

def simulate_step(self, state, action):
next_state = self._get_next_state(state, action)
reward = self.compute_reward(state, action)
done = next_state == self.goal
return next_state, reward, done

def _get_next_state(self, state: Tuple[int, int], action: int):
if action == 0:
next_state = (state, state - 1)
elif action == 1:
next_state = (state - 1, state)
elif action == 2:
next_state = (state, state + 1)
elif action == 3:
next_state = (state + 1, state)
else:
raise ValueError("Action value not supported:", action)
if (next_state, next_state) not in self.walls:
return next_state
return state

This code snippet defines several methods related to a maze-solving environment using reinforcement learning. Let’s explain each method briefly:

1. compute_reward(self, state: Tuple[int, int], action: int): This method calculates the reward for taking an action from the current state in the maze. The reward is a negative value (-1.0) if the state is not equal to the goal_pos, otherwise, it is zero. The goal is to minimize the total reward while navigating the maze.
2. step(self, action): This method takes a step in the maze environment, executing the given action. It returns a tuple containing the next_state, the reward obtained from the compute_reward method for the current state and action, and a done flag indicating whether the agent has reached the goal state or not.
3. simulate_step(self, state, action): Similar to the step method, this method simulates a step in the maze environment for a given state and action, returning the next_state, reward, and done flag without updating the actual environment state.
4. _get_next_state(self, state: Tuple[int, int], action: int): This is a private method used internally to get the next_state given the current state and the chosen action. It calculates the next state based on the direction of the action (0: left, 1: up, 2: right, 3: down) and checks if the next state is not a wall (not present in the walls list). If the next state is a wall, it returns the current state, meaning the agent stays in the same position.

### Solving the Maze

    def solve(self, gamma=0.99, theta=1e-6):

delta = float("inf")

while delta > theta:
delta = 0
for row in range(self.number_of_tiles):
for col in range(self.number_of_tiles):
if (row, col) not in self.walls:
old_value = self.state_values[row, col]
q_max = float("-inf")

for action in range(4):
next_state, reward, done = self.simulate_step(
(row, col), action
)
value = reward + gamma * self.state_values[next_state]
if value > q_max:
q_max = value
action_probs = np.zeros(shape=(4))
action_probs[action] = 1

self.state_values[row, col] = q_max
self.policy_probs[row, col] = action_probs

delta = max(delta, abs(old_value - self.state_values[row, col]))


The solve method represents the implementation of the Value Iteration algorithm to find an optimal policy for the maze environment.

Let’s go through the method step by step:

1. Initialization:

• gamma: The discount factor for future rewards (default value: 0.99).
• theta: The threshold for convergence (default value: 1e-6).
• delta: A variable initialized to infinity, which will be used to measure the change in state values during the iteration.
2. Iterative Value Update:

• The method uses a while loop that continues until the change in state values (delta) becomes smaller than the specified convergence threshold (theta).
• Within the loop, the delta variable is reset to 0 before each iteration.
3. Value Iteration:

• For each cell in the maze (excluding walls), the method calculates the Q-value (q_max) for all possible actions (up, down, left, right).
• The Q-value is determined based on the immediate reward obtained from the simulate_step method and the discounted value of the next state’s value (gamma * self.state_values[next_state]).
• The action with the maximum Q-value (q_max) is selected, and the corresponding policy probabilities (action_probs) are updated to reflect that this action has the highest probability of being chosen.
4. Updating State Values and Policy Probabilities:

• After calculating the Q-values for all actions in a given state, the state value (self.state_values[row, col]) for that state is updated to the maximum Q-value (q_max) among all actions.
• The policy probabilities (self.policy_probs[row, col]) for that state are updated to have a high probability (1.0) for the action that resulted in the maximum Q-value and 0 probability for all other actions.
5. Convergence Check:

• After updating the state values and policy probabilities for all states in the maze, the method checks whether the maximum change in state values (delta) during this iteration is smaller than the convergence threshold (theta).
• If the condition is met, the loop terminates, and the maze-solving process is considered converged.

The process of value iteration is repeated until the state values converge, and an optimal policy is determined, maximizing the expected cumulative reward for navigating the maze from the initial state to the goal state.

## Simulating the Robot with PyGame

Let’s now simulate our bot by using the Maze data in PyGame and building the walls, placing the treasure and moving the player. Create a new python script called main.py and add this code to it.

import pygame
import numpy as np
from maze import Maze

# Constants
GAME_HEIGHT = 600
GAME_WIDTH = 600
NUMBER_OF_TILES = 25
SCREEN_HEIGHT = 700
SCREEN_WIDTH = 700
TILE_SIZE = GAME_HEIGHT // NUMBER_OF_TILES

# Maze layout
level = [
"XXXXXXXXXXXXXXXXXXXXXXXXX",
"X XXXXXXXX          XXXXX",
"X XXXXXXXX  XXXXXX  XXXXX",
"X      XXX  XXXXXX  XXXXX",
"X      XXX  XXX        PX",
"XXXXXX  XX  XXX        XX",
"XXXXXX  XX  XXXXXX  XXXXX",
"XXXXXX  XX  XXXXXX  XXXXX",
"X  XXX      XXXXXXXXXXXXX",
"X  XXX  XXXXXXXXXXXXXXXXX",
"X         XXXXXXXXXXXXXXX",
"X             XXXXXXXXXXX",
"XXXXXXXXXXX      XXXXX  X",
"XXXXXXXXXXXXXXX  XXXXX  X",
"XXX  XXXXXXXXXX         X",
"XXX                     X",
"XXX         XXXXXXXXXXXXX",
"XXXXXXXXXX  XXXXXXXXXXXXX",
"XXXXXXXXXX              X",
"XX   XXXXX              X",
"XX   XXXXXXXXXXXXX  XXXXX",
"XX    XXXXXXXXXXXX  XXXXX",
"XX        XXXX          X",
"XXXX                    X",
"XXXXXXXXXXXXXXXXXXXXXXXXX",
]

env = Maze(
level,
goal_pos=(23, 20),
MAZE_HEIGHT=GAME_HEIGHT,
MAZE_WIDTH=GAME_WIDTH,
SIZE=NUMBER_OF_TILES,
)
env.reset()
env.solve()

