Mastering Path Planning Algorithm Codes: A Comprehensive Guide

Are you looking to enhance your portfolio with a cutting-edge project or eager to explore how advancements in technology are transforming various fields? You’re in the right place. By the time you finish this article, you’ll have a fully functional code demo for a path planning algorithm that can seamlessly navigate from a starting point to a destination, avoiding obstacles along the way. This article is part of our ongoing series on path planning algorithms, specifically tailored for construction robots. Here, we will delve deep into the mathematical foundations that power these algorithms and translate that math into executable code.

Mathematics is the backbone of technology, especially in artificial intelligence. Once you grasp the underlying math, you’re almost at the finish line—coding is simply the process of converting mathematical concepts into a language that machines can understand. In this guide, we will break down the path planning problem into manageable steps and develop the corresponding coding logic. For those who wish to fully comprehend the code provided at the end of this article, I highly recommend carefully studying the mathematical principles we’ll cover. We will operate under the assumption that the robot moves in a straight line, avoiding any curved paths. To simplify the learning process, we will divide the problem into two distinct stages, ensuring a clearer understanding of each component.

By the end of this tutorial, not only will you have a solid grasp of the math behind path planning algorithms, but you’ll also be equipped with practical coding skills to implement these algorithms in real-world scenarios.

Stage I: Guiding the Bot’s Movement

In this first stage, we’ll focus on navigating the bot from its current position to a target point. Let’s assume the target coordinates are ([x_f, y_f]), and the bot’s current coordinates are ([x_t, y_t]). The initial task is to determine the direction in which the bot should move. This is done by calculating the difference between the target’s and the bot’s current coordinates for both the x and y axes. If the difference is negative, the bot needs to move in the negative direction by decrementing the coordinate value by 1. If the difference is zero, the bot has reached its destination.

Here’s the calculation:

[ x_d = x_f – x_t ; \quad y_d = y_f – y_t ]Based on these differences, the bot has eight potential directions it can move in:

• Case 1: If (x_d > 0) and (y_d > 0), the bot moves diagonally to ([x_t + 1, y_t + 1]).
• Case 2: If (x_d > 0) and (y_d = 0), the bot moves horizontally to ([x_t + 1, y_t]).
• Case 3: If (x_d > 0) and (y_d < 0), the bot moves diagonally downward to ([x_t + 1, y_t – 1]).
• Case 4: If (x_d = 0) and (y_d > 0), the bot moves vertically upward to ([x_t, y_t + 1]).
• Case 5: If (x_d = 0) and (y_d < 0), the bot moves vertically downward to ([x_t, y_t – 1]).
• Case 6: If (x_d < 0) and (y_d > 0), the bot moves diagonally upward to ([x_t – 1, y_t + 1]).
• Case 7: If (x_d < 0) and (y_d = 0), the bot moves horizontally to ([x_t – 1, y_t]).
• Case 8: If (x_d < 0) and (y_d < 0), the bot moves diagonally downward to ([x_t – 1, y_t – 1]).

When both (x_d) and (y_d) are zero, the bot has successfully reached the target point. This process continues until the bot arrives at its destination. But what if the bot encounters an obstacle along its path? How will it navigate around it? Continue reading to discover how the bot handles obstacles during its journey.

Stage II: Navigating Obstacles with Path Planning Algorithms

In this second stage, we’ll explore how the robot navigates around obstacles it encounters while moving towards its target. Suppose the robot is currently positioned at coordinates ([x_t, y_t]). The challenge here is to ensure that the robot can find a clear path to its destination without getting stuck when an obstacle blocks the direct route.

Step 1: Checking Forward Motion

The first step for the robot is to check if it can move forward along the x-axis. Specifically, it evaluates whether the point ([x_t + 1, y_t]) is free of obstacles. If this point is unobstructed, the robot advances to this new coordinate. Once at the new position, the robot reassesses its ability to continue moving directly towards the target using the method outlined in Stage I. If the path is clear, the robot proceeds; if not, the robot begins to trace the boundary of the obstacle.

Step 2: Tracing the Obstacle Boundary

When the robot encounters an obstacle at ([x_t + 1, y_t]), it shifts strategies. The robot now needs to move along the boundary of the obstacle to find a clear path. As it moves along each point on the boundary, the robot continually checks whether a direct route towards the target becomes feasible again using the same directional checks from Stage I. Once a clear path is identified, the robot disengages from the obstacle and resumes its journey towards the target.

