Hierarchical Quantum Pathfinding Algorithm (HQP)

Overview

The Hierarchical Quantum Pathfinding Algorithm (HQP) is an advanced pathfinding solution that combines hierarchical spatial decomposition with quantum-inspired parallel path exploration. It's designed for efficient navigation in large, complex environments with dynamic obstacles.

Key Features

• Hierarchical Region-Based Navigation: Divides the environment into manageable regions for efficient pathfinding
• Quantum Path Exploration: Generates multiple potential paths in parallel
• Path Caching: Stores previously calculated paths for quick retrieval
• Dynamic Obstacle Handling: Adapts to obstacles that appear or disappear during runtime
• Points Avoidance: Supports designating specific areas to avoid during pathfinding

Algorithm Components

Region Management

• Automatically divides the environment into regions of configurable size
• Identifies connections between adjacent regions
• Maps points to their containing regions

Pathfinding Approaches

• Local A*: Finds paths within a single region
• Region-Level Search: Plans high-level paths across regions
• Full A*: Performs traditional A* search when necessary

Quantum Path Exploration

• Generates multiple candidate paths in parallel
• Creates path variations to explore diverse solutions
• Collapses multiple paths to select the optimal solution based on length and obstacle avoidance

Cache System

• Caches paths for quick retrieval in similar scenarios
• Selectively invalidates cache entries when obstacles change

Usage Example

# Create a grid-based environment (0 = open space, 1 = wall)
maze = [
    [0, 0, 0, 0, 1, 0, 0, 0],
    [0, 1, 1, 0, 1, 0, 1, 0],
    [0, 0, 0, 0, 0, 0, 1, 0],
    [0, 1, 1, 1, 1, 0, 1, 0],
    [0, 0, 0, 0, 0, 0, 0, 0]
]

# Initialize the HQP pathfinder
pathfinder = hqp(maze, region_size=2, num_parallel_paths=3)

# Find a path from start to goal
start = (0, 0)
goal = (7, 4)
path = pathfinder.find_path(start, goal)

# Update dynamic obstacles
pathfinder.update_dynamic_obstacles([(3, 2), (4, 2)])

# Set points to avoid
pathfinder.set_points_to_avoid([(5, 3), (5, 2)])