Multiplegoal task realization utilizing redundant degrees of freedom of task and tool attachment optimization
ABSTRACT Minimizing the task completion time of manipulator systems is essential in order to achieve high productivity. In this paper, this problem is dealt with by utilizing the redundant degrees of freedom (DOF) of a given task and the tool attachment optimization. For example, in a visionbased inspection where a camera is held by a manipulator, the extra DOF can be brought about by allowing the camera to be translated along its approach axis or rotated about this axis when capturing images. Furthermore, the manipulator endeffector position and orientation is optimized by designing an additional linkage at the manipulator endeffector which is called a tool attachment. A 7DOF manipulator system is used in the simulations to verify the proposed approach. Results showed that this approach can minimize the task completion time by about 17% compared to conducting only motion coordination.
 Citations (13)
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Conference Paper: Hybrid design for multiplegoal task realization of robot arm with rotating table.
[Show abstract] [Hide abstract]
ABSTRACT: The minimization of task completion time of robot arms has been an extensively studied area in robotics. Previous researches mostly focused on optimization methods for the motion planning and collision avoidance, which did not involve any modifications in the hardware design of a robot arm. Some researches, on the other hand, fully design a specialized robot arm for a given task. In this study, we propose a hybrid design composed of a hardware design and an optimization method. The hardware design is a tool attachment, which is a fixed linkage attached between the endeffector of a robot arm and a tool. In the optimization method, we incorporate base placement design, goal rearrangement and collision avoidance through motion coordination in order to minimize the task completion time of a robot arm. Our proposed design is tested using a 6DOF robot arm and a 1DOF rotating table. The method is evaluated over a single task and a set of tasks showing its effectiveness and applicability for practical applications.2009 IEEE International Conference on Robotics and Automation, ICRA 2009, Kobe, Japan, May 1217, 2009; 01/2009  SourceAvailable from: psu.edu
Conference Paper: Multiplegoals path planning for coordinate measuring machines
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ABSTRACT: Path planning is a crucial step in automatic programming of coordinate measuring machines(CMMs). The goal is to generate an efficient and collisionfree path for the CMM to inspect a collection of points. Previous research concentrates on path planning between two points, or sequencing the points without regard to obstacles and collisions. In this paper we propose a practical path planner that considers both sequencing and collision avoidance. The main idea is to create a roadmap of freespace, where the measurement points are nodes in the network. Once all the measurement points are in a single connected component of the roadmap, then a tour of the points is found by solving the appropriate traveling salesperson problem. CMM heuristics are used to construct the roadmap in an efficient and robust manner. The planner has been implemented and tested on realworld mechanical partsRobotics and Automation, 2000. Proceedings. ICRA '00. IEEE International Conference on; 02/2000  SourceAvailable from: Philippe Bidaud
Conference Paper: Genetic design of 3D modular manipulators
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ABSTRACT: This paper proposes a method for task based design of modular robotic systems using genetic algorithms (GA). We introduce a 3D kinematic description for modular serial manipulators and a twolevel GA to optimize their topology from task specifications. Revolute and prismatic joints are considered and the number of DOF is let to the GA to determine (allowing redundant manipulators). The upperlevel GA is dedicated to the topology evolution and uses the lowerlevel GA to search for inverse kinematics problem solutions. The topology is evolved for adaptation to a global task constituted by several required end effector configurations (subtasks). The implemented GA optimizes several performance criteria under constraints. To illustrate the method capacities, an example is presented for a redundant manipulator in a cluttered workspaceRobotics and Automation, 1997. Proceedings., 1997 IEEE International Conference on; 05/1997
Page 1
Abstract— Minimizing the task completion time of
manipulator systems is essential in order to achieve high
productivity. In this paper, this problem is dealt with by
utilizing the redundant degrees of freedom (DOF) of a given
task and the tool attachment optimization. For example, in a
visionbased inspection where a camera is held by a
manipulator, the extra DOF can be brought about by allowing
the camera to be translated along its approach axis or rotated
about this axis when capturing images. Furthermore, the
manipulator endeffector position and orientation is optimized
by designing an additional linkage at the manipulator
endeffector which is called a tool attachment. A 7DOF
manipulator system is used in the simulations to verify the
proposed approach. Results showed that this approach can
minimize the task completion time by about 17% compared to
conducting only motion coordination.
I. INTRODUCTION
are ANIPULATORS
manufacturing due to their accuracy and flexibility.
