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Presented by Mohammed Irfan Rafiq Using Slides from Xiaoshan Pan(2003)

Interactive Navigation in Complex Environments Using Path Planning Salomon et al.(2003) University of North Carolina. Presented by Mohammed Irfan Rafiq Using Slides from Xiaoshan Pan(2003). Motivations.

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Presented by Mohammed Irfan Rafiq Using Slides from Xiaoshan Pan(2003)

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  1. Interactive Navigation in Complex Environments Using Path PlanningSalomon et al.(2003) University of North Carolina Presented by Mohammed Irfan Rafiq Using Slides from Xiaoshan Pan(2003)

  2. Motivations • The design and evaluation of complex engineering products requires interactive navigation using appropriate interaction modes. • Navigating in a driving mode with an unconstrained free-flying camera gives confusing views of geometry. • Earlier work on navigation with constrained camera motion are limited to be local navigation modes or in small environments.

  3. Problem & Approach • How to automatically plan a motion path to assist 3D interactive navigation with a constrained camera in a complex environment? • The approach is to combine robot motion planning techniques and driving interaction methods. • Good application for a multi-query and visibility based roadmap • Inputs • model geometry and dimensions of the avatar

  4. Constraints • Constrained avatar motion • Translation along a surface • Rotation about an axis orthogonal to the surface • Motion must lie on a walkable surface such as a floor or stairway • Can not walk up or down unreasonably steep slopes

  5. Content • 2 modes of navigation: • Global • Pre-compute a global roadmap • Graph search (inigoal) in real-time • Display motion • Local • User-steered exploration

  6. Runtime algorithm Basic Idea Preprocessing phase

  7. Rc • Connectors • - Rc > Rg Guards & Connectors (C-space) • Reachability • -neighborhood around • a config that can be • reached using a local planner • Guards • - guards can’t see each other Rg

  8. 1. Pick a random config. c 2. Can c be a Connector? See any Guards in Rc? - Yes  then connect, goto while (else goto 3) 3. Can c be a Guard? See any Guards in Rg? - no! c becomes a Guard, connect to connectors (if any), goto while - yes  reject c, goto while c c c Algorithm (build_roadmap) While (map_coverage < P_cover), do // map_coverage = guards_reachable/entire_space Return roadmap Be a Connector Be a Guard Be rejected Connector Connector Connector Guard Guard Guard Guard Guard Guard

  9. Roadmap – Connecting Nodes • Is c1 in Reach(c2,r)? • check if distance between the two locations is less than or equal to r • use the local planner to test if c1 is reachable from c2

  10. Roadmap – Pruning Connectors • To remove redundant connectors and keep connectors with highest number of linked guards • If an existing reachable connecter join the same set of guards as the new connector, then discard the new connector • If an existing reachable connector only joins a subset of guards that is reachable from the new connector, then add the new connector and remove the existing connector

  11. ini goal Search for a path: init  goal • Initial position (Rc radius) • Goal position • Graph search…

  12. Display Motion: Smooth Path • Walk along the path • Smoothing path (cutting redundant corners while walking) ini goal

  13. Shooting rays Random Rays Gravity Roadmap - Sampling

  14. Gravity Roadmap - Sampling • Shooting rays • Walkable surface • Construct roadmap ө ө

  15. Roadmap - Analysis • Roadmap size • Number of guards is limited by mutual unreachability, number of connectors is minimized by connector pruning • In Practice, less than one connector for every guard • Estimated coverage • Maintain a tally of the number of samples that are reachable from at least one guard • The ratio of reachable samples to total samples is a lower bound on the ratio Nreachable/N • As N grows large, Nreachable/N converges to Areachable/A

  16. User-steered exploration (local walk) • User has control • A directional vector • Robot do not penetrate objects • Robot always stays on a walkable surface • In free space • Surface within a tolerance angle • Steps ok, cliffs NO!!

  17. Local Walk Algorithm • Follow the directional vector, if • - Goal is reached, stop • - Collision, project along obstacle edge • - New surface, step up/down (not a cliff!) • - Edge, step up/down or project along the edge

  18. Local Walk • collisions below a certain height with non -walkable surfaces are permitted so that the avatar is able to step over low obstacles • when redirected the avatar is not allowed to move in a direction that makes an angle > 90 with the original direction

  19. Results

  20. Limitations • the avatar follows the path in linear segments, hence the paths may look unnatural • the avatar cannot bend to look under objects • does not address the narrow passage problem • the precomputation process is time consuming • would require recomputing the graph for a dynamic environment

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