Following Line based on Centroid Detection

This is a simple solution for line following tasks.

GitHub_Link

1. Solution Introduction

Key implementation points:

• Objective: Enable autonomous line following for the robot
• Core concept: Detect and create a "ball" in the line for the robot to follow - this is the Centroid Detection
• Technical implementation: Color-based recognition using OpenCV for image processing
• Special features: Includes obstacle avoidance and other special condition handling

2. Solution Framework and Process

3. Centroid Detection Principle

3.1 Binary Processing

• Image contains only yellow and black colors
• Convert image to binary matrix: black represents "0", yellow represents "1"
• Binary processing facilitates subsequent mathematical calculations

3.2 Image Moment Calculation

In the yellow area, calculate the following:

• Zero-order moment (M00): Represents the total area
• First-order moments (M10, M01): Weighted sums along x and y axes

Calculation formulas:

$$M_{00} = \sum\sum I(x,y)$$

$$M_{10} = \sum\sum x \cdot I(x,y)$$

$$M_{01} = \sum\sum y \cdot I(x,y)$$

3.3 Centroid Coordinate Calculation

Using the calculated moments, we can obtain the centroid coordinates (cx, cy) of the yellow area:

$$cx = \frac{M_{10}}{M_{00}}$$

$$cy = \frac{M_{01}}{M_{00}}$$

4. Motion Control Implementation

4.1 Error Calculation

To ensure accurate line following, calculate the error between the centroid and image center:

$$error = cx - \frac{width}{2}$$

Where:

• cx: detected centroid x-coordinate
• width: image width
• error: deviation from center

4.2 P Controller

Based on practical testing, using only a P controller achieves good control results:

$$angular_speed = -K_p \cdot error$$

Notes:

• Simple P control is used instead of full PID control
• Testing showed P control alone works better in this scenario
• Robot response sensitivity can be adjusted through Kp value

5. Multi-State Decision Implementation

5.1 State Definitions

The system defines three basic states:

• State1 (line): Yellow line detection state
• State2 (obstacle): Obstacle detection state
• State3 (explore): Exploration state

5.2 State Transition Logic

if detect_line():
    # Line detected, follow centroid using P control
    follow_centroid()
elif not (detect_line() or detect_obstacle() or is_exploring):
    # No line detected and not exploring, rotate to search
    rotate_search()
    if search_timeout():
        set_explore_mode(True)
elif not (detect_line() or detect_obstacle()) and is_exploring:
    # Exploration mode, move forward to find target
    move_forward()
else:
    # Obstacle encountered, use left-hand rule for avoidance
    left_wall_follower()

6. System Limitations and Future Work

6.1 Current Limitations

• Color Recognition Limitations:
  • Only supports specific color line detection
  • Challenges with multi-colored lines or actual roads
• Obstacle Avoidance Constraints:
  • May lose original line during avoidance
  • Lacks line memory and relocation capabilities

6.2 Future Improvements

• Introduce deep learning methods to enhance line recognition
• Integrate machine learning algorithms to optimize decision system
• Add reinforcement learning for smarter path planning
• Develop more reliable line detection and following algorithms

This implementation provides a stable line-following system while highlighting areas for future enhancement through advanced AI techniques.