Typical tasks of manipulators are inspection and spot
welding wherein several goals have to be reached. In
realizing these tasks, there are two factors that are essential
in order to minimize the task completion time: (1) the
redundancy inherent to a given task and (2) the suitability of
the manipulator to the task.
The factor stated in (1) can be related to how goals are
defined as input to the problem of multiple goal task
realization. In [1], for instance, a goal corresponds to a
distinct solution in the manipulator inverse kinematics (IK).
In other works [2][3], goals are defined by positions with
corresponding orientations in the Cartesian spaces. In some
research [4], each goal is mapped to a goal group, which is a
set of manipulator configurations. In this study, however,
(1) is defined based on the given task without reference to
the manipulator system used. To expound, consider a
manipulator inspecting an object by capturing images on
some parts of it. In this task, a camera, which is attached at
commonly used in
L. B. Gueta, J. Cheng and J. Ota are with Research into Artifacts, Center for
Engineering, at the University of Tokyo, 515 Kashiwanoha, Kashiwa,
Chiba, Japan, 2778568.(email:{gueta, ota}@race.utokyo.ac.jp).
T. Arai is with Department of Precision Engineering, School of
Engineering, at the University of Tokyo, 731 Hongo, Bunkyoku, Tokyo,
Japan, 1138656. (email: araitamio@robot.t.utokyo.ac.jp).
R. Chiba is with Faculty of System Design, Tokyo Metropolitan
University, 66, Asahigaoka, Hinoshi, Tokyo, Japan, 1910065.
(email: rchiba@sd.tmu.ac.jp).
T. Ueyama is with DENSO WAVE INCORPORATED, 1, Yoshiike,
Kusaki, Aguicho, Chitagun, Aichi, Japan, 4702297
the manipulator endeffector, can capture images at a
number of candidate positions and orientations along the
approach axis. Such deviation or extra DOF of task can be
made as long as the captured image is usable in inspection.
As for (2), it is possible that a manipulator is mismatched
to a give task since normally the manipulator is assumed to
be given prior to defining a task. A 6DOF manipulator with
a spherical wrist, for instance, is considered as a
generalpurpose manipulator; however, it may have
limitations due to its structure such as link lengths. In
dealing with this limitation, the taskbased manipulator
optimization proposes creating a manipulator based on a
given task specification [5][8]. The algorithms either
directly calculates the DenavitHartenberg parameters of a
manipulator [5], [6] or creates a manipulator based on some
predefined modules [7], [8]. Although it is effective in
minimizing task completion time, this optimization is not
practical in manufacturing where variability of tasks is
unavoidable. It could entail large fabrication costs and incur
substantial delay from design to actual system setup.
In this paper, we aim to minimize the task completion time
of a manipulator system by addressing the two
aforementioned factors. One method we employed, which is
referred to as the goal pose optimization, is to utilize the
redundancy inherent to a given task as in the case of
visionbased inspection. Moreover, we propose the addition
of tool attachment, which is a linkage added between the
manipulator endeffector and tool. It is more costeffective
(i.e., lower fabrication cost) than designing an entire
manipulator. For simplicity and practical reasons, it is
designed as a fixed linkage without moving parts in this
paper. The tool attachment optimization was introduced in
our previous works [9], [10]. Since the manipulator system
(Figure 1) is kinematically redundant, we employ motion
MultipleGoal Task Realization Utilizing Redundant Degrees of
Freedom of Task and Tool Attachment Optimization
Lounell B. Gueta, Jia Cheng, Ryosuke Chiba, Tamio Arai, Tsuyoshi Ueyama and Jun Ota
M
goals
Object
Rotating table
Tool
attachment
Tool
Approach
axis
E
T
(a) (b)
Fig.1 A manipulator system with a tool attachment which is a linkage
between the manipulator endeffector and tool.
2011 IEEE International Conference on Robotics and Automation
Shanghai International Conference Center
May 913, 2011, Shanghai, China
9781612843803/11/$26.00 ©2011 IEEE 1714
Page 2
coordination as a part of the proposed approach.
II. PROBLEM FORMULATION
As shown in Fig. 1(a) the manipulator system is
composed of a 6DOF manipulator and a 1DOF rotating
table. The manipulator has to reach all goals in a specific
order. Concurrently, the table rotates and positions an object
placed on it. The task consists of n number of goals gi,
i=1...n which are located on the object. In executing the task,
the tool pose (e.g. camera position and orientation) has to be
positioned and oriented depending on gi.
