Topological Path Planning in GPS Trajectory Data.

Area of Science:

• Computational Topology
• Robotics and Automation
• Geographic Information Systems

Background:

• Computing topologically distinct paths is crucial for navigation and planning.
• Existing methods struggle with complex spaces and defining path inequivalence rigorously.
• Homotopy provides a robust framework for classifying path differences.

Purpose of the Study:

• To develop a novel computational method for identifying a set of topologically inequivalent paths between two points.
• To leverage concepts of homology and homotopy for path computation.
• To demonstrate the method's efficacy in real-world scenarios like street networks.

Main Methods:

• Computing a basis for the group of homology inequivalent loops in the sampled space.
• Identifying a specific loop element passing through the start and end points.
• Generating the set of homotopy inequivalent paths via group action.

Main Results:

• The proposed method successfully computes a set of homotopy inequivalent paths.
• Demonstrated accuracy in various spaces, including GPS trajectory data on street networks.
• The method provides a robust way to differentiate paths based on topological properties.

Conclusions:

• The novel approach offers an accurate and robust solution for computing topologically inequivalent paths.
• Applications include path planning, coverage planning, and analysis of trajectory data.
• This work advances computational topology applications in robotics and GIS.