Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex...
Transcript of Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex...
![Page 1: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/1.jpg)
Hierarchical path planning for walking (almost) anywhere
FOSS4G 2018, Dar es Salaam
Knut Landmark, Espen Messel
![Page 2: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/2.jpg)
Introduction and overview
• Problem and goal• Prospective applications• Open data (vs. restricted)• Graph partitions, hierarchical method• Accuracy• Cost of walking
Detailed National Elevation Model, http://kartverket.no/ (Norwegian Mapping Authority)
![Page 3: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/3.jpg)
Problem and goal:
• Find route between two arbitrary land area positions. • Take into account
• transport networks • topography• terrain type, land cover/use• infrastructure.
• Exploit open-access LiDAR data. • Arbitrary distance and resolution.
![Page 4: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/4.jpg)
Open-access LiDAR data
• National initiatives• All-covering aerial LiDAR survey projects• Open access policy• «Transparency, efficiency, innovation»• UK:
• UK Environmental Agency• Open Government Licence• https://data.gov.uk/
• Norway:• Norwegian Mapping Authority• National Detailed Elevation Model• Creative Commons 4.0• https://hoydedata.no/LaserInnsyn/
![Page 5: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/5.jpg)
LiDAR-based DSMs and DEM enable realistic path planning
![Page 6: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/6.jpg)
Applications and prospects
S. Knapton, The Telegraph, 30. Dec. 2017
• Archaeology, ancient networks
• Search and rescue
• Public transit planning
• Forestry
• Military operations
• Hiking, exercise, recreation
• Robotics, autonomous systems
• Animal migration patterns
• etc.
![Page 7: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/7.jpg)
Two challenges in cross-country path planning
• Realism, how to adapt data– Accurate weight (cost) function– Is a stream traversible; if so, at what cost?– What about a fence? Etc.– Answer not always found in data.
• Computational:– Manage very large graphs– Find optimum solutions efficiently
Image: US National Park Service, nps.gov
![Page 8: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/8.jpg)
Two challenges in cross-country path planning
• Realism, how to adapt data– Accurate weight (cost) function– Is a stream traversible; if so, at what cost?– What about a fence? Etc.– Answer not always found in data.
• Computational:– Manage very large graphs– Find optimum solutions efficiently
Image: www.flickr.com
![Page 9: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/9.jpg)
Road network routing and graphs
• Natural hierarchical structure• Overlays, multiple levels• Transit nodes• Table look-ups• Contractions• Orders of magnitude faster than Dijkstra
Delling and Werneck (2013)
Bast et al. (2007)
![Page 10: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/10.jpg)
Matrix-graph duality
![Page 11: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/11.jpg)
Matrix-graph duality (no parallel arcs)
![Page 12: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/12.jpg)
Assumptions
![Page 13: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/13.jpg)
Generalized path planning with graphs
![Page 14: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/14.jpg)
What is accuracy?
![Page 15: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/15.jpg)
![Page 16: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/16.jpg)
![Page 17: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/17.jpg)
Simple strategy
![Page 18: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/18.jpg)
![Page 19: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/19.jpg)
![Page 20: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/20.jpg)
![Page 21: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/21.jpg)
• Must reduce search space.• Subgraphs may become disconnected.• Consequently, no solution is found.
![Page 22: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/22.jpg)
Aggregate nodes
![Page 23: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/23.jpg)
Modified strategy
![Page 24: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/24.jpg)
Complexity-accuracy trade-off
![Page 25: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/25.jpg)
k-center problems
![Page 26: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/26.jpg)
k-centre algorithm
![Page 27: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/27.jpg)
k-center algorithm
![Page 28: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/28.jpg)
The Dijkstra wavefront
https://timrwalls.wordpress.com/
![Page 29: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/29.jpg)
![Page 30: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/30.jpg)
Two extreme cases
![Page 31: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/31.jpg)
Accuracy revisited
![Page 32: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/32.jpg)
![Page 33: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/33.jpg)
Walking patterns
Lobet, Detrembleur & Hermans (2013)
![Page 34: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/34.jpg)
Energetics: Power balance
![Page 35: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/35.jpg)
Metabolic power and Pandolf equation (rewritten)
![Page 36: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/36.jpg)
Weight function (example)
• Metabolic energy per unit mass and distance• Any path is traversible in both directions• Connected components are strongly connected• Symmetric with respect to ground condition• Assymmetric with respect to slope
![Page 37: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/37.jpg)
Data
Open data:• LiDAR: Creative Commons 4.0 (No), Open Government (UK), etc.• OpenStreetMap (ODbL)• ElVeg (roads, free data)
Restricted data:• Land cover/land use from national competent authorities (attribution)• 1:1000 – 1:5000 vector data (detailed infrastructure)
![Page 38: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/38.jpg)
Open vs restricted data
• OSM + open remote sensing data yield detailed
land cover in some areas (Schultz et al., 2017).• Dedicated public land cover datasets (e.g. CORINE)
generally good but not sufficiently detailed.• Currently detailed land cover from national
competent authorities required.• However, information from (open) LiDAR data
may reduce need for hi-res vector data.• OSM infrastructure sufficient in rural areas
Copernicus (EU) AR5 (No)
![Page 39: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/39.jpg)
Going the right way:
• LiDAR processing
• Raster/Vector pre-processing
• Data inspection
• Graph representation
![Page 40: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/40.jpg)
Going the right way:
• Optimum paths
• Processing service (WPS)
• Web application
• Graph construction, partitioning
![Page 41: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/41.jpg)
Conclusion
![Page 42: Hierarchical path planning for walking (almost) anywhere€¦ · Algorithmics of Large and Complex Networks, pp. 117-139, Springer. • Kepner and Gilbert (2011). Graph Algorithms](https://reader036.fdocuments.us/reader036/viewer/2022070910/5f9d6fbfb662384f1850e94d/html5/thumbnails/42.jpg)
References
• Bast, Funke, Sanders and Schultes (2007). Fast routing in road networks with transit nodes, Science 316, pp. 566.• Delling, Sanders, Schultes and Wagner (2009). Engineering route planning algorithms, in Lerner, Wagner and Zweig (eds.),
Algorithmics of Large and Complex Networks, pp. 117-139, Springer.• Kepner and Gilbert (2011). Graph Algorithms in the Language of Linear Algebra.• Pandolf, Givoni and Goldman (1977). Predicting energy expenditure with loads while standing or walking very slowly, Journ.
Appl. Physiol. Respir. Environ. Exerc. Physiol. 43, pp. 577-581.• Har-Peled (2008), Geometric approximation algorithms, University of Illinois.• Schultz, Voss, Auer, Carter and Zipf (2017). Open land cover from OpenStreetMap and remote sensing, Int. Journ. Appl. Earth
Observation and Geoinformation 63, pp. 206-213.