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A path planner for plm applications

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A Path Planner for PLM Applications
Etienne Ferr´e
1
and Jean-Paul Laumond
2
1
Kineo CAM, BP 27201, 31672 Lab`ege, France (eferre@kineocam.com)
2
LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse, France (jpl@laas.fr)
Abstract.
The paper presents the performance of a collision-free pathplanner designed for PLM application purposes. The algorithm princi-ple is based on a iterative probabilistic diﬀusion principle [9]. The paperputs emphasis on eﬃciency and practicality analysis. It focuses on exper-iments dealing with disassembly problems as well as robot programming.Eﬃciency is evaluated in terms of computation time and solution quality.As practicality is concerned we show that the solution should not imposeany parameter tuning.
1 Introduction
Is the windscreen wiper motor well designed to be mounted within the car? Howeasy will be the maintainability of the driver seat? Which collision-free trajectorythe spot welding robot should perform between two welding points?With the current stage of the technology oﬀered by PLM software providers itappears that such problems take several tedious hours of an experienced operatoreven with the help of eﬃcient geometric tools (e.g., collision-checkers and auto-mated local path computations). Diﬃcult problems such as some benchmarkspresented in this paper take few days to be solved.This paper presents the performance of a collision-free path planner designedfor PLM application purposes and recently published by the authors in [9]. Theplanner aims at providing an eﬃcient and practical solution. Eﬃciency shouldbe evaluated in terms of computation time and solution quality. Practicalityrequires a solution easy to use for non expert operators: the solution should notimpose any parameter tuning.The proposed approach beneﬁts from the current active research area in robotpath planning [16]. It gathers and improves several probabilistic approacheswithin an integrated solution giving rise to an srcinal parameter free algorithm.
1.1 Probabilistic path planning
After the pioneering work [3] that combines random walks and gradient descentsin the conﬁguration space (
CS
) of the considered mechanical system
3
, two kinds
3
The conﬁguration space of a mechanical system is the manifold of the parameters(e.g. degrees of freedom) required to locate the system in the workspace. It is aconcept in robot path planning (see Latombe’s book for an introduction [16]).
2
of
CS
search paradigms are investigated with success. The
sampling
approachesintroduced in [14] consist in computing a so-called roadmap whose nodes arecollision free conﬁgurations chosen at random and whose edges model the exis-tence of collision free local paths between two nodes. Sampling approaches aimat capturing the topology of the collision free conﬁguration space (
CS
free
) bothin terms of covering and connectiveness in a learning phase. The
diﬀusion
ap-proaches introduced in [10,15] consist in solving single queries by developing atree rooted at the start conﬁguration towards the goal to be reached. How tosample or diﬀuse within
CS
free
eﬃciently? Such questions give rise to numerousvariants of the srcinal algorithms (e.g., [2,5–8,11–13,17–19,21,23,26]).
1.2 Path planning for PLM
Most of the path planning applications in PLM deal with highly cluttered en-vironments. In such contexts diﬀusion techniques clearly behave better thanrandom sampling ones. For instance the solution space for a disassembly prob-lem has the shape of a long thin tube. Random sampling within a tube requiresa high density of points while tree diﬀusion beneﬁts from the shape of the tubethat naturally steers the diﬀusion process.On the basis of this simple statement, several technical issues remain to besolved. How to control the diﬀusion process? For eﬃciency purpose, it shouldprogress fast in empty rooms and more slowly in constrained spaces. How to guar-antee the safeness of the solution path under an imposed user deﬁned clearancethreshold? Such a constraint depends on the problem and should be automati-cally taken into account by the method. The proposed algorithm addresses allthese issues.As we will see, our approach beneﬁts from several sources and ideas alreadyexplored as such but never combined. The next section focuses on the key prin-ciples of the algorithm.
2 Algorithm Principles
2.1 Collision Checking: Static versus Dynamic Approaches
As collision checking is concerned, a critical problem is to perform eﬃcient col-lision checking not only for conﬁgurations (see overviews in [20,24]) but also forlocal paths. Exact collision checking along computed paths has been recentlyaddressed in [22]: path collision checking is performed with a static collisionchecker while the (usually costly) iterative process is speeded up thanks to dis-tance computations.Collision-free path checking is crucial, especially for part disassembling. Inthis case, the solution path is very close to the obstacles and the algorithm mustguarantee the safeness of the result. This question is solved by the followingDynamic Collision Checker (DCC).
