NASA Technical Reports Server (NTRS) 19930002774: A neuro-collision avoidance strategy for robot manipulators

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N93-1! 962 '
A NEURO-COLLISION AVOIDANCE STRATEGY FOR ROBOT
MANIPULATORS.
Joel P. Onema and Robert A. Maclaunchlan*
Department of Electrical Egineering and Computer Science
,Department of Mechanical Engineering and Industrial Engineering
Texas A & I University, Kingsville, Texas 78363
ABSTRACT which can beconsidered as embody by a sensitive
skin type sensors [1]. We study the following
The area of collision avoidance and path planning in problem: given the position and orientation of the
robotics has received much attention in the research manipulator, calculate all possible sets of joint angles
community. Our study centers on a combination of an over time,, which could be used to attain a given
artificial neural network paradigm with a motion planning
strategy that insures safe motion of the Articulated Two-Link object position and orientation. The initial solution
Arm with Scissor Hand System relative to an object. to the problem enables the manipulator to attain its
Whenever an obstacle is encountered, the arm attempts to goal without a planned strategy (no collision
slide along the obstacle surface, thereby avoiding collision by avoidance). The final strategy used combines motion
means of the local tangent strategy and its artificial neural planning and artificial neural networks. This
network implementation. This combination compensates the strategy is to insure a collision-free motion of the
inverse kinematics of a robot manipulator. Simulation results robot manipulator. Simulation results are presented
indicate that a neuro-collision avoidance strategy can be and a possible extension to this work is discussed.
achieved by means of alearning local tangent method, This paper is an extension to the work reported in [1,
4].
I. INTRODUCTION
The problem of collision avoidance in II. AN ADAPTIVE LEARNING APPROACH
robotics[8] Bradley, Hollerbach, Johnson and Lozano
Perez can be described as follows: given a starting The subject of neural network is hardly
and a goal configuration of some object or linked new[14], but there has been much more recent[Ill
group of objects in an environment cluttered with progress in developing methods for training more
obstacles, find a path of connecting line segments complex configurations of these networks. The
from the starting to the goal configuration, such that simplest net is the perceptron [13, 14], whose
the object to be moved follows this path without training procedure can be called an error-correcting
interfering with any obstacle of the environment. procedure. The weights are revised whenever a
mistake is made. Both the output and the correct
Traditionally [1], designing a robot control
answers are expressed as 0 or 1else an error occurs.
system involves two steps first a set of kinematic
For the perceptron, once the weighted sum is
equations which express the physical constraints of
computed, the activation of the output unit is
the robot are derived, and second, a computer
determine by a threshold logic (0 or 1) depending
program model is implemented generatin_ arm whether the threshold value was exceeded. The
configuration sequences that move the robot s end- thresholds activation function creates nonlinearity.
effector from its current position to a target position. When The Classes of behavior, etc. are linearly
While simulation runs works well in a laboratory,
separable the perceptron will find a line or a plane
they often suffer from serious limitations when
that yields no error. It concentrates on reducing
applied in realistic environments. Wear and tear on
errors, but may perform poorly when classes of
mechanical parts changes the kinematics of the robot behavior etc, are not linearly separable.
manipulators and sensor characteristics tend to
wander with time. V_rhen such changes occur, the In the LMS[12] (Least Mean Square) learning
control program must be updated or the robot must system, the correct answers are still express in terms
be maintained. The response time slows down when of 0 and 1, however they are not restricted to a
the degree of difficulty increases by unpredictable binary values but can have continuous real values.
obstacles with different shapes or change of position The goal of the LMS training procedure is to
in the workspace. A high degree of autonomous minimize the average (squared) distance from the
adaptive learning is the ultimate approach to true answer to the output. The LMS training
consider when solving these major impairments. This procedure performs relatively well when classes are
paper focuses on solving the inverse kinematics of an not linearly separable, because the best line of
articulated two-link arm with a scissor hand system separation is found in terms of the minimum error
272
distance.Tocomputeerrorrates,decisiocnriteria
is based upon a simple theoretical robot
areneededtodeterminetheclassthatisselected.
klnematics[1, 3] as presented in (fig. 1) and the value
Forasingleoutputthisistheclassthatisclosestot
of the local tangent as presented in[2].
