raster - Calculating accumulated walking pace from starting location outwards using R?

Goal

In R, I would like to calculate an accumulated cost surface around a starting location, with the cost representing the time (say, hours) to walk from the location outwards in all directions (say, 8 directions in raster's terms). The walking time (pace) is devised via the Tobler's hiking function (https://en.wikipedia.org/wiki/Tobler%27s_hiking_function).

I have indeed used ArcGIS to achieve that in the past, using the 'Path Distance' tool (http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-analyst-toolbox/how-the-path-distance-tools-work.htm), which implements the method devised by Cixiang Zhan, Sudhakar Menon, Peng Gao (https://link.springer.com/chapter/10.1007/3-540-57207-4_29). I would like to reproduce something similar in R.

Earlier threads

I have made a search in this Forum, but at the best of my knowledge the issue has been always tackled from an ArcGIS perspective.

Issue

In theory, the implementation of the methodology is simple, but I have hard time to devise the correct workflow in R. Also, I do believe that the gdistance package is the key to the calculation of an accumulated cost surface, but I cannot wrap my head around how to properly use the transition() function.

What I did so far

# Define the Tober's function for speed in kmh

tobler.kmh <- function(x){ 6 * exp(-3.5 * abs(tan(x*pi/180) + 0.05)) }

# calculate the slope from an input DTM
SLOPE <- raster::terrain(dtm, opt='slope', unit='degrees', neighbors=8)

# calculate the speed in Kmh
v.kmh <- calc(SLOPE, tobler.kmh)

# time in h to cross 1 km (p stands for 'pace')
p.hkm <- 1/v.kmh    


# express the speed in meters per hour
v.mh <- v.kmh * 1000

# time in hours to cross 1 m
p.hm <- 1 / v.mh

Where I am stuck

Now, with the ultimate goal to devise isochrones, I think I would need to accumulate the pace (in hours per meters = p.hm) outwards from a given location. I guess that the gdistance's accCost() function would make the trick, but I cannot understand how to tackle the intermediate step that entails creating a transition matrix via the transition() function. The latter (at the best of my understanding) would allow to define a traversing cost other than distance in which one incurrs when moving from one cell to an adjacent cell.

I do not know: (a) if the above formula to calculate the pace (in hours per meters) has to be somehow implemented withing the transition() function; (b) if I am approacing the whole issue from the wrong perspective.