**-k**- Use the 'Knight's move'; slower, but more accurate
**-n**- Keep null values in output map
**-r**- Start with values in raster map
**--overwrite**- Allow output files to overwrite existing files
**--verbose**- Verbose module output
**--quiet**- Quiet module output

**elevation**=*string*- Name of elevation input raster map
**friction**=*string*- Name of input raster map containing friction costs
**output**=*string*- Name of raster map to contain results
**start_points**=*string*- Starting points vector map
**stop_points**=*string*- Stop points vector map
**coordinate**=*x,y[,**x,y*,...]- The map E and N grid coordinates of a starting point (E,N)
**stop_coordinate**=*x,y[,**x,y*,...]- The map E and N grid coordinates of a stopping point (E,N)
**max_cost**=*integer*- An optional maximum cumulative cost
- Default:
*0* **null_cost**=*float*- Cost assigned to null cells. By default, null cells are excluded
**percent_memory**=*integer*- Percent of map to keep in memory
- Default:
*100* **nseg**=*integer*- Number of the segment to create (segment library)
- Default:
*4* **walk_coeff**=*a,b,c,d*- Coefficients for walking energy formula parameters a,b,c,d
- Default:
*0.72,6.0,1.9998,-1.9998* **lambda**=*float*- Lambda coefficients for combining walking energy and friction cost
- Default:
*1.0* **slope_factor**=*float*- Slope factor determines travel energy cost per height step
- Default:
*-0.2125*

The formula from Aitken 1977/Langmuir 1984 (based on Naismith's rule for walking times) has been used to estimate the cost parameters of specific slope intervals:

T= [(a)*(Delta S)] + [(b)*(Delta H uphill)] + [(c)*(Delta H moderate downhill)] + [(d)*(Delta H steep downhill)]

where:

T is time of movement in seconds,

Delta S is the distance covered in meters,

Delta H is the altitude difference in meter.

The a, b, c, d parameters take in account movement speed in the different conditions and are linked to:

- a: underfoot condition (a=1/walking_speed)
- b: underfoot condition and cost associated to movement uphill
- c: underfoot condition and cost associated to movement moderate downhill
- d: underfoot condition and cost associated to movement steep downhill

The lambda parameter of the linear equation combining movement and
friction costs:

total cost = movement time cost + (lambda) * friction costs

must be set in the option section of *r.walk*.

For a more accurate result, the "knight's move" option can be used (although it is more time consuming). In the diagram below, the center location (O) represents a grid cell from which cumulative distances are calculated. Those neighbours marked with an x are always considered for cumulative cost updates. With the "knight's move" option, the neighbours marked with a K are also considered.

K K K x x x K x O x K x x x K K K

The minimum cumulative costs are computed using Dijkstra's
algorithm, that find an optimum solution (for more details see
*r.cost*, that uses the same algorithm).

Once *r.walk* computes the cumulative cost map as a linear
combination of friction cost (from friction map) and the altitude and
distance covered (from the digital elevation model), *r.drain*
can be used to find the minimum cost path.

- Aitken, R. 1977. Wilderness areas in Scotland. Unpublished Ph.D. thesis. University of Aberdeen.
- Steno Fontanari, University of Trento, Italy, Ingegneria per l'Ambiente e il Territorio, 2000-2001. Svilluppo di metodologie GIS per la determinazione dell'accessibilità territoriale come supporto alle decisioni nella gestione ambientale.
- Langmuir, E. 1984. Mountaincraft and leadership. The Scottish Sports Council/MLTB. Cordee, Leicester.

Antony Awaida,

Intelligent Engineering

Systems Laboratory,

M.I.T.

James Westervelt,

U.S.Army Construction Engineering Research Laboratory

Updated for Grass 5

Pierre de Mouveaux (pmx@audiovu.com)

**Initial version of r.walk:**

Steno Fontanari, 2002

**Current version of r.walk:**

Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia

Correction by: Fontanari Steno, Napolitano Maurizio and Flor Roberto

In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and Tolotti Mathias, 2004

**Updated for Grass 6.1**

Roberto Flor and Markus Neteler

*Last changed: $Date: 2005-12-16 13:04:29 -0800 (Fri, 16 Dec 2005) $*

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