Path Planning Algorithms for Drone Navigation

Finding the optimal path from point A to point B while avoiding obstacles is one of the most fundamental problems in drone autonomy. Think of it like planning a road trip — you need the fastest route that avoids construction, tolls, and traffic jams, but for a drone navigating through 3D airspace.

The Path Planning Problem

Path planning asks a deceptively simple question: "How do I get there safely and efficiently?" The challenge explodes in complexity when you add obstacles, wind, dynamic environments, and the drone's own physical constraints.

Key Definitions

• Configuration Space (C-Space): The set of all possible positions and orientations the drone can occupy
• Free Space: The subset of C-Space without collisions
• Cost Function: A mathematical measure of path quality (distance, energy, time)
• Kinodynamic Planning: Planning that respects the drone's dynamics (velocity, acceleration limits)

Graph-Based Search: A* Algorithm

A* is the gold standard for grid-based path planning. It combines the best of Dijkstra's algorithm (guaranteed shortest path) with greedy best-first search (directional guidance).

How A* Works

The algorithm maintains two lists:

• Open Set: Nodes to be evaluated
• Closed Set: Nodes already evaluated

For each node, A* calculates:

f(n) = g(n) + h(n)

where g(n) is the cost from start, and h(n) is the heuristic estimate to goal.

A* Grid Search Visualization

A* Implementation

Sampling-Based Methods: RRT and RRT*

When the configuration space is high-dimensional (6+ DOF for a drone), grid-based methods become computationally expensive. Rapidly-exploring Random Trees (RRT) solve this by randomly sampling the space.

RRT Tree Growth Visualization

RRT Implementation

Probabilistic Roadmap (PRM)

PRM builds a roadmap of the configuration space by randomly sampling collision-free configurations and connecting nearby ones. It excels in multi-query scenarios where the same environment is used for many planning tasks.

PRM Algorithm Steps

1. Construction Phase: Sample nodes and connect nearby ones
2. Query Phase: Connect start/goal to roadmap, find shortest path

Artificial Potential Fields

Potential fields treat the drone as a particle in an artificial force field. The goal attracts (attractive potential) while obstacles repel (repulsive potential). The drone follows the resultant force gradient.

Potential Field Force Diagram

Potential Fields Implementation

Trajectory Optimization

Trajectory optimization refines a initial path into a smooth, dynamically feasible trajectory. It considers the drone's full dynamics model.

Cost Function Components

The optimization typically minimizes a weighted sum of:

• Path length: Total distance traveled
• Smoothness: Jerk (derivative of acceleration)
• Obstacle clearance: Minimum distance to obstacles
• Dynamic feasibility: Actuator limits, velocity constraints

RRT* — Asymptotically Optimal

RRT* extends RRT with rewiring operations that improve path quality over time. As the number of iterations approaches infinity, RRT* converges to the optimal solution.

Key additions to RRT:

1. Nearby node discovery: Find all nodes within a changing radius
2. Rewiring: Reconnect nodes through lower-cost parents
3. Cost tracking: Maintain cost_to_come for each node

Algorithm Comparison

Hands-On Project: 3D Path Planner

Build a complete 3D path planner for a quadrotor drone:

Key Takeaways

• A* excels in grid environments with guaranteed optimality
• RRT/RRT* scale to high dimensions and handle complex constraints
• PRM is ideal when replanning frequently in the same environment
• Potential fields provide real-time reactive control
• Trajectory optimization produces smooth, dynamically feasible paths
• Always combine global planning with local reactive avoidance for safety