Homology-Class Guided Rapidly-Exploring Random Tree For Belief Space Planning

Area of Science:

• Robotics
• Artificial Intelligence
• Computational Geometry

Background:

• Path planning in obstacle-cluttered environments is a significant challenge in robotics.
• Existing methods often struggle with complex topological spaces and narrow passages.
• Belief space planning is crucial for handling uncertainties in robot localization and state estimation.

Purpose of the Study:

• To develop an efficient homology-guided belief space planning method for obstacle-cluttered environments.
• To enhance trajectory planning by incorporating topological information (homology classes).
• To minimize uncertainties in locally optimal trajectories within identified homology classes.

Main Methods:

• A two-step approach combining homology-guided tree-based exploration and belief space optimization.
• Introduction of a h-signature guided rapidly-exploring random tree (HRRT) algorithm for parallel construction of homology-aware sub-trees.
• Extension to a h-signature guided RRT* algorithm with an inter-homology-class rewire procedure to improve discovery of narrow passages.
• Application of an iLQG-based belief space planning algorithm for local trajectory optimization and uncertainty minimization.

Main Results:

• The proposed HRRT algorithm successfully generates nominal trajectories across different homology classes.
• The extended RRT* algorithm demonstrates increased probability of discovering homology classes, particularly in constrained spaces.
• The iLQG-based planner effectively finds locally optimal trajectories while minimizing state uncertainties within each homology class.
• The integrated method provides efficient and robust path planning in complex, obstacle-rich environments.

Conclusions:

• The developed homology-guided belief space planning method offers an efficient solution for complex robotic navigation tasks.
• Incorporating topological information significantly improves the planner's ability to handle challenging environments and uncertainties.
• The method provides a foundation for more sophisticated autonomous navigation systems in cluttered and uncertain domains.