Step 3: Exploring Alternative Axes

If the forward motion along ([x_t + 1, y_t]) is blocked, the robot explores alternative directions:

• Option 1: The robot checks the vertical axis by evaluating the point ([x_t, y_t + 1]). If this point is free of obstacles, the robot moves there and repeats the process of checking for a clear path to the target. If an obstacle is present, the robot will start tracing the boundary of the obstacle from this new point, just as it did along the x-axis.
• Option 2: If both ([x_t + 1, y_t]) and ([x_t, y_t + 1]) are blocked by obstacles, the robot then evaluates the point behind it at ([x_t – 1, y_t]). The same boundary-tracing procedure is applied if this point is free or blocked.
• Option 3: If all previous checks fail and obstacles surround the robot on the three sides mentioned, the robot finally checks the downward motion towards ([x_t, y_t – 1]). If this point is clear, the robot moves and continues to check if it can re-engage with the target direction. If not, the boundary of the obstacle is traced as before.

Optimizing Path Planning: Beyond Anti-Clockwise Navigation

In the previous section, we observed that the robot follows an anti-clockwise path around obstacles. While this approach ensures the robot reaches its target without collisions, it’s not the most efficient route. The robot’s fixed anti-clockwise direction can lead to longer paths than necessary. Although this logic can be optimized to find shorter routes, we’ll leave that discussion for a future article in this series. For now, let’s dive into the most exciting part—coding the path planning algorithm and getting hands-on with the implementation.

Python Implementation of Path Planning Algorithm

Below is the Python code to simulate the path planning algorithm we discussed. This code will guide the robot from a starting point to a target, navigating around obstacles using the logic we’ve developed. Open your favorite Python environment or Google Colab to run the code and see the algorithm in action.

# Importing necessary libraries
import numpy as np
import matplotlib.pyplot as plt

# Flag to show animation
show_animation = True

# Defining the Path Planning Algorithm class
class PathPlanningAlgorithm:
    def __init__(self, start_x, start_y, target_x, target_y, obstacle_x, obstacle_y):
        self.target_x = target_x  # Target x-coordinate
        self.target_y = target_y  # Target y-coordinate
        self.obstacle_x = obstacle_x  # List of obstacle x-coordinates
        self.obstacle_y = obstacle_y  # List of obstacle y-coordinates
        self.start_x = [start_x]  # Initial x-coordinate of the robot
        self.start_y = [start_y]  # Initial y-coordinate of the robot
        self.boundary_x = []  # x-coordinates along the obstacle boundary
        self.boundary_y = []  # y-coordinates along the obstacle boundary
        
        # Marking the obstacle boundary
        for obs_x, obs_y in zip(obstacle_x, obstacle_y):
            for x, y in zip([1, 0, -1, -1, -1, 0, 1, 1], 
                            [1, 1, 1, 0, -1, -1, -1, 0]):  # Checking all 8 possible directions around each obstacle
                cord_x, cord_y = obs_x + x, obs_y + y
                flag = True
                for _obs_x, _obs_y in zip(obstacle_x, obstacle_y):
                    if cord_x == _obs_x and cord_y == _obs_y:
                        flag = False
                        break
                if flag:
                    self.boundary_x.append(cord_x)
                    self.boundary_y.append(cord_y)
    
    # Algorithm to move the robot towards the target
    def algorithm(self):
        # Loop until the robot reaches the target
        while not (self.start_x[-1] == self.target_x and self.start_y[-1] == self.target_y):
            x_current = self.start_x[-1]
            y_current = self.start_y[-1]
            x_diff = self.target_x - x_current
            y_diff = self.target_y - y_current
            
            # Determine the next move based on the direction towards the target
            if x_diff > 0:
                x_next = x_current + 1
            elif x_diff < 0:
                x_next = x_current - 1
            else:
                x_next = x_current

            if y_diff > 0:
                y_next = y_current + 1
            elif y_diff < 0:
                y_next = y_current - 1
            else:
                y_next = y_current
            
