The document presents an approach for clustering non-convex polygons into hierarchical groups to optimize motion planning for robots or vehicles. The approach involves representing polygons as nested rectangles at different levels, including frames, containers, families, and groups, with the goal of decreasing calculation time during planning. It was tested on real-world data involving over 1000 polygons clustered into hierarchical groups.

1. Non-convex polygons
clustering algorithm
Ekaterinburg 2016
Presenter: Mikhail Vasilenko

2. Introduction
• Use all obstacles
• How to decrease
calculation time?
• How to optimize for quick
motion planning?

3. Approach
• Rectangles (frames)
• Hierarchy
• Different properties
on different levels

4. Frames to Containers
Inclusion? Intersection? One-element container?

5. Containers to Family
Intersection? Chains of containers? One-element family?

6. Families to Groups
Inclusion? Intersection? Close distance? One-element group?

7. Step-by-step solution

8. Parallel approach

9. Summary
• Described algorithm is implemented in C++
• Tested on real-world data
• Algorithm is used in route-planning project
• Integration of parallelism is underway

10. Thanks for your
attention!

11. • To cluster families into groups each of the former is
assigned a rough hull
• All the groups have non-intersecting rough hulls
• Merges groups with distances lower than twice that
value
Last step

12. Test data
• The case depicted had 1031 polygons
• which were clustered into 310 containers
• 201 families
• and 12 families groups.