DESCRIPTION

r.walk outputs 1) a raster map layer showing the lowest cumulative cost of moving between each cell and the user-specified starting points and 2) a second raster map layer showing the movement direction to the next cell on the path back to the start point (see Movement Direction). It uses an input elevation raster map layer whose cell category values represent elevation, combined with a second input raster map layer whose cell values represent friction costs. This function is similar to r.cost, but in addiction to a friction map, it considers an anisotropic travel time due to the different walking speed associated with downhill and uphill movements.

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
    • It has been proved that moving downhill is favourable up to a specific slope value threshold, after that it becomes unfavourable. The default slope value threshold (slope factor) is -0.2125, corresponding to tan(-12), calibrated on human behaviour (>5 and <12 degrees: moderate downhill; >12 degrees: steep downhill). The default values for a, b, c, d are those proposed by Langmuir (0.72, 6.0, 1.9998, -1.9998), based on man walking effort in standard conditions.

    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).

    Movement Direction

    The movement direction surface is created to record the sequence of movements that created the cost accumulation surface. Without it r.drain would not correctly create a path from an end point back to the start point. The direction shown in each cell points away from the cell that came before it. The directions are recorded as GRASS standard directions:

           112.5 90  67.5         i.e. a cell with the value 135 
157.5  135   0   45   22.5    means the cell before it is 
       180   x   0            to the south-east.
202.5  225  270  315  337.5
       247.5     292.5

    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. Make sure to use the -d flag and the movement direction raster map when running r.drain to ensure the path is computed according to the proper movement directions.

    SEE ALSO

    r.cost, r.drain, r.in.ascii, r.mapcalc, r.out.ascii

    REFERENCES

    AUTHORS

    Based on r.cost written by :

    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: $Date$