theoutput.Theerrordistancteothecorrecatnswer
canbesmall,whileerroneouasnswerms ayhave III. LOCAL TANGENT
largerdistanceor beon thewrong sideof the
boundaryE.ventuallyL,MStrainingshouldconverge The robot arm attempts to slide along the
totheminimumdistanceT.hisiterativetechniquoef obstacle surface as reported in [2] (Fig. 2), whenever
minimizatioinsalso an obstacle is encountered. This sliding is
called gradient descent[12]. The
accomplished by a coordinated move between joints
weights are constantly adjusted in the direction of
J1 and J2, based on the value of the local tangent
the greatest reduction of error, example we expect
Fig. 4). The local tangent is obtained from the
that we are moving "down bill" in tile direction of ollowing formulas depending on were the obstacle
the minimum. The main problems for gradient occurs in the work space. There are three categories
descent methods is oscillation and not converging or (Fig. 3). Note: a complete derivation of the following
poor convergence rate. The rate of convergence equation can be found in [2]
highly depends on the learning rate[11, 12]. The Type I are those obstacles that obstruct link
LMS learning system is completely linear. The
1. Since link 2 is irrelevant in this case, then d01=0
weighted sum is directly used to activate the output
and d02 # 0. The local tangent for
unit; no additional mapping by tile activation
function is made. A linear function would not be
Type I is vertical [2].
useful, because the overall system would still be
linear and would not effectively use the hidden units. Type II consists of the obstacles that obstruct
While the thrcshold logic of the activation function link 2. Assume that link 2 is obstructed at point C
perceptron is nonlinear, from tbe mathematical view by a type II obstacle, at the distance L,_ from the
point, the LMS needs a continuously differentiable joint J2 (Fig. 4). Then, the estimates [2]_of d01,and
function. This is not the case for threshold logic. d02 at C can be found as follows:
Thus an alternative is activation function which is
differentiable is used known as a logistic or sigmoidal cx=L 1COS(0)+LdCOS(01 +02)
function. For any real valued numbers, the
activation function is a continuous value, this is a x coordinate of C (1)
valid range in probability, these functions have been
widely used in statistics. cy=LiSIN(01)+LdSlN(01+02)
Both the perceptron and the LMS learning
y coordinateofC
System attempt to derive a linear separator from
The expressionforthe localtangentof type IIat
labeled data. Perceptron and LMS can be described
point C is given by the estimate [2]:
as single layer neural networks, where a layer
represents a set of output devices. The weights are
termed feed forward, because they flow in the = os0_+l (2)
forward direction. Starting with the inputs node and
weights, no weight cycles back to an input node or Type III are obstacles that obstruct the
output node of previous layers. wrist. Sliding of the wrist P along the obstacle
corresponds to its moving along the llne segment LM
Very few real-world applications are truly
(Fig. 4). fl1 is the angle between the line
linearly separable this basic discussion is beyond the
perpendicular to link 2 and the line from P to the
scope this paper. The multilayer neural network can obstacle and flo is the angle between the line LM and
be trained as by a generalized version of the LMS
the positive x $xis. Then
training procedure for a nonlinear logistic outputs
32 = 01+ 82+ fll-X. The expression for the local
known as Backpropagation [11]. We consMer this
tangent estimate [2] of type III. appears as:
paradigm to be the most suited for our needs. It is L
flexible and can be easily implemented. It is one
dO /_+COS82+SIN02 tan(02+fll)\
the most popular and widely used neural networks 2 2
today. Backpropagation has the ability to learn
mappings by example, by a process of learning [1, 3,
5, 9, 10]. It uses a learning procedure that aims to IV. LEARNING STRATEGY
minimize the mean squared error between the actual
The Neural Network is trained to map the
outputs of the network and some desired outputs.
