Interactive Navigation in Complex Environments Using Path Planning

Salomon et al.(2003) University of North Carolina

Presented by Mohammed Irfan RafiqUsing Slides from Xiaoshan Pan(2003)

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

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

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

2 modes of navigation: Global

– Pre-compute a global roadmap– Graph search (inigoal) in real-time– Display motion

Local– User-steered exploration

Basic Idea

Preprocessing phase

Runtime algorithm

•Connectors - Rc > Rg

Rc

Guards & Connectors (C-space)

•Reachability -neighborhood around a config that can be reached using a local planner

Rg•Guards - guards can’t see each other

- yes reject c, goto while

c

- no! c becomes a Guard, connect to connectors (if any), goto while

Algorithm (build_roadmap)

While (map_coverage < P_cover), do // map_coverage = guards_reachable/entire_space

Return roadmap

Connector

GuardGuard

Connector

GuardGuard

Connector

GuardGuard

2. Can c be a Connector? See any Guards in Rc? - Yes then connect, goto while (else goto 3)

1. Pick a random config. c

c

3. Can c be a Guard? See any Guards in Rg?

c

Be a Connector Be a Guard Be rejected

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

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 Initial position (Rc radius)

ini

goal

Goal position Graph search…

Display Motion: Smooth Path Walk along the path

ini

goal

Smoothing path (cutting redundant corners while walking)

Roadmap - Sampling

Gravity

•Shooting rays

Random Rays

Roadmap - Sampling

Gravity

•Shooting rays

ө ө

•Walkable surface

•Construct roadmap

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 has control– A directional vector

Robot always stays on a walkable surface

– In free space– Surface within a tolerance

angle– Steps ok, cliffs NO!!

Robot do not penetrate objects

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

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

Results

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