Navigation Functions with Time-varying Destination Manifolds in Star-worlds

Area of Science:

• Robotics and Control Systems
• Differential Geometry
• Computational Geometry

Background:

• Navigation functions are crucial for robot motion planning.
• Existing methods often struggle with dynamic environments and complex obstacle geometries.
• Previous formulations were limited to simpler environments like sphere worlds.

Purpose of the Study:

• To develop navigation functions for star worlds with time-varying destinations.
• To introduce a novel, simplified method for modeling n-dimensional obstacles.
• To enable dynamic target tracking in complex environments.

Main Methods:

• Formal construction of navigation functions using diffeomorphic transformations.
• Development of a new obstacle modeling technique reducing analytical complexity.
• Integration of dynamic target tracking capabilities.

Main Results:

• Successfully extended sphere-world navigation function formulation to star worlds.
• The new obstacle modeling method provides unified expressions for various obstacle types.
• Validated the approach through simulations and experimental results, demonstrating effective dynamic target tracking.

Conclusions:

• The proposed method offers a robust framework for navigation in complex, dynamic environments.
• The simplified obstacle modeling enhances the applicability of navigation functions.
• This work advances the state-of-the-art in robot motion planning and control.