A method for autonomously planning collision free paths for two cooperating robots in a static environment was developed at the Center for Intelligent Robotic Systems for Space Exploration (CIRSSE). The method utilizes a divide-and-conquer type of heuristic and involves non-exhaustive mapping of configuration space. While there is no guarantee of finding a solution, the planner was successfully applied to a variety of problems including two cooperating 9 degrees of freedom (dof) robots. Although developed primarily for cooperating robots the method is also applicable to single robot path planning problems. A single 6 dof version of the planner was implemented for the truss assembly east, at NASA Langley's Automated Structural Assembly Lab (ASAL). The results indicate that the planner could be very useful in addressing the ASAL path planning problem and that further work along these lines is warranted

Derby, Stephen J.

Weaver, Jonathan M.

English

NASA Technical Reports Server

&Application of the CIRSSE Cooperating
Robot Path Planner to the NASA
Langley Truss Assembly Problem
Jonathan M. Weaver and Stephen J. Derby
Rensselaer Polytechnic Institute
Troy, New York
27
_NG PAGE BLANK NOT F)LMED
https://ntrs.nasa.gov/search.jsp?R=19940021777 2020-06-16T14:08:41+00:00Z
! N94- 26280
Application of the CIRSSE Cooperating Robot Path Planner
to the NASA Langley Truss Assembly Problem
Jonathan M. Weaver Stephen J. Derby
Research Assistant Associate Professor
Center for Intelligent Robotic Systems for Space Exploration
Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics
Rensselaer Polytechnic Institute, Troy, New York 12180-3590
Abstract
A method for autonomously planning collision f1_ee
paths for two cooperating robots in a static environ-
ment has been developed at CIRSSE. The melhod uti-
lizes a divide-and.conquer type of heuristic and in-
volves non-exhaustive mapping of configuration space.
While there is no guarantee of finding a solution, the
planner has been successfully applied to a variety of
problems including two cooperating 9 dof robots.
Although developed primarily for cooperating robots,
the method is also applicable to single robot path plan.
ning problems. A single 6 dof version of the planner
has been intplemented for the truss assembly task at
NASA Langley's Automated Structural Assembly Lab
ASAL). The results indicate that the planner could
very useful in addressing the ASAL path planning
problem and thai further work along these lines is war-
ranted.
1 Introduction
The robot path planning problem involves deter-
mining if a continuous and obstacle avoiding path ex-
ists between start and goal positions, and, if so, to
find such a path. The complexity of the path plan-
ning problem has been shown to be exponential in
the number of dof [1, 2]. A review of the many path
planning techniques is beyond the scope of this paper.
Reference [3] presents a recent survey paper on the
subject.
A method has been developed at Rensselaer's Cen-
ter for Intelligent Robotic Systems for Space Ex-
ploration (CIRSSE) to autonomously plan collision
free paths for two robots working cooperatively in
a known, static environment [4, 5, 6]. Cooperation
refers to the case whereby both robots simultaneously
grasp and manipulate a common, rigid, payload. The
planner is based around a divide-and-conquer heuristic
aimed at traversing c-space while performing selective
mapping on an as-needed basis. This path pla|mer
has been applied to the CIRSSE testbed. The testbed
consists of two 9 dof robots, each of which consists of a
3 dofplatform and a 6 dof Puma. A sample path found
by the cooperating 9 dof planner is shown in Figure 1.
This example required approximately 10 minutes so-
lution time on a SparcStatioa 1.
Although developed primarily for the cooperat-
ing robot case, the c-space traversal heuristic around
which the planner is based may also be applied
to single robot path planning problems. This pa-
per discusses a single arm version of the planner
which was implemented for the truss assembly task
at NASA Langley's Automated Structural Assembly
Lab (ASAL). The purpose of the implementation was
to assess the potential usefulness of the planner for the
ASAL path planning problem.
The ASAL path planning problem is described in
Section 2. Our path planning strategy is discussed in
Section 3. Sections 4 and 5 present some implemen-
tation details and results for application of the plan-
ner to the ASAL path planning problem. Section 6
presents some conclusions and areas for future work.
2 Problem Statement
A CimStation model of NASA Langley's ASAL is
shown in Figure 2 (CimStation model provided by
NASA Langley). The system consists of a 6 dof Merlin
robot, shown In Figure 3, mounted to a xy-positioning
table (referred to as the carriage), and a turntable.
The turntable includes a trianl_ular platform which
can rotate around a vertical ares through its center.
The Merlin robot is kinematically similar to a Puma.
The objective of the ASAL is to assemble truss struc-
tures consisting of 102 2 meter long struts. Such a
truss is illustrated in Figure 4. The truss bs assem-
bled upon the turntable of the ASAL by positioning
the carriage and the turntable such that the Merlin
may take each strut from a canister near the base of
the Merlin and install it in its final pmition in the
assembly.
The ASAL path planning problem as addressed
herein is defined as follows: Given a carriage and
turntable position for each strut, determine a suitable
path for the Merlin to safely move the robot and its
payload from a start position to a prescribed goal po-
sition. The start position is above the canister holding
the as-yet unassembled struts. The goal position for
each strut is taken as I0 cm from the final position in
