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Planning Short Paths with Clearance using Explicit Corridors

This paper presents a fast and flexible 2D path planning system designed for real-time navigation of thousands of characters in environments with local hazards. By leveraging explicit corridor maps, which utilize medial axes and annotated event points, this approach computes clear and smooth paths while maintaining safe distances from obstacles and other characters. The algorithms run in linear time and are capable of generating natural movements, making them suitable for dynamic simulations in gaming and robotics.

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Planning Short Paths with Clearance using Explicit Corridors

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  1. Planning Short Paths with Clearance using Explicit Corridors Roland Geraerts ICRA 2010

  2. Requirements • Fast and flexible 2D path planner • Real-time planning for thousands of characters • Dealing with local hazards • Global path • Natural paths • Smooth • Short • Keeps some distance toobstacles • Avoids other characters • … Titan Quest: Immortal throne

  3. Path planning system • Build a data structure • Explicit Corridor Map: Medial Axis + annotated event points • Perform query • Compute corridor • Compute Indicative Route • Compute path Explicit Corridor Map Corridor Indicative Route Path

  4. Data structure: Explicit Corridor Map • Basis: Medial Axis • Plus: annotated event points on the edges • Placed at curve change on the edges • Occurs at crossing between site normal and edge • Annotation: its two closest points on the sites • Equals: planar subdivision • Memory footprint: linear in the number of vertices • There is no need for storing pixels GPU computation Perspective view (Z-buffer) Top view (Frame buffer)

  5. Query phase • Perform query (on-line) • Find the retraction of the start and goal • Connect the start and goal to the Explicit Corridor Map • Compute the shortest backbone path (using A*) Explicit Corridor Map Query Explicit Corridorwith backbone path

  6. Explicit Corridors: Obtaining clearance • Minimum clearance in Explicit Corridors • Move each closest point cp toward its center point c • The displacement equals the desired clearance clmin • Insert event point(s) if clmin > distance(c, cp) c cp Explicit Corridor Shrunk corridors Shrinking a corridor

  7. Explicit Corridors: Shortest paths • Computing the shortest path • Construct a triangulation • At most 2n+2 triangles • If the start/goal is not included, add a triangle • Compute the shortest path • Funnel algorithm [Guibas et al. 1987] ri+1 li+1 g ri li s Triangulation Shortest path Explicit Corridor

  8. Explicit Corridors: Shortest paths • Computing the shortest minimum clearance path • Shrink the corridor • Construction time: linear in the number of event points • Compute the shortest path • Adjust Funnel algorithm to deal with circular arcs • Construction time: linear in the number of event points Triangulation Shortest path Explicit Corridor

  9. Query phase • Compute a smooth path: Indicative Route Method • Compute the shortest minimum-clearance path • Define the attraction force • Pulls the character toward the goal • Define the boundary force • Keeps the character inside the corridor • Define other forces • Leads to other behaviors • Time-integrate the forces • Yields a smooth (C1-continous) path

  10. Query phase • Query phase • Using other forces Crowd simulation Smooth path Short path Obstacle avoidance Coherent groups Path variation Camera path Stealth-based path planning

  11. Explicit Corridor Map: Experiments • Performance • Setup • NVIDIA GeForce 8800 GTX graphics card • Intel Core2 Quad CPU 2.4 GHz, 1 CPU used • Experiments • City: 500x500 meter, 4000x4000 pixels, 548 convex polygons

  12. Explicit Corridor Map: Experiments • Performance • Setup • NVIDIA GeForce 8800 GTX graphics card • Intel Core2 Quad CPU 2.4 GHz, 1 CPU used • Experiments • City: 500x500 meter, 4000x4000 pixels, 548 convex polygons time: 0.3s

  13. Query phase: Experiments • Performance • Setup • Intel Core2 Quad CPU 2.4 GHz, 1 CPU • Experiments • City: 500x500 meter, 1.000 random queries • Results (average query time)

  14. Query phase: Experiments • Performance • Setup • Intel Core2 Quad CPU 2.4 GHz, 1 CPU • Experiments • City: 500x500 meter, 1 query • Results (query time) • 2.8 ms ECM (0.3s) Explicit corridor Shrunk corridor Triangulation Shortest path Smooth path

  15. Conclusions • Advantages • Flexible path planner generates natural paths • Computation of smooth, short minimum clearance paths • The algorithms run in linear time and are fast in practice • The algorithms are simple • Open problems • Handle large dynamic changes efficiently • Handle 2.5D/3D environments

  16. Questions • Contact • Roland Geraerts (roland@cs.uu.nl) • Home page: www.cs.uu.nl/~roland • Conference: www.motioningames.org

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