Planning.

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Presentation transcript:

Planning

Cognition Where am I going ? How do I get there ? (global) Path Planning (local) Obstacle Avoidance

Configuration Space

Path Planning Overview Assumptions There exists a good enough map of the environment for navigation Topological map: graph-like structure (nodes/edges) Grid map Representation of environments Road map Identify a set of routes within the free space Cell decomposition Discriminate between free and occupied cells Potential field Impose a mathematical function over the space

Visibility Graph

Visibility Graph V-graph path Shortest path Simple implementation Number of nodes and edges increase with the number of obstacle polygons Take the robot as close as possible to obstacle

Voronoi Diagram Not shortest path Safe path

Voronoi Diagram

Cell-Decomposition Exact cell decomposition Number and size of cells depends on the density and complexity of objects Cell Connectivity graph

Cell-Decomposition Approximate cell decomposition Grid-based representation Low computational complexity of path planning algorithm (ex) wave-front algorithm Large memory & loss of object shape Adaptive cell decomposition

Path Planning Algorithm for Road-Map & Cell Decomposition

Path Planning: Wavefront Expansion

Path Planning: Breadth-First Search

Path Planning: Depth-First Search

Path Planning: A*

Potential Field

Potential Field

Potential Field

Path Planning: Potential Field Local minimum problem

Obstacle Avoidance Local path planning Changing robot’s trajectory as informed by its sensors during robot motion

Obstacle Avoidance: Bug 1

Obstacle Avoidance: Bug 1 Exhaustive search to find leave point

Obstacle Avoidance: Bug2

Obstacle Avoidance: Bug2 Greedy search to find leave point

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Tangent Bug

Obstacle Avoidance: Vector field histogram(VFH) Polar histogram https://www.youtube.com/watch?v=caRj3OLA10Q

Obstacle Avoidance: VFH+ Considering kinematic limitations (ex) Turning radius of vehicle Masked polar histogram

Obstacle Avoidance: Bubble Band Concept

Obstacle Avoidance: Curvature velocity approach Basic curvature velocity method (CVM) Assumption robot only travels along arcs with curvature c = w/v Adding physical constraints from the robot and the environment to a velocity space Robot’s kinematic and dynamic constraints -vmax < v < vmax , -ωmax < ω < ωmax Constraints from obstacle blocking certain v and ω Obstacles are approximated by circular objects New velocity (v and ω) is made by an object function tv: translational velocity rv: rotational velocity

Obstacle Avoidance: Dynamic window approach Local dynamic window approach

Obstacle Avoidance: Dynamic window approach https://www.youtube.com/watch?reload=9&v=mech98HdWCI

Obstacle Avoidance: ASL approach

Obstacle Avoidance: ASL approach

Obstacle Avoidance: Overview

Obstacle Avoidance: Overview

Obstacle Avoidance: Overview