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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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slide1

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)

motivations
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.
problem approach
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
constraints
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
content
Content
  • 2 modes of navigation:
  • Global
    • Pre-compute a global roadmap
    • Graph search (inigoal) in real-time
    • Display motion
  • Local
    • User-steered exploration
basic idea

Runtime algorithm

Basic Idea

Preprocessing phase

guards connectors c space

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

algorithm build roadmap

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

roadmap connecting nodes
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
roadmap pruning connectors
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

search for a path init goal

ini

goal

Search for a path: init  goal
  • Initial position (Rc radius)
  • Goal position
  • Graph search…
display motion smooth path
Display Motion: Smooth Path
  • Walk along the path
  • Smoothing path (cutting redundant corners while walking)

ini

goal

roadmap sampling1

Gravity

Roadmap - Sampling
  • Shooting rays
  • Walkable surface
  • Construct roadmap

ө

ө

roadmap analysis
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
user steered exploration local walk
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!!
local walk algorithm
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
local walk
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

limitations
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
ad