the negative of the approach direction. The assembly
sequence is as specified by NASA Langley.
It is assumed that feasible and collision free start
and goal joint configurations of the robot are known.
28
(a) Start Position (b)
(c)
(e)
(d)
(f) Goal Position .... .,.
Figure 1: Sample Results for Cooperating 9 DOF Robots
29
(a) Isometric View
(b) Top View
7
I
(c) Side View
Figure 2: NASA Langley's Automated Structural Assembly Lab
3O
Figure 3:6 DOF Merlin Robot with End Effector for Truss Assembly
(a) Isometric View (b) Top View
Figure 4:102 Strut Truss Structure
33.
3 Strategy
Like the single robot planner presented by
Dupont [7], the principle strategy of our planner is to
minimize the computationally expensive mapping of
configuration space by performing mapping on an as
required basis. The approach is based around a divide-
and-conquer style heuristic for traversing through
e-space. Computationally expensive precomputations
and exhaustive c-space mappings are avoided. The
approach is applicable regardless of the number and
type of joints in the robot and for any number of ob-
stacles in the workspace. A string tightening algorithm
may be applied to modify any safe path found by the
planner into a more efficient one, where efficiency is
measured by joint space trajectory length.
The path planning method involves first attempt-
ing to traverse a c-space vector from the start to the
goal of one of the robots. If this vector passes through
unsafe space, the hyperspace orthogonal to and bi-
secting the unsafe segment of the vector is systemat-
ically searched to identify an intermediate goal point
for consideration as a via point. An attempt is made
to traverse from the last safe point to the intermediate
goal point. This process is repeated as necessary un-
til the attempted traversal to the newest intermediate
goal .point is entirely safe. At that point, progres-
sion Is attempted toward all previous guide points in
the opposite order in which they were found, where
guide points include not only previous intermediate
goal points but also the safe points found on the goal
end of each unsafe region which invoked a search.
When progression to a particular guide point is not
entirely safe, that point is permanently dismissed and
progression is attempted toward the next g_dde point
in the specified sequence. The progression continues
until an attempt has been made to progress to the
global goal point. If that attempted progression is not
entirely successful the overall process is repeated until
the global goal point has been safely traversed to.
In 2D, the hyperspace orthogonal to all unsafe vec-
tor (the space which the heuristic searches) is simply
a line. For 2D problems, the initial search is per-
formed equally in both directions until a safe point
is found. Subsequent searches will first exhaustively
search in the direction which has a component in the
previously successful search direction. Only when no
safe point can be found in that direction will the other
direction be considered. A 2D example of the c-space
traversal heuristic is shown in Figure 5. This example
involves non-disjoint safe space and requires multiple
searches. More 2D examples and a vector description
of the heuristic may be found in [6].
In the general nD case, the search space will be
n-1 dimensional. In this case, several approaches
were considered for computing search directions. The
most effective method found involves considering all
combinations of 4-1 and 0 (except all zeros) times a
set of orthogonal basis vectors for the subspace. This
yields 3n- 1 _ 1 search directions for an n dof prob-
lem. The following vectors may be calculated in the
sequence shown and then normalized to yield one such
orthogonal basis:
B1 = (1,hl,0 .... ,0)
B 2 = (bll,P2, h2,0...,O )
B3 = (b21,b22,P3, h3,0...,O) (1)
Bn-1 = (bn-21 ,bn-22,...,bn-2n_ 2,
Pn-1, hn-1)
where the Pi are chosen so that the B i and B i_ 1 are
orthogonal, then the h i are chosen so that the B i lie
in the search hyperplane.
Initial searches favor all directions equally, whereas
subsequent searches sort the i directions S i into g
equal breadth bins by the following rule:
S i Ebin(j) if j-----_l < dPi-dpmin < J-- (2)
g - dpmaz-dPmi n - g
where dpi is the dot product of S i with the previously
successful search direction, and dPmin and dpmaz are
the minimum and maximum dPi , respectively.
Searches then exhaust bin(i) before considering
bin( i + 1).
3.1 Completeness
Unfortunately, this path planning method is not
complete, i.e., it cannot guarantee finding a solution
even if one exists. Though certainly undesirable, this
lack of completeness does not seem unreasonable since
researchers have thus far been unable to develop algo-
rithms which achieve both completeness and practical-
ity for reasonably difficult yet practical pathplanning
problems for more than a few degrees of freedom. We
sacrificed completeness in exchange for the possibil-
ity of solving some practical yet potentially difficult
problems as quickly as possible.
3.2 String Tightening
Once a safe path is found, it may be modified to
reduce the joint space trajectory length of the path.
This process is referred to as string tightening [7].
Since the path planner produces discretized paths, the
objective during string tightening is to reduce the fol-
lowing cost function:
N-I I n
Liv = _ _(0j(i+l)-0j(i))' (3)
i=l j=l
where:
L1N = the joint space trajectory length
N = number of knot points in path
n = number of dof
Oj(i) = i th knot point for joint j
32
goaL
.-k
I
So.£e space , • •
safe
Figure 5: 2D Example of C-Space Traversal Heuristic
The tightening algorithm involves examining each
sequence of three adjacent knot points and performing
whichever of the two options below produces the most
desirable effect on L_:
