The way to go with WPS Knut Landmark and Espen Messel The Norwegian - - PowerPoint PPT Presentation

The way to go with WPS

Knut Landmark and Espen Messel The Norwegian Defence Research Establishment (FFI)

Path planning: Best route between two points

• Quickest
• Shortest
• Cheapest
• Safest
• Least exposed

Path planning: Best route between two points

• Quickest
• Shortest
• Cheapest
• Safest
• Least exposed

Image: Aurtjern, by Michal Klajban (unmodified) https://creativecommons.org/licenses/by-sa/3.0/deed.en

Path planning: Best route between two points

• Quickest
• Shortest
• Cheapest
• Safest
• Least exposed

Image: Hurrungane, by Tore Urnes https://creativecommons.org/licenses/by/2.0/deed.en

Task: Path planning in terrain

• Cover all of Norway

– 325.000 km2 – 2000 km

• Shortest or safest route for

vehicles or troops

• Motion not restricted to

roads or paths

• Estimate travel time
• Estimate exposure/visibility

?

Nordmarka, Oslo (25 km2)

• Situation-dependent path planning in large graph
• Service-oriented information infrastructure
• Detailed land cover data
• Hires elevation data (1 m) awaited
• Simulations of ground physics

Perspective

Image: Norwegian Mapping Authorities (Kartverket). Pilot study, detailed national elevation model

Road map

• Graph/weight generation
• Routing examples
• WPS implementation
• Outlook

km2

Image: http://www.skiforeningen.no

Graph types

• Regular
• Random
• Visibility graph
• Voronoi graph
• Navigation mesh

Graph types

• Regular
• Random
• Sight graph
• Voronoi graph
• Navigation mesh

Graph types

• Regular
• Random
• Visibility graph
• Voronoi graph
• Navigation mesh

Data types

• Elevation (10 m)
• Land cover
• Road network
• Path network (OSM)
• Aerial Lidar
• Ground physics model
• Weather forecasts
• Hazards
• Aerial photography

Data types

• Elevation (10 m)
• Land cover
• Road network
• Path network (OSM)
• Aerial Lidar
• Ground physics model
• Weather forecasts
• Hazards
• Aerial photography

Axial variance

Data types

• Elevation (10 m)
• Land cover
• Road network
• Path network (OSM)
• Aerial Lidar
• Ground physics model
• Weather forecasts
• Hazards
• Aerial photography

Land cover polygons

Data types

• Elevation (10 m)
• Land cover
• Road network
• Path network (OSM)
• Aerial Lidar
• Ground physics model
• Weather forecasts
• Hazards
• Aerial photography

Land cover polygons

Lidar (4 km2 test dataset, 1 m grid)

Graph generation principles

1) Random graph with node density depending on terrain attributes 2) Triangulation 3) Hierarchical representation based on clustering of nodes

Node placement (roads)

• All vertices are preserved

and used for computing weights

• Additional nodes are

inserted

Node placement (roads+paths)

• All vertices are preserved

and used for computing weights

• Additional nodes are

inserted

Node placement (terrain, probabilistic)

• All vertices are preserved

and used for computing weights

• Additional nodes are

inserted

Triangulated graph

• All vertices are preserved

and used for computing weights

• Additional nodes are

inserted

Graph: Sparse matrix representation

ji ij

w G w         =            

Node: i j

Graph: Hierarchical representation

• Based on cluster analysis of detailed graph
• Distance measure is travel time
• Cluster distance based on

representatives or centroids

• Form hierarchy of partitions,

𝑇1, . . , 𝑇𝑀, with decreasing number of clusters

• Path planning at step 𝑙

performed on union of clusters in shortest path at step 𝑙 − 1

• In step 𝑙, may also include

neighbors of SP at step 𝑙 − 1

Cluster problem formulation and solution:

• 𝐵 = 𝑤1, … , 𝑤𝑂 is a set of nodes.
• For 𝐷 ⊆ 𝐵, 𝐸(𝐷) measures cluster size.
• Specify an upper limit on cluster size, 𝑆 = max

𝑙

𝐸(𝐷𝑙).

• Find partition such that 𝐵 = ⋃

𝐷𝑙

𝐿 𝑙=1

and 𝐿 is minimal.

• Exact solution is impossible in practice for sizable 𝑂 (NP-hard).
• Use non-optimal «greedy» algorithm instead (𝑙-centre based).
• Requires one single-source, all-shortest paths computation per

cluster.

Partition with size 𝐄 = 𝟐𝟐 mi min walking distance

Cost functions

• Cost functions for standard conditions for roads, paths, and terrain.
• Based on literature, physics, empirical data
• Scale factors account for effect of snow, surface roughness etc.

(work in progress).

• Standard cost functions used to generate grid, weights computed

dynamically for SP solution

• Different categories (work in progress):

– hikers/soldiers – vehicles – bicycles

Cost functions for pedestrians

Downhill Uphill

Our system

• The ZOO WPS-server handles all the requests
• The graph is stored in Postgres with PostGIS extension
• Our own Postgres module calculates edge weights
• We use pgRouting (two-way shortest path A*) to estimate the time to

traverse the route

Chained (nested) WPS request

• Run routing on different graph

resolutions in a nested request

– Starts on a rough graph and loops down to the graph with the best resolution

• Needed for speeding up:

– Cost calculations – Routing algorithm

WPS client

Routing example

Routing example

Routing example

Routing example

Routing example

Example: shortest path in three (coarse) levels

Example: shortest path in three (coarse) levels

Example: shortest path in three (coarse) levels

Further work: ground physics

• Norwegian Meterological Institute R&D
• Validation against observations
• Predict snow depth, temperature profile, load carrying capacity, fresh-water run-off

Summary

• Path planning in terrain
• Situation-dependent edge weights
• Random graph, hierarchical representation
• Service-oriented implementation with WPS and ZOO
• PostGIS with pgRouting

Aknowledgements

Thank you!