SCREEN_HEIGHT = 700
SCREEN_WIDTH = 700

TILE_SIZE = GAME_HEIGHT // NUMBER_OF_TILES

# Initialize Pygame
pygame.init()

# Create the game window
screen = pygame.display.set_mode((SCREEN_HEIGHT, SCREEN_WIDTH))
pygame.display.set_caption("Maze Solver")  # Set a window title

surface = pygame.Surface((GAME_HEIGHT, GAME_WIDTH))
clock = pygame.time.Clock()
running = True

# Get the initial player and goal positions
treasure_pos = env.goal_pos
player_pos = env.state

def reset_goal():
# Check if the player reached the goal, then reset the goal
if env.state == env.goal_pos:
env.reset()
env.solve()

# Game loop
while running:
x.daemon = True
x.start()

for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False

# Clear the surface
surface.fill((27, 64, 121))

# Draw the walls in the maze
for row in range(len(level)):
for col in range(len(level[row])):
if level[row][col] == "X":
pygame.draw.rect(
surface,
(241, 162, 8),
(col * TILE_SIZE, row * TILE_SIZE, TILE_SIZE, TILE_SIZE),
)

# Draw the player's position
pygame.draw.rect(
surface,
(255, 51, 102),
pygame.Rect(
player_pos * TILE_SIZE,
player_pos * TILE_SIZE,
TILE_SIZE,
TILE_SIZE,
).inflate(-TILE_SIZE / 3, -TILE_SIZE / 3),
)

# Draw the goal position
pygame.draw.rect(
surface,
"green",
pygame.Rect(
env.goal_pos * TILE_SIZE,
env.goal_pos * TILE_SIZE,
TILE_SIZE,
TILE_SIZE,
).inflate(-TILE_SIZE / 3, -TILE_SIZE / 3),
)

# Update the screen
screen.blit(
surface, ((SCREEN_HEIGHT - GAME_HEIGHT) / 2, (SCREEN_WIDTH - GAME_WIDTH) / 2)
)
pygame.display.flip()

# Get the action based on the current policy
action = np.argmax(env.policy_probs[player_pos])

# Move the player based on the action
if (
action == 1
and player_pos > 0
and (player_pos - 1, player_pos) not in env.walls
):
player_pos = (player_pos - 1, player_pos)
env.state = player_pos
elif (
action == 3
and player_pos < NUMBER_OF_TILES - 1
and (player_pos + 1, player_pos) not in env.walls
):
player_pos = (player_pos + 1, player_pos)
env.state = player_pos
elif (
action == 0
and player_pos > 0
and (player_pos, player_pos - 1) not in env.walls
):
player_pos = (player_pos, player_pos - 1)
env.state = player_pos
elif (
action == 2
and player_pos < NUMBER_OF_TILES - 1
and (player_pos, player_pos + 1) not in env.walls
):
player_pos = (player_pos, player_pos + 1)
env.state = player_pos

x.join()

# Control the frame rate of the game
clock.tick(60)

# Quit Pygame when the game loop is exited
pygame.quit()


Here’s a step-by-step explanation of the code:

1. Import libraries and create constants:

• The code imports the required libraries, including Pygame, NumPy, and a custom Maze class.
• Several constants are defined to set up the maze environment, screen dimensions, and tile sizes.
2. Create the maze environment:

• The maze layout is defined using a list of strings called level.
• An instance of the Maze class is created, passing the level and goal position as parameters.
• The env object is then used to reset the maze and find the optimal policy using the solve method.
3. Initialize Pygame:

• Pygame is initialized, and a game window is created with a specified caption.
4. The main game loop:

• The program enters a loop that runs until the running variable becomes False.
• The reset_goal function is called in a separate thread to check if the player has reached the goal and reset the goal if needed.
5. Drawing the maze:

• The maze is drawn on the screen by iterating through the level list and drawing tiles based on wall characters (“X”).
• The player’s position is drawn as a rectangle filled with a specific color (red) and centered in the maze cell.
• The goal position is drawn as a green rectangle with rounded corners.
6. Update the game state and player movement:

• The player’s action is determined based on the current policy (env.policy_probs) at the player’s position. The action with the highest probability is chosen using np.argmax.
• Based on the chosen action, the player’s position is updated if it is a valid move (not hitting walls).
• The player’s position in the env object is updated as well.
7. Frame rate control:

• The game loop is controlled with a frame rate of 60 frames per second using clock.tick(60).
8. Exiting the game:

• The game loop exits when the running variable becomes False, typically triggered by the user closing the game window.
• Pygame is closed with pygame.quit().

That’s all. Now you can run main.py.

Hope this was useful for you guys to understand the basics of reinforcement learning. @2023 by Akshay Ballal

Call
+31-0645791146
Email
arballal95@gmail.com
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