# Transition matrix of a Markov chain that guides the movement of an autonomous patrolling robot

### Description

Transition matrix of a Markov chain that guides the movement of an autonomous patrolling robot. The chain has been computed according to game-theoretic techniques as the equilibrium solution of a leader-follower game between a potential intruder and a patroller. See the references section.

### Usage

1 2 3 |

### Format

`transRobot`

is a 10x10 2D matrix, `linguisticTransitions`

is another 10x10 matrix of strings,
and `robotStates`

is a vector of state names of length 10.

### Details

In the game-theoretic patrolling model proposed in Amigoni et al., the equilibrium solution of the leader-follower game is a Markov chain
that can be computed by solving a set of independent linear programming problems. The transition probabilites are described in Fig. 1 of Amigoni et al.
`linguisticTransitions`

is a matrix of labels whose names should match the tags of the `fuzzynumbers`

list argument in the
call to `fuzzyStationaryProb`

when `linguisticTransitions`

is passed as first argument.

### Author(s)

Pablo J. Villacorta Iglesias, Department of Computer Science and Artificial Intelligence, University of Granada (Spain).

pjvi@decsai.ugr.es - http://decsai.ugr.es/~pjvi/r-packages.html

### References

Amigoni, F., Basilico, N., Gatti, N. Finding the Optimal Strategies for Robotic Patrolling with Adversaries in Topologically-Represented Eenvironments. In Proc. of ICRA 2009, pp. 819-824.