Dependency Tracking for Fast Marching. Dynamic Replanning for Ground Vehicles

Transcription

1 Dependency Tracking for Fast Marching Dynamic Replanning for Ground Vehicles Roland Philippsen Robotics and AI Lab, Stanford, USA Fast Marching Method Tutorial, IROS 2008

2 Overview Path Planning Approaches Costmap Planning with E Motivation Mobile Tour-Guides example: Robox, Expo.02 Autonomous Cars example: SmartTer, Elrob 2006

3 Overview Path Planning Approaches Costmap Planning with E Talk Outline 1 Path Planning for Mobile Robots 2 3

4 Overview Path Planning Approaches Costmap Planning with E Classes of Path Planning Approaches road maps: extract network then search graph cell decomposition: compute sub-regions then search graph potential fields: attraction to goal, repulsion from obstacles navigation functions: potentials without local minima randomized search: approximate rapid roadmaps

5 Overview Path Planning Approaches Costmap Planning with E Overview of Costmap Planning general idea steps incur cost such as energy use or collision risk paths accumulate cost find the optimum path the approach of E but avoid this: cost attached to nodes (as opposed to edges) graph semantics, user-defined interpolation usually though: 1 st order upwind propagation on a grid

6 Overview Path Planning Approaches Costmap Planning with E E in Context (Related Approaches) user configurable E [Philippsen, 2004] information reuse D [Stentz, 1995] multi-resolution Field-D [Fergusson, 2006]

7 Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning Navigation Functions from Wavefront Propagation variable speed crossing-time propagation speed depends only on position Fast Marching Method!

8 Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning Using the Level Set Method for Interpolation but Γ(t) : closed (N 1)D surface solve Φ Φ( x, t) : R N R +F Φ = 0 where t t 0 : Φ( x, t = 0) = ±d( x, Γ(t = 0)) Γ(t) = { x Φ( x, t) = 0} [Sethian, 1996]

9 Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning Cost Maps as Speed Maps costmap propagation speed { Φ obstacle: F = 0 +F Φ = 0 t free: F = 1 example with C projection

10 Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning Dependency Tracking for Replanning upwind tracking cost increase (speed decrease): re-propagate to downwind neighbors cost decrease: re-propagate to all neighbors

11 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Scopes of Space and Time information transitions local global W C realtime non-rt

12 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Requirements for Wheeled Robots integrate planning with (at least) mapping and control building a costmap W or C? projected C? representation grid, graph, multiresolution? bounds? grow on demand map changes during lifetime exploration changing environment change in localization controllers require smooth and always available paths overall responsiveness, reuse information

13 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Example: Robox, Expo.02

14 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Growable E System Architecture separate the costmap from the planning space cost modification buffer possibly different domain descriptions well-defined places for preferences and heuristics manage shared access to costmap navigation function planned path

15 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Illustration diff drive scenario autonomous car scenario

16 Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook Conclusion and Outlook costmap planning allows to concisely express complex optimization criteria handle non-binary and incomplete world models integrating replanning means addressing multiple scopes of information buffering changes to the world model pushing the E concept... generlized interpolation kernel? kinodynamic planning non-uniforms grids, lattices, triangulated surfaces... replanning for general case LSM?