Cartesian coordinate to the joint angle coordinate
Because of convergence problems that found in the
transformation for the three degree of freedom robot
LMS and the learning rate constraints as previously
arm. The net learns the topology and unknown
mentioned we opted for modular[i] approach. It is
transformation from presentation of examples such
much faster to train several smaller networks than
that a solution to the inverse kinematics is found
one large one. We kept the number of neuron as and an obstacle can be avoided. First, the network
small as possible, since removal of redundant neurons
is presented with a set of examples for training, then
can make noticeable difference in the training time.
tested to generate an output within an acceptable
The learning strategy that permits to solve the
tolerance. Our study centers on the following
inverse kinematics problem [5, 7] and avoid obstacles
mapping: given the Cartesian position (x, y),
273
generate the accurate joint angles. Secondly, the results of the neuro-collision avoidance Strategy have
net is trained and tested to recognize the obstacle been obtained. Our experiments have indicated that
types, (I, II, III). This permits the usage of the a modular approach is the most appropriate. The
network was able to learn and mimic a decision
local tangent and the generation of a collision
avoidance motion, in other words, the arm learns to making strategy by means of the learning tangent
slide along the obstacle surface with no contact at approach, thereby allowing the manipulator to
the tangential point. A combination of the modules achieve a collision free motion. Real-time
described above can be an important tool that can implementation of this experiment will require a
carry out the extensive computation and planning parallel architecture that can be of great benefit to
needed to achieve an intelligent move, therefore the enhancement of the overall system performance.
avoiding an obstacle. Because of the sensor data complexity, in future
work the Learning Tangent method could be
A possible real-time architecture [2] compensated by a fuzzy logic system [15] that bases
implementation of this study is presented in Fig. 10.
its decisions on inputs in the form of linguistic
Sensitive Skin sensor information and arm position
variables, for example smooth, slippery and rough.
are passed to the neural planner/ controller that In our case it will be the obstacle types (I, II, III).
generates a safe motion of the arm.
Our ultimate goal is to enhance the capabilities of
the experimental arm/hand system by means of
V. SIMULATION RESULTS
applicable findings leading to its real-time
As already stated, we opted for a modular implementation. Current applications could include
approach, since it is much faster to train several the NASA EVA Retriever and related space
smaller networks than one large net. Fig. 5 shows operation. In manufacturing, the learning tangent
the general network configuration followed by can play an important (safety) role in discerning the
subnets configurations. The subnets configurations sudden presence of an operator in the working space
are three layer networks ranging from two to five resulting from careless behavior.
nodes at the input layer and six to twelve nodes for
the middle layer and raging from one to three nodes
for the output layer. We have trained and tested the
nets for a complete mapping of the kinematic REFERENCES
transformation of the experimental arm/hand system [1] Joel P. Oncma, A Motion Planning
3 degree of freedom (dof). In our experiments [1] we StrateEv and _ its
focused on training the net by mapping the joint __ for an Articulated
angles (shoulder, elbow and wrist) and their joint Two-Link Arm yith _cissor
position. Our experiment has indicated an ease in ttand_v___._q_MS Thesis, EE_CS
training the wrist, the elbow and shoulder, because of Department Texas A_I University,
the modularity and proper data normalization. Our May 1991.
first experiment focused on the kinematics [2] Cheung, E and Lumelsky,
transformation when there is no obstacle. Maximum V. _ Proximity sensing in
and RMS (Root Mean Square) error values for a case Robot Manipulator Motion
study of 2 dof (fig. 6a, 6b) illustrate a downward Planning System and Implementation _,
IEEE Conference on Robotics and
trend, indicating the smoothness of the learning
Automation, Vol. 5 No. 6.
curves. Fig. 7a shows the expected joint position
December 1989. pp. 740-751.
results graph from the examples presented to the
network by training. Fig, 7b shows a graph
[3] Josin, G. , Charney, D. and
.depicting the network output when tested. As one
might observe the network performance is within Vofhitea,:n: UnknoAwnNeuInravlerse Representation
tolerable range when compared to the expeted results
Kinematics, Transformation",
graph. The second experiment targets the type II
Neural Systems Inc. 1989,
obstacle using simulated sensor data. Fig. 8a shows
Vancouver, B. C. Canada.
the expected results graph from examples presented
[4] Joel P. Onema, Barbara S,
to the network via training and fig. 8b depicts the
Schreur, Robert A.
network output when tested. The network output is
Maclaunchlan, Muhammed
an adaptation of the joint angles as the robot
Ashtijou, _: A Motion Planning
manipulator moves from an initial to final
Strategy and its Neural
configuration space by sliding along the obstacle
Network Implementation
surface. As one mi_.ht observe the network for an Articulated Two-Link
performance is also within tolerable range when
Arm with Scissor Hand System",
compared to the expected results graph.
IJCNN-91. Seattle, _ashington.
