Le fil d'ariane : une méthode de planification générale. Application à la planification automatique de trajectoires
Résumé
The ultimate goal of a path planner is to find a path in the configuration
space from the initial position to the target. However, while
searching for this path, an interesting sub-goal to consider may be to
try to collect information about the free space and about the
possible paths to go about in that space. The ARIADNE'S CLEW algorithm
tries to do both at the same time. An EXPLORE algorithm collects
information about the free space with an increasingly fine resolution,
while, in parallel, a SEARCH algorithm opportunistically checks if the
target can be reached. The EXPLORE algorithm works by placing
landmarks in the search space in such a way that a path from the
initial position to any landmark is known. In order to learn as much
as possible about the free space the EXPLORE algorithm tries to spread
the landmarks all over this space. To do so, it tries to put the
landmarks as far as possible from one another. For each new landmark
produced by the EXPLORE algorithm, the SEARCH algorithm checks with a
local method if the target may be reached from that landmark. The
ARIADNE'S CLEW algorithm is fast in most cases, in addition, it is a
complete planner which will find a path if one exists.
The resolution at which the space is scanned and the time spend to do
so, automatically adapts to the difficulty of the problem. Both the
EXPLORE and the SEARCH algorithms are expressed as optimization
problems.
A massively parallel implementation of our method has been implemented
for a six degree-of-freedom arm in a parallel machine (The Mega-Node)
. In our experimental setup two robots are used. The first robot named
MOBILE ROBOT is under the control of the Mega-Node running the
parallel implementation of the Ariadne's Clew algorithm. The second
robot named OBSTACLE ROBOT is used as a dynamical obstacle: it is
controlled by our robot simulation package ACT which generates random
moves in order to disturb the MOBILE ROBOT.
First we use our robot simulation package ACT to describe the scene
with the two robots. We place the static obstacles giving an initial
position for the OBSTACLE ROBOT. Then, we compile automatically this representation
into a special one which is downloaded into the Mega Node. A final position
is then specified to the MOBILE ROBOT, the Mega-node quickly (2 seconds)
produces a plan which assumes that the OBSTACLE ROBOT is standing still.
When the position of the OBSTACLE ROBOT changes under the control of
ACT the MOBILE ROBOT stops and the Mega-Node (re)computes another
path using the new position of the OBSTACLE ROBOT. This loop continues
until the MOBILE ROBOT has reached the specified final position. At
this moment, a new goal can be specified.
space from the initial position to the target. However, while
searching for this path, an interesting sub-goal to consider may be to
try to collect information about the free space and about the
possible paths to go about in that space. The ARIADNE'S CLEW algorithm
tries to do both at the same time. An EXPLORE algorithm collects
information about the free space with an increasingly fine resolution,
while, in parallel, a SEARCH algorithm opportunistically checks if the
target can be reached. The EXPLORE algorithm works by placing
landmarks in the search space in such a way that a path from the
initial position to any landmark is known. In order to learn as much
as possible about the free space the EXPLORE algorithm tries to spread
the landmarks all over this space. To do so, it tries to put the
landmarks as far as possible from one another. For each new landmark
produced by the EXPLORE algorithm, the SEARCH algorithm checks with a
local method if the target may be reached from that landmark. The
ARIADNE'S CLEW algorithm is fast in most cases, in addition, it is a
complete planner which will find a path if one exists.
The resolution at which the space is scanned and the time spend to do
so, automatically adapts to the difficulty of the problem. Both the
EXPLORE and the SEARCH algorithms are expressed as optimization
problems.
A massively parallel implementation of our method has been implemented
for a six degree-of-freedom arm in a parallel machine (The Mega-Node)
. In our experimental setup two robots are used. The first robot named
MOBILE ROBOT is under the control of the Mega-Node running the
parallel implementation of the Ariadne's Clew algorithm. The second
robot named OBSTACLE ROBOT is used as a dynamical obstacle: it is
controlled by our robot simulation package ACT which generates random
moves in order to disturb the MOBILE ROBOT.
