Dependency Tracking for Fast Marching Dynamic Replanning for - - PowerPoint PPT Presentation

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control

Dependency Tracking for Fast Marching — Dynamic Replanning for Ground Vehicles

Roland Philippsen

Robotics and AI Lab, Stanford, USA

Fast Marching Method Tutorial, IROS 2008

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Overview Path Planning Approaches Costmap Planning with E∗

Motivation

Mobile Tour-Guides example: Robox, Expo.02 Autonomous Cars example: SmartTer, Elrob 2006

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Overview Path Planning Approaches Costmap Planning with E∗

Talk Outline

1 Path Planning for Mobile Robots 2 Wavefront Dependency Tracking 3 Interweaving Mapping, Planning, and Control

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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 but avoid this: the approach of E∗ cost attached to nodes (as opposed to edges) graph semantics, user-defined interpolation usually though: 1st order upwind propagation on a grid

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Overview Path Planning Approaches Costmap Planning with E∗

E∗ in Context (Related Approaches)

information reuse D∗ [Stentz, 1995] user configurable E∗ [Philippsen, 2004] multi-resolution Field-D∗ [Fergusson, 2006]

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning

Navigation Functions from Wavefront Propagation

variable speed crossing-time propagation speed depends

• nly on position

⇒ Fast Marching Method!

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning

Using the Level Set Method for Interpolation

= but ≡

solve ∂Φ ∂t +F|∇Φ| = 0 where            Γ(t) : closed (N − 1)D surface Φ( x, t) : RN → R t0 : Φ( x, t = 0) = ±d( x, Γ(t = 0)) ⇒ Γ(t) = { x | Φ( x, t) = 0}

[Sethian, 1996]

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Wavefronts for Navigation Cost Maps as Speed Maps Dependency Tracking for Replanning

Cost Maps as Speed Maps

costmap ≡ propagation speed ∂Φ ∂t +F|∇Φ| = 0

• bstacle:

F = 0 free: F = 1 example with C projection

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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

• verall responsiveness, reuse information

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook

Example: Robox, Expo.02

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control 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

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook

Illustration

diff drive scenario autonomous car scenario

Roland Philippsen Replanning for FFM — IROS 2008

Path Planning for Mobile Robots Wavefront Dependency Tracking Interweaving Mapping, Planning, and Control Navigational Components Planning, Mapping, Control on Growable Costmaps Conclusion and Outlook

Conclusion and Outlook

costmap planning allows to concisely express complex

• ptimization 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? http://estar.sourceforge.net/

Roland Philippsen Replanning for FFM — IROS 2008