3
The commonly used approach is the test of discrete points up to a ﬁxedresolution
∆s
. If each point is tested collision free, the algorithm answers thatthe whole path is collision free:(
∀
i,
q
(
i
×
∆s
)
∈ CS
free
)
⇒
path
⊂ CS
free
The main drawback of this solution is the non guaranty of collision avoidance.Hence, even if no tested points on the path are colliding, pieces of the path inbetween are not checked and a collision may occur. Moreover this collision isnot quantiﬁed: it can be just a small touch of the part or the part crossing awall. Finally, the ﬁxed resolution is an abstract value and may be hard to chooseproperly.Our DCC method is similar to [22]. Even if it is impossible to avoid collisionsby testing discrete points on the path, the collision can nevertheless be quantiﬁed.Hence, our Dynamic Collision Checker computes the step between two testedpoints relative to the maximal swept motion of points of the moving object. Theinput parameter is then a distance
ǫ
in the workspace and the step
∆s
i
betweentwo tested points is computed in such a way that no points of the object movealong a distance larger than 2
ǫ
. Once the step has been computed, the part ismoved to the corresponding point on the path and a collision test is performed:(
∀
i,
q
(
s
i
)
∈ CS
free
)
⇒
path
⊂ CS
free
s
i
=
s
i
−
1
+
f
(
q
(
s
i
−
1
,ǫ
))The function
f
is determined in such a way that (if
A
is the set of points of thepart):
∀
P
∈ A
/
s
i
+1
s
i
dP ds
(
q
(
s
))
ds <
2
ǫ
The method does not avoid the problem of potential collisions between two testedpoints (Fig. 1(a)).Nevertheless if a collision occurs, it can now be quantiﬁed. Indeed, in theworst case, the covered distance of one point is 2
ǫ
. Then the penetration insideobstacles is bounded by
ǫ
(Fig. 1(b)). This point can so penetrate an obstacleof
ǫ
and must go back because the next tested point is collision free. The re-sulting penetration can then be controlled and bounded by a so-called ”
dynamic penetration
” user-deﬁned parameter
ǫ
.This Dynamic Collision Checker algorithm fully controls the path quality.By setting the
dynamic penetration
to a large value, the path is authorized topenetrate the obstacle. It can be a way to shrink the obstacle in order to makethe path planning problem easier to solve. This idea is the core of the iterativediﬀusion described in 2.2.Finally, as we control the maximal penetration along the path, the collisioncan be maintained outside the real obstacle by setting a
static tolerance
of theCollision Checker to a value larger than the
dynamic penetration
. If the distancebetween the body and the obstacles is smaller than the
static tolerance
, theconﬁguration is considered colliding as if the obstacles were virtually enlarged.
4(a) The step in
CS
is computed withrespect to the maximal allowedpenetration in the workspace(b) The control of the motion inthe workspace bounds theparasite penetration in case of collision between two testedpoints.
Fig.1.
Penetration control discretization.
Thus, when a collision appears due to the parasitic penetration side eﬀect, themovable part penetrates the enlarged area keeping the real obstacles safe. Thepath is then guaranteed to be continuously collision free. Moreover, the algo-rithm assures that the path is not closer to the obstacles than the so-called
eﬀective clearance
which is imposed by the user and which appears as the dif-ference between the
static tolerance
and the
dynamic penetration
. Notice thatthe approach is applicable as soon as the collision-checker integrates the notionof static tolerance. This is the case of almost all the marketed collision-checkers.
2.2 Speed-up the Search: an Iterative Approach
To overcome the expansive cost of conﬁguration and path collision checking,some approaches have been deﬁned to put back the tests and then to avoiduseless computations. This is the case of the lazy approaches [6,21] where thealgorithms put back collision checking as long as the probability of failure ishigh. Our algorithm starts from a rough solution path and iteratively reﬁnesit. The iterative procedure is based on an srcinal penetration distance control.When the procedure fails, then the search re-starts with a roadmap composedof the portions of the path that are collision-free. That kind of procedure hasbeen recently introduced in [1] to improve the connectiveness of roadmaps.The principle of the algorithm is illustrated in Figure 2 (see [9] for technicaldetails). A ﬁrst path is computed while allowing some penetration within theobstacles. Then the current paths are iteratively re-shaped by decreasing theallowed penetration threshold. The cases of failure of the iterative process areautomatically detected and solved (Fig. 4).
5(a) Step 1a (b) Step 1b(c) Step 2a (d) Step 2b(e) Step 3a (f) Path
Fig.2.
Iterative Diﬀusion: each iteration consists in a diﬀusion process followed by aconversion of the computed path into roadmap with a reduced
dynamic penetration
value.

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