GLOBAL NAVIGATION GLOBAL NAVIGATION Examples - - PowerPoint PPT Presentation

▶
global navigation global navigation
SMART_READER_LITE
LIVE PREVIEW

GLOBAL NAVIGATION GLOBAL NAVIGATION Examples - - PowerPoint PPT Presentation

Jan 02, 2023 378 likes •940 views

GLOBAL NAVIGATION GLOBAL NAVIGATION Examples http://www.youtube.com/watch?v=ABJjdpxeMtE&no redirect=1 http://www.youtube.com/watch?v=tro-fjsBs9g 2 University of North Carolina at Chapel Hill ENVIRONMENT REPRESENTATION 3

slide-1
SLIDE 1

GLOBAL NAVIGATION

slide-2
SLIDE 2

University of North Carolina at Chapel Hill

GLOBAL NAVIGATION

2

  • Examples
  • http://www.youtube.com/watch?v=ABJjdpxeMtE&no

redirect=1

  • http://www.youtube.com/watch?v=tro-fjsBs9g
slide-3
SLIDE 3

University of North Carolina at Chapel Hill

ENVIRONMENT REPRESENTATION

3

slide-4
SLIDE 4

University of North Carolina at Chapel Hill

GLOBAL NAVIGATION

4

  • Navigation in an environment where local navigation

techniques are insufficient

  • “Local”
  • Walk straight to goal
  • Always turn such that direction is most toward

goal as possible

  • Local Minima
  • Local techniques can lead to globally inefficient

choices

slide-5
SLIDE 5

University of North Carolina at Chapel Hill

ENVIRONMENT REPRESENTATION

5

  • Visual representation more detailed than necessary
  • Very common for dynamics simulation
  • Typically true for navigation as well
  • The more complex the representation, the more

expensive

slide-6
SLIDE 6

University of North Carolina at Chapel Hill

ENVIRONMENT REPRESENTATION

6

  • Full 3D polygonal

representation

  • Quite expensive
  • Details smaller than

~0.2 m probably don’t matter.

  • Floor plan matters more than

vertical space

  • (vertical clearance)
slide-7
SLIDE 7

University of North Carolina at Chapel Hill

ENVIRONMENT REPRESENTATION

7

  • 2D footprint
  • Saving an entire dimension
  • How much detail?
  • Coarse bounding volumes
  • Visually clear regions are no longer clear
slide-8
SLIDE 8

University of North Carolina at Chapel Hill

ENVIRONMENT REPRESENTATION

8

  • Keep polygons or rasterize to grid?
  • Grid offers simple “is colliding” query
  • (Compatible with potential field methods)
slide-9
SLIDE 9

University of North Carolina at Chapel Hill

GLOBAL NAVIGATION

9

  • Solving requires two things
  • Represent the navigable space and its relationships
  • Search the navigable space for optimal paths
slide-10
SLIDE 10

University of North Carolina at Chapel Hill

NAVIGATION GRID

10

  • Various names
  • Guidance field
  • Potential field
slide-11
SLIDE 11

University of North Carolina at Chapel Hill

NAVIGATION GRID - DEFINITION

11

  • Discretization of space
  • Cells don’t have to be uniform or square
  • Rectangle, hex, etc.
  • Cells are either marked as free or occupied
  • Non-boolean values possible
slide-12
SLIDE 12

University of North Carolina at Chapel Hill

NAVIGATION GRID - USAGE

12

  • Select a goal point
  • Each cell contains the direction of travel along the

shortest path from that cell to the goal point

  • Compute:
  • Compute shortest path distance to goal from each

cell center

  • Solve using front propagation algorithms
  • (e.g. https://www.ceremade.dauphine.fr/~peyre/teaching/manifold/tp2.html)
  • Compute gradient of the field – gradient is the

direction of the shortest path

slide-13
SLIDE 13

University of North Carolina at Chapel Hill

NAVIGATION GRID - ANALYSIS

13

  • Pros
  • O(1) preferred direction computation
  • (even with bi-linear interpolation of the grid)
  • Cons
  • Expensive creation
  • Pre-computation or created by hand
  • Suffers from discretization errors
  • One field per goal
  • Requires planar topology – can’t walk over and under a

bridge

slide-14
SLIDE 14

University of North Carolina at Chapel Hill

ROAD MAP - DEFINITION

14

  • A discrete sampling of free space
  • Each sample is guaranteed to be collision free
  • Links between samples is guaranteed to be a collision

free trajectory

slide-15
SLIDE 15

University of North Carolina at Chapel Hill

ROAD MAP - USE

15

  • Given start (s) and goal (g) positions
  • Link to roadmap
  • Find path on roadmap

s g

slide-16
SLIDE 16

University of North Carolina at Chapel Hill

ROAD MAP - USE

16

  • Path
  • P = [p1, p2, p3, …, pn, g]
  • Ordered list of waypoints
  • Preferred direction is direction toward “next”

waypoint – the target waypoint

  • When do you change which waypoint is the target

waypoint?