The configuration of the manipulator and rotating table at
goal i is denoted as qi = ( i 0... i 6) where i 0 is the table
joint angle and i 1... i 6 are the manipulator joint angles. In
Fig. 1(b), E and T denote the reference coordinate frames of
the manipulator endeffector and tool tip, respectively. In
this paper, the transformation matrix between these two
frames is optimized through the tool attachment
optimization.
A. Goal Pose Definition
Figure 2 illustrates the definition of goal pose. Commonly,
a goal is defined by a position (x, y, z) and an orientation (roll,
pitch and yaw). In this paper, a goal is defined by a position
(x, y, z) with an associated tool approach axis (zaxis). This
definition is distinct in two ways:
1) The goal rotation about the zaxis, a, can be varied for
a certain range of values:
min
where min
maximum values of a.
2) The z value of the goal coordinate along the tool
approach axis can be varied and is bounded by:
z min
where zmin
of z a measured along the approach axis of a given goal. As
shown in Fig. 2, the possible goal poses or locations can be
a a max
a are userdefined minimum and
a (1)
a and max
a z a z max
a are the minimum and maximum values
a (2)
a and zmax
represented as a line along the approach axis with an
associated orientation about that axis.
B. Manipulator EndEffector Pose
With the addition of a tool attachment, the manipulator
endeffector E is adjusted relative to T depending on the tool
attachment design. The tool attachment is defined by the
following parameters: (ExT, EyT, EzT) is the displacement of
the tool tip T relative to the manipulator endeffector E. The
(ET, ET, ET) are the roll (rotation about the zaxis), pitch
(rotation about the yaxis), and yaw rotation about the
xaxis) describing the relative orientation of T and E.
C. Performance Index and Constraints
The total pointtopoint motion of the manipulator and
table in reaching all goals has to be minimized and is
calculated using (3).
1
cggcf
ii
where f is the task completion time, c(•) is the motion time
from gi to gi+1 and g0 is the home position of the manipulator
and table before and after task execution.
Minimization of f is subject to the joint and velocity limits
of the manipulator and table. Further, a calculation time limit
is imposed so that solutions are derived within a reasonable
amount of time.
),(),(min
0
0
1
gg
n
n
i
, (3)
D. Design Variables
In summary, the following variables are designed:
A = (zi
B = (ExT, EyT, EzT, ET, ET, ET ), and
qi, i=1…n.
The subscript i corresponds to goal i. The parameter A
corresponds to the optimized goal pose parameters such as
the translation zi
approach axis. The variable zi
axis; thus if it is varied the xi, yi, zi values of gi will change.
The parameter B corresponds to the tool attachment
parameters wherein ExT, EyT,
the tool tip from the manipulator endeffector and ET, ET,
ET are the roll, pitch, and yaw describing the relative
orientation of the tool tip with respect to the endeffector.
The variable qi, i=1…n denotes the manipulator
configurations at gi i=1…n.
a, i
a), i=1...n,
a along and rotation i
a is defined along the approach
a about the tool
EzT describe the displacement of
III. PROPOSED APPROACH
In this section, the problem is first analyzed and the
proposed approach is then discussed.
A. Problem Analysis
Figure 3 illustrates the case when a tool attachment is
added between the manipulator endeffector and tool and is
z
zmina
zmaxa
a
zaxis
a, min
a, max
Tool attachment
Tool
Fig. 2 Goal pose definition. A goal shown as a red dot is defined by a range
of positions from zmin a to zmax a along the tool approach axis (the zaxis) and
a range of rotational values from a,min to a,max about the zaxis.
1715
Page 3
rotated about the tool approach axis (i.e., when
The manipulator endeffector position and orientation E
relative to that of the tool tip T can be thought of as a single
vector for a goal defined by a single pose (i.e., position and
orientation). With the goal definition in this paper, the
possible positions of a tool attachment can be described by a
cylindrical surface as a result of the translation along and
rotation about the approach axis. These manipulator
endeffector positions are valid provided that the
manipulator can achieve its corresponding configuration and
no collision occurs. A valid location of E on this surface
depends primarily on the manipulator link lengths and joint
limits. The search space for selecting the optimized goal
pose and the tool attachment design can therefore be thought
of as surfaces of concentric cylindrical shape. In addition,
since the manipulator system is kinematically redundant, the
goal locations as the table is rotated into several angles are
numerous which means that the number of inverse kinematic
solutions is infinite.