First we use our robot simulation package ACT to describe the scene
with the two robots. We place the static obstacles giving an initial
position for the OBSTACLE ROBOT. Then, we compile automatically this representation
into a special one which is downloaded into the Mega Node. A final position
is then specified to the MOBILE ROBOT, the Mega-node quickly (2 seconds)
produces a plan which assumes that the OBSTACLE ROBOT is standing still.
When the position of the OBSTACLE ROBOT changes under the control of
ACT the MOBILE ROBOT stops and the Mega-Node (re)computes another
path using the new position of the OBSTACLE ROBOT. This loop continues
until the MOBILE ROBOT has reached the specified final position. At
this moment, a new goal can be specified.
Nous presentons une methode generale de planification : L'algorithme Fil d'Ariane. Cette methode est appliquee au probleme de la planification automatique de trajectoires. L'originalite de la methode reside dans son adaptation automatique a la complexite du probleme pose. La planification automatique de trajectoires est transformee en un probleme d'optimisation d'une fonctionnelle de
l'espace des plans dans $R^+$. Cette optimisation permet d'explorer
les positions accessibles a partir d'une configuration initiale. La
methode ne construit pas l'espace des configurations; par contre, a
mesure que le temps passe, une approximation de plus en plus fine de
l'espace accessible est construite. Cette approximation est faite par
un premier algorithme appele l'algorithme $EXPLORE$ qui garantit la
completude pour une resolution donnee de la methode. D'autre part,
un deuxieme algorithme, l'algorithme $SEARCH$, permet d'accelerer
la recherche d'un chemin et d'atteindre la configuration finale. En
resume, la methode proposee permet de construire un planificateur
complet pour une resolution donnee qui exploite d'une maniere
efficace l'espace des plans pour explorer l'espace des configurations.
Nous avons implante deux planificateurs bases sur l'algorithme Fil
d'Ariane : le premier est un planificateur de trajectoires pour un
robot mobile holonome, et le deuxieme, notre experimentation
principale, un planificateur de trajectoires pour un bras manipulateur
a six degres de liberte. Pour ce dernier, nous avons realise une
implantation de notre algorithme sur une machine massivement
parallele et planifie les mouvements d'un bras a 6 degres de
liberte.
Pour optimiser les fonctions des algorithmes EXPLORE et SEARCH nous
avons utilise les algorithmes genetiques. Ces algorithmes
sont des methodes d'optimisation stochastiques facilement
parallelisables.
l'espace des plans dans $R^+$. Cette optimisation permet d'explorer
les positions accessibles a partir d'une configuration initiale. La
methode ne construit pas l'espace des configurations; par contre, a
mesure que le temps passe, une approximation de plus en plus fine de
l'espace accessible est construite. Cette approximation est faite par
un premier algorithme appele l'algorithme $EXPLORE$ qui garantit la
completude pour une resolution donnee de la methode. D'autre part,
un deuxieme algorithme, l'algorithme $SEARCH$, permet d'accelerer
la recherche d'un chemin et d'atteindre la configuration finale. En
resume, la methode proposee permet de construire un planificateur
complet pour une resolution donnee qui exploite d'une maniere
efficace l'espace des plans pour explorer l'espace des configurations.
Nous avons implante deux planificateurs bases sur l'algorithme Fil
d'Ariane : le premier est un planificateur de trajectoires pour un
robot mobile holonome, et le deuxieme, notre experimentation
principale, un planificateur de trajectoires pour un bras manipulateur
a six degres de liberte. Pour ce dernier, nous avons realise une
implantation de notre algorithme sur une machine massivement
parallele et planifie les mouvements d'un bras a 6 degres de
liberte.
Pour optimiser les fonctions des algorithmes EXPLORE et SEARCH nous
avons utilise les algorithmes genetiques. Ces algorithmes
sont des methodes d'optimisation stochastiques facilement
parallelisables.
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