  • What if the target waypoint is lost?
slide-17
SLIDE 17

University of North Carolina at Chapel Hill

ROAD MAP - USE

17

  • When do you advance the target waypoint?
  • Simply measure distance (d) – d < D à

reached

  • D – threshold
  • Big enough to be robust
  • Small enough that the next waypoint is

reachable

  • What if the crowd keeps me from reaching the

waypoint?

  • What if the crowd sweeps me PAST the waypoint

along my path, but I don’t get close?

slide-18
SLIDE 18

University of North Carolina at Chapel Hill

ROAD MAP - USE

18

  • When do you advance the target waypoint?
  • Visibility tests
  • Set the target waypoint to be the most advanced

waypoint that is visible

  • This keeps the waypoint as far in “front” as

possible

  • Also detects if the agent is pushed from the path
slide-19
SLIDE 19

University of North Carolina at Chapel Hill

ROAD MAP - USE

19

  • What if you lose sight of the target waypoint (pushed
  • ff the path)?
  • Replan
  • Create a new path
  • Rewind
  • Try testing previous waypoints (or successive)
  • Replan if all else fails
  • Remember
  • Remember where you were when you last could

see it and work toward that

slide-20
SLIDE 20

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

20

  • Paths are dependent on sampling and connectivity
  • Path is only “optimal” w.r.t. the graph – not the

environment

  • “Smoothing” the path helps
  • Earlier visibility query implicitly smooths the path
  • All but the last visible nodes are culled
slide-21
SLIDE 21

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

21

  • That form of smoothness depends on the roadmap
slide-22
SLIDE 22

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

22

  • Paths are dependent on sampling and connectivity
  • How close it is to optimal depends on how close the

roadmap samples come to the optimal path

  • No link à

no path

slide-23
SLIDE 23

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

23

  • Clearance
  • Roadmaps are computed with one clearance in

mind

  • What if there are entities of varying size?
  • Big agents will attempt to travel links with

insufficient clearance on a small-agent map

  • Small agents will skip valid paths when using

big-agent maps

  • Encode each link with maximum clearance
slide-24
SLIDE 24

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

24

  • More choices à

more complexity

  • The only way to give agents more paths to reach

their goal is to increase the complexity of the map

  • Search algorithms are worse than linear in the

length of the optimal path (length = # of links)

  • Double the # of links, more than double the

computation time

  • Also increase memory footprint
slide-25
SLIDE 25

University of North Carolina at Chapel Hill

ROAD MAP - ANALYSIS

25

  • Pros
  • Easy to create
  • Graph search straight-forward and generally effective
  • Pre-computed
  • Allows for non-planar topologies
  • Cons
  • Hard to create a good roadmap
  • Paths non-optimal and non-smooth
  • Requires acceleration structure and visibility query to link

to the graph

slide-26
SLIDE 26

University of North Carolina at Chapel Hill

NAVIGATION MESH - DEFINITION

26

  • Discretization of free region into a mesh of convex

polygons

slide-27
SLIDE 27

University of North Carolina at Chapel Hill

NAVIGATION MESH - USE

27

  • Discretization of free region into a mesh of convex

polygons

  • Graph search the mesh for an envelope
  • Compute path in the envelope
slide-28
SLIDE 28

University of North Carolina at Chapel Hill

  • Envelope Path
  • Centroid path
  • Edge center path
  • “Optimal” path

NAVIGATION MESH - USE

28

slide-29
SLIDE 29

University of North Carolina at Chapel Hill

  • Funnel algorithm (approximate)
  • How we select the “optimal” path

NAVIGATION MESH - USE

29

slide-30
SLIDE 30

University of North Carolina at Chapel Hill

  • Define an origin: o
  • Define the cone of visibility

spanning the first portal

  • For each successive portal
  • Contract the funnel
  • If funnel collapses, create a

waypoint on that portal vertex

  • Reset the origin to that waypoint

NAVIGATION MESH - USE

30

http://cs.brown.edu/courses/cs195u/lectures/06.pdf

slide-31
SLIDE 31

University of North Carolina at Chapel Hill

  • Implicit connectivity

NAVIGATION MESH - ANALYSIS

31

slide-32
SLIDE 32

University of North Carolina at Chapel Hill

  • Clearance for range of sizes
  • In the graph – make edge weight depend on

clearance

NAVIGATION MESH - ANALYSIS

32

slide-33
SLIDE 33

University of North Carolina at Chapel Hill

  • Convexity is good
  • Any two points inside a convex polygon are

“linkable”

  • Progress easy to track
  • Given target portal, as long as I’m in the

polygon, I can move to a point on the portal

NAVIGATION MESH - ANALYSIS

33

slide-34
SLIDE 34

University of North Carolina at Chapel Hill

NAVIGATION MESH - ANALYSIS

34

  • If the edges are wide enough, is the mesh clear?
  • Not necessarily
  • Further classification needs to be done
  • Clearance can depend on which way one travels

“A Generalized Exact Arbitrary Clearance Technique for Navigation Meshes.” R. Oliva, N. Pelechano ACM SIGGRAPH conference on Motion in Games (MIG'2013). November 7-9. Dublin (Ireland). 2013.

slide-35
SLIDE 35

University of North Carolina at Chapel Hill

NAVIGATION MESH - ANALYSIS

35

  • What is the path distance between two polygons for

graph search?