The problem is highlydimensional given the number of
design variables. For n number of goals, the number of
design variables in the goal pose optimization is 2n (i.e., zi
and i
number of unknowns increases with n. In the tool attachment
optimization, the number of design variables is 6 which are
the translation and rotation parameters of the transformation
matrix of T relative to E. Considering the manipulator
system having 7 DOFs, the total number of variables is at
least 9n+6.
In optimization problems, the mathematical expression
for the objective function is necessary to derive optimal or
neartooptimal solutions. In this study, deriving this
expression is complex due to the nonlinearity in the
manipulator kinematics, the existence of several goals, the
redundancy of the system, and potential collision among the
manipulator, tool, and object. A straightforward solution to
this problem is to treat all the design variables as a single set
and use a monolithic solver or optimizer to find the best
a is varied).
a
a for every goal i). Note that in this optimization the
solution. Such a solution, however, may not consider the
uniqueness of subdomain problems constituting the entire
problem that may have existing practical solutions.
Furthermore, a monolithic solver may require substantial
calculation time as the number of goals increases.
B. Overview of Proposed Approach
In this paper, we propose to divide the problem into
subproblems for the purpose of finding a practical solution
within a reasonable amount of time. Figure 4 shows the
proposed approach composed of two stages. Stage 1 is the
goal pose and tool attachment optimizations while Stage 2 is
the motion coordination between the manipulator and table.
The tool attachment and goal pose are first derived; then the
motion coordination is dealt with. Afterwards, the task
completion time is calculated. The optimization is an
iterative process and is terminated if the design time limit
tdesign is reached.
The first stage precedes the second stage because the
former defines the manipulator system kinematics that is
necessary in the second stage to calculate manipulator
configurations, perform collision detection, and compute
task completion time. The motion coordination is important
so that the object can be oriented at a position reachable by
the manipulator. The goals can be located around the object
and may not reachable without motion coordination.
Stage 1 is discussed in Section IIIC while Stage 2 is
discussed in Section IIID. The detail of task completion
time calculation is provided in Section IIIE.
C. Goal Pose and Tool Attachment Optimizations
In the goal pose optimization, the objective is to derive the
A value (i.e., zi
tool attachment optimization it is to derive the B value (i.e.,
ExT,
mathematical function expressing f is difficult to derive;
therefore a direct method is used in this study. Exploring all
the solutions is not feasible given the size of the search space
(i.e., all the possible solutions). Moreover, due to collision
a and i
a), of every goal i i=1…n while in the
EyT,
EzT,
ET,
ET,
ET). As aforementioned, the
Possible pose of
manipulator endeffector E
T
a
Fig. 3 Endeffector pose. The figure is the result of superimposing images
of the manipulator when the tool is rotated about its approach axis.
Fig. 4 Proposed approach
Input parameters Output parameters
yes
Task completion time calculation
Tool positions and orientations
 Manipulator and table
kinematic properties.
 Design time limit, tdesign .
no
Is calculation
time< tdesign?
Motion coordination
 Tool attachment length
and orientation
 Goal position and
orientation
Manipulator and table
configurations
Goal pose and tool attachment
optimizations
1716
Page 4
occurrences, the search space can have several local minima
which prevent from deriving a goodquality solution. To
avoid such case, stochastic direct methods are applicable. In
this paper, we used the simulated annealing (SA) algorithm.
SA is based on stochastic local neighbor search method. It
is robust despite the search space complexity and can avoid
local minima. It is unique from other algorithms on how it
chooses its neighborhood and selects a worse solution over
the current solution. The probability of accepting a worse
solution is too high at the start and is subsequently reduced
for each phase. The decreasing probability of accepting
solution is analogous to the temperature reduction in the
actual annealing of a metal, which is slowly cooled from a
high to a low temperature to allow the formation of a
highquality metal. See [11] and [12] for details of SA.
Figure 5 shows the steps in SA. Suppose we denote X as
the set of all design variables of the goal pose and tool
attachment optimizations (i.e., A and B). Moreover, current,
best and new denote the current, best, and new solutions.
The values of f from these solutions are denoted as f current
f new, and f best, respectively. The variable C controls the
degree of accepting a worse solution. Initially, C=Cmax,
which is prespecified with a high value. Gradually, the
value of C is reduced by a factor Cfactor, a prespecified value
between 0 and 1. SA iterates (i.e. one execution of Step 3) as
long as the calculation time is less than tdesign. One iteration
consists of several phases; the phasemax value sets the
maximum number of phase per iteration. In Step 3.1, the
neighbor( ) is a function that returns a randomly generated
value adjacent to which is calculated by incrementing or
decrementing the values of the design variables. In Step 3.4,
the function U returns a value between 0 and 1 from a
uniformly distributed random number.
