R. Cerulli et al., THE AUCTION TECHNIQUE FOR THE SENSOR-BASED NAVIGATION PLANNING OF AN AUTONOMOUS MOBILE ROBOT, Journal of intelligent & robotic systems, 21(4), 1998, pp. 373-395
The problem of finding a path for the motion of a small mobile robot f
rom a starring point to a fixed target in a two dimensional domain is
considered in the presence of arbitrary shaped obstacles. No a priori
information is known in advance about the geometry and the dimensions
of the workspace nor about the number, extension and location of obsta
cles. The robot has a sensing device that detects all obstacles or pie
ces of wails lying beyond a fixed view range. A discrete version of th
e problem is solved by an iterative algorithm that at any iteration st
ep finds the smallest path length from the actual point to the target
with respect to the actual knowledge about the obstacles, then the rob
ot is steered along the path until a new obstacle point interfering wi
th the path is found, at this point a new iteration is started. Such a
n algorithm stops in a number of steps depending on the geometry, find
ing a solution for the problem or detecting that the problem is unfeas
ible. Since the algorithm must be applied on line, the effectiveness o
f the method depends strongly on the efficiency of the optimization st
ep. The use of the Auction method speeds up this step greatly both for
the intrinsic properties of this method and because we fully exploit
a property relating two successive optimizations, proved on paper, tha
t in practical instances enables the mean computational cost requested
by the optimization step to be greatly reduced. It is proved that the
algorithm converges in a finite number of steps finding a solution wh
en the problem is feasible or detecting the infeasibility condition ot
herwise. Moreover the worst case computational complexity of the whole
algorithm is shown to be polynomial in the number of nodes of the dis
cretization grid. Finally numerical examples are reported in order to
show the effectiveness of this technique.