  • Moving from red to blue
  • Correcting this brings back graph density
slide-36
SLIDE 36

University of North Carolina at Chapel Hill

NAVIGATION MESH - ANALYSIS

36

  • Paths between portals not necessarily clear
slide-37
SLIDE 37

University of North Carolina at Chapel Hill

NAVIGATION MESH - ANALYSIS

37

  • Pros
  • Generally more compact than equivalent graphs
  • Envelopes of trajectories encoded
  • Cons
  • VERY difficult to produce
  • Properly handling clearance is tricky
slide-38
SLIDE 38

University of North Carolina at Chapel Hill

CORRIDOR MAPS - DEFINITION

38

  • Roadmap + “convex polygons” (aka circles)
  • To the white board!

http://www.staff.science.uu.nl/~gerae101/

slide-39
SLIDE 39

University of North Carolina at Chapel Hill

WAYPORTALS

39

  • Narrow passages
slide-40
SLIDE 40

University of North Carolina at Chapel Hill

  • Wide passages

WAYPORTALS

40

slide-41
SLIDE 41

University of North Carolina at Chapel Hill

  • Wide passages

WAYPORTALS

41

slide-42
SLIDE 42

University of North Carolina at Chapel Hill

WAYPORTALS

  • Global Planning

– Understands full domain – For agent and goal:

  • Find “optimal” path to goal
  • Only consider static obstacles
  • Nearby agents have similar paths

42

slide-43
SLIDE 43

University of North Carolina at Chapel Hill

WAYPORTALS

  • Local Planning

– Limited domain knowledge

  • Waypoint

– Move towards waypoint

43

slide-44
SLIDE 44

University of North Carolina at Chapel Hill

WAYPORTALS

  • Local Planning

– Limited domain knowledge

  • Waypoint

– Move towards waypoint – Avoid collisions

44

slide-45
SLIDE 45

University of North Carolina at Chapel Hill

WAYPORTALS

  • Local Planning

– Limited domain knowledge

  • Waypoint

– Move towards waypoint – Avoid collisions

45

slide-46
SLIDE 46

University of North Carolina at Chapel Hill

WAYPORTALS

  • Local Planning

– Only knows waypoint – Unable to exploit additional space – Solution: – Small change to global planner to communicate more semantics – Extend local planner to use new information

46

slide-47
SLIDE 47

University of North Carolina at Chapel Hill

WAYPORTALS

  • Previous work in Global Planning
  • Roadmaps

[Latombe, 1991], [LaValle, 2006]

  • Navigation Mesh

[Hertel and Mehlhorn, 1985], [Tozour, 2003], [Mononen, 2009], [Snook, 2000], [Kallmann, 2010], [Van Toll et al., 2011]

  • Potential field

[Khatib, 1986]

  • Dynamic adaptation

[Jaillet and Simeon 2004; Kallman and Mataric 2004; Ferguson et al. 2006, Zucker et al. 2007], [Sud et al. 2007; Yang and Brock 2007], [Kretz et al, 2012]

47

slide-48
SLIDE 48

University of North Carolina at Chapel Hill

  • Limited knowledge leads to limited response
  • Promote 1D waypoint to 2D wayportal
  • Preferred velocity becomes an arc of velocities

WAYPORTALS

48

vi0 vi0

slide-49
SLIDE 49

University of North Carolina at Chapel Hill

WAYPORTALS

49

  • Using Wayportals
slide-50
SLIDE 50

University of North Carolina at Chapel Hill

WAYPORTALS

50

  • Improved space utilization and flow
slide-51
SLIDE 51

University of North Carolina at Chapel Hill

WAYPORTALS

51

  • Improved space utilization and flow

Waypoints Wayportals

slide-52
SLIDE 52

University of North Carolina at Chapel Hill

WAYPORTALS

52

  • Improved space utilization and flow
slide-53
SLIDE 53

University of North Carolina at Chapel Hill

WAYPORTALS

53

  • Summary
  • Formulation for improving space utilization and flow

consistent with human behavior

  • Efficiency: minimal increase
  • 10% more expensive over waypoint for 700

agents (from 2.0 μs to 2.2 μs per agent)

  • Correctness: space utilization more consistent with
  • bserved human behavior
slide-54
SLIDE 54

University of North Carolina at Chapel Hill

WAYPORTALS

54

  • Limitations
  • Optimization function is non-convex; approximation

constrains the full space of responses

slide-55
SLIDE 55

University of North Carolina at Chapel Hill

QUESTIONS?

55