[5] Guez, A. and Ahmed, Z. :'Solution
to the Inverse Kinematics
VI. CONCLUSION AND
Problem in Robotics by Neural
FUTURE PROJECTION
Networks _, Proceeding of the Second
In this paper we have shown that a neural InternationalConference on Neural
network paradigm can compensate the inverse Networks, San Diego,
kinematic behavior of our model and promising California, 1988, Vol. 2, pp. 14-20.
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[6] Richard P. Paul, _ _obot KINEMATICS E_UATIONS
Manipulators:Mathematic_
rogramminz. and _", Forward transformation :
ambridge _ MA: MIT Press 1986. X= LIC{}SOI+L2COS(OI+ 02) and
[7] Guo, J. and Cherkassky, V. Y= LISINoI+L2SIN(oI+o2)
'_A Solution to the Inverse
Kinematics Problem in Inverse transformation :
Robotics Using Neural
Network Processing. COS02=(X2+y2-L21-L22!/2L1L 2
Proceeding of the IJNCNN-Sg,
7ashington DC, Yol 2.PP. 289-304. Ol=arctan (X/Y)arctan[ L2SIN02/(LI+L2COS02) ]
[8] Brady, M. J , Hollerbach, T.,
Johnson, T. Lozano' Perez L1 : length of first link
C'Robot Motion planning",
MIT Press, MA. 1982. L2 : length of second link
[9] Judith E. Dayhoff,_Neural
Network Architectures", O1 : joint of first link
Van Nostrand Reinhold, NY,1990.
[10] Kung, S. Y. and Hwang, J. N. "Neural 02 : joint of second link
Network Architecture for robotics".
IEEE Transaction on Robotics and Fig. 1
Automation. 1989. Vol. 5
Nr. 5. PP. 641-657.
[11] Rumerlhart, D.,E. and McClelland, "'.._
J. L., Parallel Distributed
Processing: Explorations in
Microstructure of Cognition,
vol. I , MIT Press, 1986. 2 / __ iY
[12] Vidrow, B., and Stearns,
S. D. Adaptive Signal
Processing , Prentice-Hall, Inc.,
Engelwood Cliff, NJ, 1985.
[13] R.P. Lipman: _ An Introduction To
Computing With Neural Nets",
IEE ASSP Magazine, April 1987, O, x
pp.4-22, perceptron.
[14] Minsky M. L. S. Paper, Perceptrons:
Pig. 2 Fig. 3
_An introduct_o_ to
computational _eometry",
MITe_E_____, Cambridge. Mass 1969.
[153 Bart Kosko ,_' Neural Network I
and Fuzzy $ystesms _,
Prentice hall, Inc.
Engelwood Cliff, NJ, 1991.
X J,
Fig. 4
275
Neural Network configuration
Learnlng the Kinematics Transformatlot_
with no Obstacle
Corrocted
|olnt inglem
OUTPUT for a oo|IlllOrl free plth
1.000
] t I 0.960 I 3 I I I I I 1 I
0,920
0.680
0,840
0.800
0,760
0.720
0,680
0.640
0,600
0,560
O.520
O.+80
iJ)
x 0.440
n,* 0.400
t t t t t I t I 1
0.360
0.320
0.280
Arm uncorrected obstacle obstacle o.240
poa|tlon Joint angles location type 0.200
O._eO
0.120
INPUT 0,080
0.040
0,003 I I I J I _ .
0 100 200 300 400 500 BOO700 BDO g001000
MODULAR APPROACH Number of Rerotlon
fig. 6a.
X Yuncorrected Joint angle. 1,000
0.960 I I I I --I _ I'" I I I
0.920
0.880
0.840
0.800
0.760
(
O.720
0.680
0.840
0.600
(
0.5_0
O.520
O.480
O.440
corrected Joint 8ngles
0.400
0.360
robot arm position 0.320
O.280
0.2+0
0.'J00
obstacle TyDe 0.160
oo+co0.n120
0,080
0.040
0.000
I I | I 1 I 1 ._l I
0 t00 200 300 400 500 600 700 800 gO0 1000
Number of Iteration
fig. 6b.
Fig. 5.
276
Expected Output Network Output
0.g95 -
0.g54 I I I I' 0,996
0,g13 0,954 I I I
0.871 0,913
0.8.30 0.871
0.788
0.747 0.8.30
0.705 0.788
'_ 0.6_ 0.747
0.705
0._1 0,664
,_ 00..564202 0.6Z,?.