,
D. Motion Coordination
In the motion coordination, the extra DOF (the table
rotation) is utilized to avoid collision while imposing a
straightline motion in the manipulator configuration space.
A graph search method is employed wherein a stage is
defined as the motion of the manipulator and table from a
previous goal position to the next goal position. The stages
i = 0 and i = n+1 correspond to the position of the
manipulator and table at g0. Every vertex in each stage
represents the goal position rotated by the table at various
angles. The table angle i
variable l defined in (4).
i
d(r) = ( 0,max  0,min )/r, r1 (5)
where r is a userdefined resolution of the table rotation, d is
the step, and 0,min, and 0,max
minimum search limit values for i
assigned with values ranging from 0,min to 0,max
assigned value, i
manipulator inverse kinematics (IK). If an IK solution
exists, the configuration is said to be valid. For every valid
configuration, the motion time is calculated using (6), which
assumes that a joint achieves its maximum velocity in a very
short time.
c (gi, gi+1)=
6...0
j
where v j,max is the maximum velocity of joint j.
A different motion profile can be considered that takes
into account acceleration; a related work is conducted in
[13] employing a trapezoidal joint motion profile.
In dealing with the multiple IK solutions, the next
configuration of a manipulator when reaching a goal is
selected based on the previous configuration. This method
does not provide a global minimum solution but reduces the
complexity of the configuration search space.
The size of the search space and the method employed in
finding the solution determine the required amount of design
time. With respect to the number of goals and resolution, the
size of the search space is n·r. An exhaustive search method
that evaluates all the possible i
of rn combinations which is exponential with n and can
require a large amount of calculation time.
0 is parameterized into a single
0(l) = 0,min + r·l·d(r) , l{0,1/r, 2/r…1} (4)
are the maximum and
0. The parameter i
0
is
. For every
1… i
6
are derived by solving the
max
( i+1 j  i j /v j,max) (6)
0 values can require a total
E. Task completion time calculation
Based on the abovementioned search space, the joint
angle value of i
neighbor algorithm because it is fast and noting that the
motion coordination is invoked several times (i.e., it is
invoked every time an X value is evaluated). For the nearest
neighbor algorithm, the number of i
n·r, which is linear with n.
In calculating the task completion time based on the
nearest neighbor algorithm, the cl (gi, gi+1) is the motion time
from stage i to stage i+1 at a valid goal location defined by l
and C i is the least motion time at stage i.
)},({ min
10
1 ...0l
1
21
1 ...0
l
i
iil
l
1 ...0
0
for every gi is selected using the nearest
0 values evaluated is
1
ggcC
l
, (7)
2
)},({ minCggcC
l
, (8)
i
CggcC
)},({min
1
1
, (9)
Fig. 5 SAbased algorithm
1. Initialize design variable current.
2. Set best current and C = Cmax.
3. while calculation time < tdesign
3.1. new neighbor( current).
3.2. If fnew< fbest, then best
3.3. =fnew fcurrent.
3.4. If ≤0, then current new. Else, generate uU.
3.4.1 If u e(/C), then current new.
3.4.2 Else, do not change current.
3.5. phase=phase+1.
3.6. If phase<phasemax, go back to 3.1.
3.7. C= Cfactor*C.
4. Exit.
new.
1717
Page 5
n
n
Cggcf
),(
0
. (10)
The f value is the calculated task completion time as a
result of evaluating the goal pose and tool attachment design
and deriving the manipulator and table configurations in the
motion coordination.
IV. SIMULATION, RESULTS AND DISCUSSION
This section describes the simulations conducted, the
results and discussion. The setting of the important
parameters is provided in Table I. In the values of zmin
zmax
given positions along their corresponding approach axes.
The rotation about the approach axis has limits of min
180 and max
attachment parameters (ExT, EyT, EzT) is varied from 0 to 300
[mm], which is set based on the initial setting. Figure 6
shows the initial simulation setting wherein the tool is
directly held by the manipulator. The number of goals is
varied from 20 to 40. The positions are located around the
object such that the table has to be rotated so that the
manipulator can be able to reach goals without collision. The
goals are not lying on the object but are instead at a distance
from the object as in the case of an inspection task. The
initial manipulator base placement, although is not
optimized, is derived based on an empirical method, e.g.