            # Check if the next point is an obstacle
            if [x_next, y_next] in list(zip(self.obstacle_x, self.obstacle_y)):
                x_next, y_next = self.avoid_obstacle(x_current, y_current)
            
            # Move the robot to the next point
            self.start_x.append(x_next)
            self.start_y.append(y_next)
            
            if show_animation:
                self.plot_current_position()
    
    # Method to avoid obstacles by following their boundary
    def avoid_obstacle(self, x_current, y_current):
        for x_boundary, y_boundary in zip(self.boundary_x, self.boundary_y):
            if abs(x_boundary - x_current) <= 1 and abs(y_boundary - y_current) <= 1:
                return x_boundary, y_boundary
        return x_current, y_current
    
    # Method to plot the robot's current position
    def plot_current_position(self):
        plt.plot(self.start_x, self.start_y, '-og')
        plt.plot(self.target_x, self.target_y, 'xr')
        plt.plot(self.obstacle_x, self.obstacle_y, 'sk')
        plt.grid(True)
        plt.pause(0.1)

# Main function to run the path planning algorithm
def main():
    # Define start and target positions
    start_x, start_y = 10, 10
    target_x, target_y = 60, 20
    
    # Define obstacles
    obstacles_x = []
    obstacles_y = []
    
    # Hardcoding obstacle locations
    for i in range(30, 50):
        for j in range(20, 40):
            obstacles_x.append(i)
            obstacles_y.append(j)

    for i in range(60, 100):
        for j in range(40, 80):
            obstacles_x.append(i)
            obstacles_y.append(j)

    for i in range(120, 140):
        for j in range(80, 100):
            obstacles_x.append(i)
            obstacles_y.append(j)

    for i in range(0, 20):
        for j in range(60, 100):
            obstacles_x.append(i)
            obstacles_y.append(j)

    for i in range(20, 40):
        for j in range(80, 100):
            obstacles_x.append(i)
            obstacles_y.append(j)

    for i in range(125, 150):
        for j in range(40, 60):
            obstacles_x.append(i)
            obstacles_y.append(j)

    # Create an instance of the PathPlanningAlgorithm class
    my_bot = PathPlanningAlgorithm(start_x, start_y, target_x, target_y, obstacles_x, obstacles_y)
    my_bot.algorithm()

if __name__ == '__main__':
    main()

Code Detailed Explaination:

1. Importing Libraries

import numpy as np
import matplotlib.pyplot as plt

• NumPy (np): This powerful library is typically used for numerical computations, although it’s not directly used in this particular code snippet.
• Matplotlib (plt): A plotting library used to visualize the robot’s path, obstacles, and the target location on a 2D grid.

2. Global Variables

show_animation = True

• This variable controls whether the robot’s movement is displayed as an animation. When set to True, each step the robot takes will be plotted.

3. Path Planning Algorithm Class (PathPlanningAlgorithm)

• This class is designed to manage the robot’s movement towards a target while avoiding obstacles.

4. Constructor Method (__init__)

def __init__(self, start_x, start_y, target_x, target_y, obstacle_x, obstacle_y):

Parameters:

• start_x, start_y: The initial coordinates where the robot starts.
• target_x, target_y: The coordinates of the target the robot aims to reach.
• obstacle_x, obstacle_y: Lists containing the x and y coordinates of obstacles on the grid.

Attributes:

• self.start_x and self.start_y: Lists that will store the path of the robot. Initially, they contain the starting coordinates.
• self.boundary_x and self.boundary_y: Lists that store the boundary coordinates around the obstacles.
• Marking the Obstacle Boundary: The code checks 8 possible directions (up, down, left, right, and the four diagonals) around each obstacle point to mark its boundary. This helps in identifying the points the robot should avoid or move along when an obstacle is encountered.

5. Path Planning Algorithm (algorithm)

def algorithm(self):

Core Logic: The robot continues to move towards the target by calculating the difference between its current position and the target.

• Direction Decision: The robot decides to move one step closer to the target in either the x or y direction based on where the target is located relative to its current position.

Obstacle Handling: Before moving, the robot checks if the next position is an obstacle. If so, it triggers the avoid_obstacle() method to determine a safe path.

Animation: If show_animation is True, the current state of the robot’s path is plotted, providing a visual representation of its movement towards the target.

