Reliable Computing 7: 1–15, 2001.
2001 Kluwer Academic Publishers. Printed in the Netherlands.
Path Planning Using Intervals and Graphs
Laboratoire des Signaux et Syst
emes, CNRS, Sup
elec, Plateau de Moulon, 91192 Gif-sur-Yvette
Cedex, France, e-mail: firstname.lastname@example.org
On leave from Laboratoire d’Ing
enierie des Syst
es, ISTIA, 62 avenue Notre Dame
du Lac, 49000 Angers, France
(Received: 15 April 1999; accepted: 2 February 2000)
Abstract. In this paper, the problem of interest is to ﬁnd a path with given endpoints such that the
path lies inside a compact set
given by nonlinear inequalities. The proposed approach uses interval
analysis for characterizing
by subpavings (union of boxes) and graph algorithms for ﬁnding short
feasible paths. As an illustration, the problem of ﬁnding collision-free paths for a polygonal rigid
object through a space that is cluttered with segment obstacles is considered.
A , L , S
L Graphs, subpavings, lists.
Nodes of a graph.
In this paper, we present a new approach to ﬁnd a collision-free path for an object
in a given space with obstacles. The issue of path planning in a known environment
has been addressed by many researchers (see, e.g., , , , ). Most of
the current approaches to path planning are based on the concept of conﬁguration
space (C-space) . Each coordinate of the C-space represents a degree of freedom
of the object. The number of independent parameters needed to specify an object
conﬁguration corresponds to the dimension of the C-space. The start conﬁguration
and the goal conﬁguration become two points a
of the C-space. An example of
such objects are industrial robots which are kinematic chains in which adjacent links
are connected by n prismatic or rotary joints, each with one degree of freedom. The
positions and orientations of each link of the industrial robot can be characterized
by n real numbers, which are the coordinates of a single n-dimensional point in the
C-space (see , for more information).
The feasible conﬁguration space
is the subset of the C-space corresponding
to feasible conﬁguration of the object, i.e.,
contains all conﬁguration vectors for