0.498 0._$1
" ,457 0.5_
0.41,5 0.4.98
"'_ 00.,33.7342 0,4.57
0.2gl 0._,15
0.249 0,37,;
O.2O8 0.:132
0.166 0.291
0.125 0.249
0,0_ 0.2O8
0,0'1-2 0.166
0.000 I, ,, 0.125
0.0 0.S 1.2 1.S 2.4 3.0 0.0_
0.042
0.000
0.0 0.8 I._ 1.8 2._ _.0
_me (.¢ond,)
0.Q98 - Rrst UnI¢
t I ...... I" I-.......
0,954
0.913
0.B71
O.83O
0.788 0,g98 ,- I I I ! m_.
0.747 0.954
0.705 0.9t3
'_" 0.664 0.871
0.830
0.5t51 0.788
00..544908 0.747
00..6_272 0.705
0.415 0.664
"_ 0.374 0.622
0.332 0.581
0.291 0.54"0
0.249 0.4.98
0.208 0.4.,57
0.168 0,4.15
0.125 0,374
00..00_42 O.3.32
0.000 I I I | 0.291
0.0 o.s 1.2 I.B 2., _.o 0.249
0.208
"_,_ (_) 0.166
Sec_cmdUnk 0,125
0,O83
0.042
FLg. 7a. 0,000 I I I I
0.0 0.6 1.2 1.B 2.4 3.0
"r;me (seconds)
Seeond Unk
Fig. 7 b
277
Learnlng the kJne_atlcs transFornatlon
For a Type II Ob_tscle
0,1'30
1 I 'I I I I t I
0,096
0,092
0.088
0.084
0081
0.077
0.073
0.069
0.065
_. 0.001
w 0.058
0.054
0.050 robot _olition
0.0¢6 1
0.042
0.038
0.035
0.031 Joint ingle
0.027 oommandl Robot
0.023 Neuroplanrler/ II |
Arm
0.019
I,. I I
0 100 200 300 400 500 600 700 80(3 900 1000 Cont roller_ l
Number of Iteration
0.98S
I I I I I I I I I -
0,950
0.912
0,874
0,836 Sensitiveskin _I
0,798
0,760
0,722
0,684
0,646
0.608
0.570
0.532
0.¢94
Array
00..445188 Proceleor
0.380
0,342
0.304
0.266
0.228
0.190
0.152
Pig . 10.
0.114
O.070
0.038
0,000 I. I I I I L I i I
0 100 200 300 400 500 600 700 800 gO0 i000
Number of I_ero_Jon
Fig. 8.
278
e×pected output Network Output
0.972 I I I I 0.972 f I ! I
0,9.30 0.930
0.900 0.900
0.864 0,864
0,828 0.528
o.792 0.792
0.756 0.756
0,720 0.720
0.684
, 00..6684,_ _" 0.648
o.571 =. 00..651726
._ 00.,6514:(
-- 0.50, "_ 00..554004
00.,446382
0.391 00,3.39860
00.,33621 o 0.324
0.2_ 0.288
0.25: 0.252
0.21 i 0,216
0.18o 0.180
o.144 0.144
0.108 " =,.. 1 0A08
0,072 0,072 I I I I 1
0.036 0.036
0.000 0.000
0.0 0.6 1.2 1.8 2.4 3.0 0.0 O.S 1.2 1.8, 2.4 3.0
Time(_conds) for Link 1 Time(_econds) for L_nkI
0,g96 0.972 _- I f I I
0.930
0.g13 I i ] I I I ]- I [ =7] 0.900
0.864
0.830 0.628
0.792
0.756
0.747 0,720
0.684
_' 0.664
'_ 0,581 0.576
-"_"0.498 _ 0,504
_ 00..446362
_' 0.415 00,3.39660
"_ 0.332 0,324
0.288
0.252
0.249 0.216
0.180
0,166 0.144
0.t08
0.083 0,072
0,036
0.000
0._0 I I I I I I I I ,| 0.0 0.6 1.2 1.8 2.4 3.0
0.0 0.3 0.6 O.g 1.2 1.5 1.R 2.1 2.4 2.7 3.0
13me(seconds) for Unk 2
13me(,econd,)
Seoond Link
Fi_. 8.b
Fig. Sa.
279