Finding the Best Point: Disparity Selection

When environments get more complex — with tighter spaces and more obstacles — basic “farthest point” methods can become less reliable. Disparity methods offer a smarter way to steer through tight environments.

🛠 What is a Disparity?

• A disparity is a large jump between two consecutive LiDAR distance readings.

• It typically happens at the edge of an obstacle.

For example:

Angle	Distance (m)
10°	2.5
11°	2.5
12°	0.5

A big drop from 2.5m to 0.5m → indicates an obstacle edge!

🧠 Why Use Disparity?

Problem	How Disparity Solves It
Farthest point may not be safest	Disparity finds edges and aims between them
Can’t detect narrow gaps	Disparity highlights tight spaces
Unclear safest direction	Disparity clarifies open regions

✅ Disparity methods naturally guide the car between obstacles, rather than just toward distant points.

🛠 How It Works

Step 1: Focus on the Largest Gap

After preprocessing LiDAR data and masking close obstacles, select the largest gap.

Step 2: Detect Disparities

Compare each consecutive range. If the distance changes by more than a disparity threshold, mark it.

Step 3: Find the Open Region

Use the detected disparities to find spaces between obstacles.

Step 4: Aim for the Middle

Pick a point halfway between two disparities.

✏️ Python Example (Disparity-Based Selection)

def find_best_point_disparity(self, ranges, start_idx, end_idx, disparity_threshold=0.5):
    """
    Find the best point within a gap using disparity detection.

    Disparities (large jumps in distance) indicate obstacle edges.
    We aim for the middle of the free space between disparities.

    Args:
        ranges (np.array): Processed LiDAR data
        start_idx (int): Starting index of the gap
        end_idx (int): Ending index of the gap
        disparity_threshold (float): Minimum distance change to count as disparity

    Returns:
        best_point_idx (int): Index of the selected steering point
    """
    gap_ranges = ranges[start_idx:end_idx+1]

    disparities = []
    for i in range(len(gap_ranges) - 1):
        if abs(gap_ranges[i] - gap_ranges[i+1]) > disparity_threshold:
            disparities.append(i)

    if len(disparities) >= 2:
        # Aim for the middle between the first two disparities
        middle_idx_in_gap = (disparities[0] + disparities[1]) // 2
        best_point_idx = start_idx + middle_idx_in_gap
    else:
        # Fallback to farthest point if no clear disparities
        best_point_idx = self.find_best_point(ranges, start_idx, end_idx)

    return best_point_idx

✅ This logic gracefully falls back to farthest point if no disparities are found.

📊 Visual Diagram

Obstacle Left     Free Space       Obstacle Right
       |               |               |
       v               v               v
[0.4] [0.5] [2.5] [2.5] [2.5] [0.6] [0.5]

Big disparity -->    Free space    <-- Big disparity

• Disparity detection finds obstacle edges.

• We aim toward the center of the safe free space.

⚡ Advantages Over Farthest Point

Farthest Point	Disparity Method
May steer near obstacles	Steers between obstacles
Works best in wide-open areas	Works better in tight environments
Can be fooled by noise	Disparity uses clear jumps

🚀 Summary

• Detect sudden changes (disparities) in LiDAR data.

• Use disparities to find open spaces.

• Aim between obstacles for safer, smarter navigation.

• Improves performance in cluttered or narrow environments.

✅ Disparity-based selection is more robust in complex, tight environments!