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Project: Particle Filter-Based Robot Localization
November 12, 2023
Abstract
Based on the information from the ”Particle Filter” slides, here is a project idea for students involving the implementation of a Particle Filter for localization and navigation using Python. The project is designed to be straightforward enough for students with some programming experience, yet challenging enough to provide a comprehensive understanding of Particle Filters in a practical
scenario.
1 Project Description
In this project, students will implement a Particle Filter to estimate the position of a robot moving in a two-dimensional space. The robot’s environment will be represented as a grid, where each cell can be either an obstacle or free space. The robot will have access to a simple sensor that provides noisy measurements of its distance to the nearest obstacle in its front, left, right, and back directions.
1.1 Objectives
- Implement a Particle Filter: Students will develop a Particle Filter to estimate the robot’s location based on sensor readings and a map of the environment.
- Simulate Robot Movement: Create a simulation where the robot moves a certain number of steps in the environment, making random turns and moves.
- Sensor Data Simulation: Generate simulated sensor data based on the robot’s actual position and the map.
- Visualization: Implement real-time visualization of the particle cloud and the estimated position of the robot in comparison to its actual position.
1.2 Implementation Approaches
Basic Python Implementation: - Use standard Python libraries (‘numpy‘, ‘matplotlib‘ for visualization). - Represent the map as a 2D array, the robot’s position as coordinates, and particles as objects with position and weight attributes. - Implement particle resampling, motion update, and measurement update functions.
Object-Oriented Approach: - Define classes for the Robot, Particle, and Map. - Implement methods for movement, sensing, and updating in each class. - Use inheritance to showcase different types of particles or robots, if desired.
Advanced Visualization with Pygame: - Utilize the ‘pygame‘ library for more interactive and sophisticated visualization. - Allow real-time interaction, e.g., manually controlling the robot’s movement or altering the environment.
2 Example Template
Import Necessary Libraries
1 import numpy as np
2 import matplotlib . pyplot as plt
3 from matplotlib . animation import FuncAnimation
Define the Robot and Particle Classes
1 class Robot :
2 def __init__ ( self , x , y , orientation ) :
3 self .x = x
4 self .y = y
5 self . orientation = orientation # in degrees
6
7 def move ( self , delta_x , delta_y , delta_orientation ) :
8 self .x += delta_x
9 self .y += delta_y
10 self . orientation = ( self . orientation + delta_orientation ) % 360
11
12 # Simulate sensor reading based on robot ’s position
13 def sense ( self , environment_map ):
14 # Implement sensor reading logic here
15 pass
16
17 class Particle :
18 def __init__ ( self , x , y , orientation , weight ) :
19 self .x = x
20 self .y = y
21 self . orientation = orientation
22 self . weight = weight
23
24 def move ( self , delta_x , delta_y , delta_orientation ) :
25 # Add noise to movement
26 self .x += delta_x + np . random . normal (0 , 0.1)
27 self .y += delta_y + np . random . normal (0 , 0.1)
28 self . orientation = ( self . orientation + delta_orientation ) % 360 + np . random .normal (0 , 5)
29
30 # Update weight based on measurement
31 def update_weight ( self , measurement , robot_measurement ):
32 # Implement weight updating logic here
33 pass
Initialize Robot and Particles
1 robot = Robot (50 , 50 , 0)
2 particles = [ Particle ( np . random . randint (100) , np . random . randint (100) , np . random .
randint (360) , 1.0) for _ in range (1000) ]
Particle Filter Algorithm
1 def particle_filter ( particles , robot , environment_map , move_command ):
2 # Move the robot and particles
3 robot . move (* move_command )
4 for particle in particles :
5 particle . move (* move_command )
6
7 # Update particles ’ weights based on sensor reading
8 robot_measurement = robot . sense ( environment_map )
9 for particle in particles :
10 particle_measurement = particle . sense ( environment_map ) # Particle ’s sense method not shown
11 particle . update_weight ( particle_measurement , robot_measurement )
12
13 # Resampling
14 weights = np . array ([ particle . weight for particle in particles ])
15 weights /= np .sum( weights ) # Normalize weights
16 indices = np . random . choice ( range (len( particles )) , size =len( particles ) , p= weights )
17 resampled_particles = [ particles [i] for i in indices ]
18
19 return resampled_particles
Visualization using Matplotlib
1 def update ( frame_number ):
2 global particles , robot
3 move_command = (1 , 0, 10) # Example move command
4 particles = particle_filter ( particles , robot , environment_map , move_command )
5
6 # Clear current plot
7 plt . cla ()
8
9 # Plot particles
10 xs , ys = zip (*[( particle .x , particle .y) for particle in particles ])
11 plt . scatter (xs , ys , color =’blue ’, s =1)
12
13 # Plot robot
14 plt . scatter ( robot .x , robot .y , color =’red ’, s =10)
15
16 plt . xlim (0 , 100)
17 plt . ylim (0 , 100)
18 plt . title (" Particle Filter Robot Localization ")
19
20 fig = plt . figure ()
21 ani = FuncAnimation ( fig , update , frames =10 , interval =1000)
22 plt . show ()
Note:
- This code provides a basic framework and requires further development to fully simulate the environment, sensor readings, and particle weight updates.
- The move and sense methods for the Robot and Particle classes should be tailored to the specific problem and sensor model.
- The visualization updates the particles and robot position at each step, illustrating the working of the particle filter.
This implementation serves as a foundational guideline, and students are encouraged to build upon it, refining and adding complexity as needed for their specific project requirements.
3 Expected Outcomes
- - Understand the concept and application of Particle Filters in localization.
- - Gain experience in simulating robot movement and sensor readings.
- - Develop skills in probabilistic reasoning and algorithm implementation.
4 Evaluation Criteria
- - Accuracy of the localization (how close the estimated position is to the actual position).
- - Efficiency of the implementation (number of particles used vs. accuracy).
- - Quality of the visualization and ease of understanding the Particle Filter process.
This project provides a balance of theoretical understanding and practical application, making it an excellent exercise for students to grasp the fundamentals of Particle Filters in robotics.