1. Make no changes to tile knot points.
2. Modify the second knot point so that the three
knot points are straight in the robot's joint space
(if not already so).
The feasibility of option 2 must be determined by
checking the configuration for interference. These lo-
cal adjustments are continued along tile length of the
path until no significant improvement can be obtained
from further adjustments.
4 Implementation
In addition to having been implemented for sin-
gle and cooperating robot path planning problems for
the CIRSSE testbed, the path planning strategy de-
scribed in this paper has been implemented for the
ASAL path planning problem described ill Section 2.
The programs are written in C and utilize sections of
code developed by Schima [8]. They also ius:oke meth-
ods and code developed by Hamlin and Kelley [9, 10].
The polytope representation scheme was chosen be-
cause it permits accurate modeling of the robots and
typical obstacles in the workcell while enabling rel-
atively fast interference checking. Paths are visually
simulated using CimStation [11]. The implementation
uses 242 search directions and 5 bins for search direc-
tion prioritization.
Since this was a preliminary implementation in-
tended to evaluate the possible usefulness of the path
planner for the ASAL path planning problem, some
simplifications were made:
• Nodes were not modeled.
• In the ASAL, panels are installed (the first set af-
ter the 60 fh strut). These panels were not mod-
eled (except for one particular strut as a case
study).
5 Results
The path planner quickly found paths for the first
21 struts since there is little possible interference at
that stage. Due to symmetry, the assembly of the
remaining 81 struts can be accomplished using only 21
unique trajectories for the Merlin with the appropriate
carriage and turntable positions for each strut. The
path planner was able to find feasible paths for all
102 struts with solution times ranging from 1 to 30
minutes on a SparcStation 1, with the vast majority
of solution times in the 2 to 5 minute range.
The 61 st strut is possibly the most difficult from a
path planning perspective due to the confined location
of the goal position and due to the presence of an
installed panel above the goal position. Although this
implementation generally ignored the panels, a panel
was modeled as an obstacle for this strut. In spite
of the panel, a path was found without requiring any
intermediate carriage/turntable positions. The path
found for this strut is illustrated in Figure 6.
Some particular comments regarding this imple-
mentation follow:
• The path planner has no trouble with goal posi-
tions placing the load or robot in very close prox-
imity to obstacles.
• The path planner performs well even with a large
number of obstacles. For example, the final few
struts of the assembly involve over 100 workspace
obstacles. The additional collision checks re-
quired near the end of the assembly seem to
increase execution time by a factor of approxi-
mately two.
33
(a) Start Position
(c)
(e)
(b)
-;q '.:,::.
'_,,_Sa@'.N;,,-, /kR==
,,._.._,......_;-, // \\
.,.'_,. -.,
•,-...'_..,:,,,'_.,_:,//XX
(d)
(f) Goal Position
Figure 6: Sample Results for 61st Strut (Side Views)
3h
• The paths found typically include segments which
are obstacle boundary tracing. Because of the
close tolerances involved, it is not practical to sim-
ply model the objects larger than actual size to
provide a safety margin since doing so would often
result in an unsolvable problem.
• Panels and nodes were not modeled. As a result,
some of the paths might collide with the panels or
nodes if the paths were used in an actual assem-
bly. This could be remedied simply by modeling
the panels and nodes and including them in the
collision Checking routine. Due to the small size
of the nodes it is expected that including them
would have little impact on the difficulty of the
path planning problems. Although the panels
will typically represent significant obstacles to be
avoided, a strut for which the panels would seem
to interfere the most was solved with the relevant
panel modeled.
• In a few cases the path planner was not able to
solve the problem quickly in the forward direction
but could quickly solve the problem in the oppo-
site direction. Although a very confined goal po-
sition makes it likely that solving in reverse may
prove easier, trial and error was the only sure way
to decide which direction would yield better per-
formance.
• Return paths for the robot after inserting a strut
were not planned.
6 Conclusions and Future Work
This implementation of the path planner for the
ASAL assembly task illustrates the potential useful-
ness of the path planning technique developed at
CIRSSE for solvingthe practical and potentially very
difficult ASAL path planning problem. Based oil the
results of this study, additional work appears war-
ranted towards applying this planning teclmique to
the path planning problems at the ASAL. Some par-
ticular issues which would need to be addressed before
paths created by the planner could be executed on the
actual hardware are as follows:
• Nodes and panels need to be modeled.
• An improved string tightening algorithm or an al-
ternate method of path modification is required
to provide paths with adequate clearances. This
could be done by modifying the current string
tightening cost function to include a penalty
on clearance or by utilizing the path found by
the planner as input to a potential fields based
smoothing algorithm.
Acknowledgments
This work was supported by NASA grant NAGW-
1333.
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35


Application of the CIRSSE cooperating robot path planner to the NASA Langley truss assembly problem

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