6. Obstacle Avoidance (avoid_obstacle)

def avoid_obstacle(self, x_current, y_current):

Purpose: This method helps the robot avoid collisions by moving along the boundary of an obstacle when it encounters one.

Boundary Check: The method looks for a boundary point around the obstacle that is closest to the robot’s current position. This allows the robot to “slide” around the obstacle rather than colliding with it.

7. Visualization (plot_current_position)

def plot_current_position(self):

Plotting: The robot’s current path is plotted in green, the target is marked with a red cross, and obstacles are shown as black squares.

Animation: The plt.pause(0.1) command introduces a brief pause in the animation, making the movement visible.

8. Main Function (main)

def main():

Setup:

• Start and Target Positions: Sets the initial and target positions of the robot.
• Obstacle Creation: Hardcodes the locations of obstacles in the grid, creating several rectangular blocks of obstacles.

Algorithm Execution:

• An instance of the PathPlanningAlgorithm class is created with the start, target, and obstacle positions as input.
• The algorithm() method is then called to initiate the path planning process.

9. Execution Block

Purpose:

• This ensures that the main() function is executed only when the script is run directly, not when it’s imported as a module in another script.

How It Works Overall

• Initialization: The robot starts at a specified position and needs to reach a target while avoiding obstacles.
• Path Planning: The robot moves step by step towards the target. It checks the direction and moves in that direction unless an obstacle is encountered.
• Obstacle Avoidance: If the robot detects that its next move will land on an obstacle, it calculates a way to move around the obstacle by sticking to its boundary.
• Visualization: Throughout the process, the robot’s movements are plotted on a grid, showing the path taken, obstacles, and the target.

This code essentially demonstrates a basic grid-based path planning algorithm with obstacle avoidance, which could be a starting point for more complex path planning strategies like A* or Dijkstra’s algorithm.

Running the Code: What’s Next?

Once you run the code above in your Python environment or Google Colab, you will see the robot successfully navigating towards the target while avoiding obstacles. The movement is visualized in a simple 2D plot where the green line represents the robot’s path, red marks the target, and black squares denote obstacles.

Enhancing the Algorithm with Machine Learning

The current implementation relies on hardcoded obstacle locations, which is practical for a controlled environment but not adaptable to dynamic, real-world scenarios. To make the algorithm more robust, we can integrate machine learning models to predict obstacles in real-time using computer vision techniques.For example, we could use object detection algorithms like YOLO (You Only Look Once), Faster R-CNN, or Mask R-CNN to identify obstacles in the environment through a camera feed. By integrating these models into our path planning algorithm, the robot could dynamically adjust its path based on real-time obstacle detection, making the system far more adaptable and efficient.

Conclusion

In this article, we’ve delved into the intricacies of path planning algorithms, focusing on both the theoretical and practical aspects. We began by understanding the fundamental concepts of movement in a 2D space, emphasizing how mathematical logic drives the decision-making process of a robot navigating towards a target while avoiding obstacles. By breaking down the problem into manageable stages, we developed a simple yet effective path planning algorithm, which was then translated into Python code.

The implementation we explored provides a clear demonstration of how a robot can autonomously navigate a grid, avoiding predefined obstacles and making progress towards a target. While the approach we’ve taken—moving in an anti-clockwise direction around obstacles—ensures collision-free navigation, it’s important to recognize that this isn’t always the most efficient path. This highlights the potential for further optimization and enhancement, which we’ll explore in future articles.

Moreover, we touched upon the exciting possibility of integrating machine learning models into our path planning algorithm. By leveraging object detection techniques, we can move beyond static obstacle detection and create a more dynamic, real-world applicable navigation system. This would allow robots to adapt to changing environments in real-time, opening up new avenues for innovation in robotics and autonomous systems.

As we conclude this segment of our series on path planning algorithms for construction robots, it’s clear that while we’ve covered a lot of ground, there’s still much more to explore. The intersection of mathematics, coding, and machine learning in path planning is vast, and the journey to mastering it is just beginning. Stay tuned as we continue to refine and expand upon these concepts, bringing you closer to building sophisticated, intelligent robotic systems.

Stay tuned for future articles in this series, where we’ll dive deeper into optimizing the path planning algorithm and integrating machine learning models to create a more advanced and intelligent navigation system.