70% of manipulator reach [13]. The calculation time limit is
1 hour which is, based on our experience, enough to derive a
good quality solution for the given number of goals. Similar
to typical SA implementation, C is initialized to a large value
C0 (e.g. 100) and is gradually reduced by a factor of 0.99.
The simulation is conducted using an Intel Core Duo
3.0GHz processor with 4GB memory.
a
and
a, gi are varied from 10[mm] to 10[mm] relative to the
a =
a= 180 to cover one full rotation. The tool
A. Evaluation of Proposed Approach and Other Methods
The following methods are compared:
MC: motion coordination only,
TA+MC: tool attachment (TA) with MC,
GO+MC: goal pose optimization (GO) with MC,
TA+GO+MC: TA with GO and MC (the proposed
approach)
MC is the reference method since it is the most basic; the
other methods are combinations of one or two optimizations.
Each method is run 5 times and the best solution of each
method is selected.
Figure 7 shows the performance of compared methods.
For all n settings, the same trend is observed in which
TA+GO+MC (the proposed approach) has the best
performance; the improvement is significant which is on the
average 16.65 % relative to MC. On the other hand, the
performance of TA+MC is 12.00% relative to MC. With
GO+MC, it can be seen that minimal task completion time
can be achieved by properly choosing the goal pose, which
is better than MC by 10.52%. Based on the result of
TA+MC and GO+MC, the tool attachment optimization
provides more flexibility than the goal pose optimization.
For example, the tool orientation can be varied by 3 design
variables using the tool attachment optimization whereas in
the goal pose optimization, only the rotation in the approach
axis is varied. Furthermore, a tool attachment adds
reachability (i.e., ExT,
performing task. The combined effect of TA and GO is
evident in the proposed approach, which achieves the least
task completion time among the compared methods.
Figure 8 shows some snapshot of the animation for
TA+GO+MC. These figures shows the manipulator and
table configurations when reaching goals. We observed that
when the manipulator is moving from one goal to another
goal especially in those goals at the corner of the object, the
tool is being rotated about its approach axis that results to
minimal motion time. This observation is not evident in MC
and TA+MC.
EyT,
EzT) to the manipulator in
E: (0, 0, 600)
T: (0, 0, 500)
B: (600, 0, 0)
(0, 0, 0)
z
z
x
y
x
y
200
Values are in [mm].
100
Fig. 6 Initial simulation setting
TABLE I
SIMULATION SETTING
Parameters Values
zmin
min
(ExT, EyT,EzT)
(ET, ET,ET)
a
, zmax
a, max
a z a /+ 10 [mm]
/+ 90
(0,10..290, 300) [mm]
180, 170…,170, 180)
a
n 20, 30, 40
0
0.5
1
1.5
2
2.5
3
3.5
4
30 4050
MC
Fig. 7 Performance of compared methods
TA+MCGO+MC TA+GO+MC
Task completion time (s)
20 30 40
Number of goals
1718
Page 6
We also performed a simulation to know if integrating the
motion coordination is justified in our proposed approach.
This evaluation is necessary since the calculation time
requirement would be lessened if the motion coordination is
not included in the iteration. We found that the motion
coordination has to be integrated with the tool attachment
and goal pose optimizations in order to derive goodquality
solution. Without integrating the motion coordination, the
table rotation angles can be derived only at the start of the
optimization of the goal pose and tool attachment; the
improvement of this method is minimal (i.e., at most 3%
relative to MC).
The proposed approach can be evaluated to other
manipulator systems. Since the goals in this paper are at a
distance to the object inspected, it will be interesting to
consider more restrictive condition. In addition, instead of
employing simple motion coordination, sampling based
motion planning can be utilized to evaluate the proposed
approach.
V. CONCLUSION
In this paper, the motion of a 6DOF manipulator and a
1axis rotating table is minimized in a multiplegoal task.
We propose optimizing the goal and manipulator
endeffector poses. The proposed approach is different from
a conventional method wherein the manipulator endeffector
pose is directly derived based on given goal poses in a way
that the achievable manipulator configurations are
constrained by a given goal pose. As a solution, the goal
position along the tool approach axis and the rotation about
this axis are optimized. In addition, the tool attachment
optimization is employed to optimize the manipulator
endeffector pose. The result showed that the proposed
approach has the best performance compared to other
methods. The reduction in the task completion time is 17%
compared to employing only motion coordination.
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Fig. 8 Snapshots of the result in using the proposed approach with 20 goals. From left to right, the manipulator and table configurations at g1, g3, g4 and g5.
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