Kinematic resolved-rate control from one robot arm is extended to the coordinated control of multiple robot arms in the movement of an object. The structure supports the general movement of one axis system (moving reference frame) with respect to another axis system (control reference frame) by one or more robot arms. The grippers of the robot arms do not have to be parallel or at any pre-disposed positions on the object. For multiarm control, the operator chooses the same moving and control reference frames for each of the robot arms. Consequently, each arm then moves as though it were carrying out the commanded motions by itself

Barker, L. K.

Soloway, D.

English

NASA Technical Reports Server

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Coordination of Multiple Robot Arms
L.K. Barker and D. Soloway /_j _)NASA Langley Research Center _i_)
Hampton, VA 23665-5225 /J
1. Abstract / _% "; i • (;" /'/
Tjd_i_per_extends_.ktnemat|c resolved-rate control from one robot am/_o the coordinated control
of moltlple robot arms'tn the movement of an object. The structure supports the general movement of
one axis system (moving reference frame) with respect to another axis system (control reference frame)
by one or more robot arms. The grippers of the robot arms do not have to be parallel or at any pre-
disposed positions on the object. For multtam control, the operator chooses the same moving and
control reference frames for each of the robot am. Consequently, each arm then moves as though _
it were carrying out the commanded motions by ttself.
2. Introduction .......
In the Intelligent Systems Research LaboratO_ (ISRL) at the Langley Research Center, an operator sits at a
remote console wtth a stx-axts hand controller and commands the motion of a robot arm. The operator has
opttonal control modes, but of particular intg_rest in this paper is kinematic resolved-rate control [1], which,
for example, enables the operator to dtrec)Ely control the robot hand. The operator views the robot hand,
decides that he wants tt to move in a cert_itn direction, and commands a velocity in that direction with the
controller. The robot hand then moves in /Lhe desired direction with a velocity proportional to the controller
deflection. Commanded hand velocities are/transformed (resolved) Into. requisite move,_..n_t) (velocitles)of :bee
individual Joints in the robot arm to ef/fect the commanded hano motion. ,.urrentmy, I_KL nas _wo SlX-oegr -
of.freedoe industrial robot arms. /
There are some tasks which can not/be done with Just one robot arm, and other tasks which can be done with
one robot arm, but not in a reasonabl/e time. The advantage of using multiple robot arms is evidenced by humans
In everyday activity. The major prgblem with multlarm control is that we de not know how to control robot arms
in a general cooperative manner to accomplish a task. As noted in [2], the study of coordination problemso
between two robots doing a slngl_ job is in its infancy. Even then, work in dual-arm control ([2]-[4], for
example) has dealt mostly with )he master/slave architecture -- which is not of interest in the present paper.
Recently, however, H_yatl [5] p_oposed an interesting control architecture for positlon/force-torque control of
multlarm cooperating robots. / But, implementing this solution would require precise knowledge of the mass
property of the arms as well as the object that is being grasped. In the present paper a simple kinematic (no
mass properties) solution I)/ devised and then implemented using two industrial robot arms. Toward this end,
the well-known kinematic resolved-rate control is extended from the control of one robot arm to the coordinated
control of multiple robot arms.
Resolved-rate control appears to he a natural way not only to move an object with one robot arm but also
with multiple robot arms. After symbols/strings and axis systems are specified, equations are discussed for
the general movement of one axis system (moving reference frame) with respect to another axis system (control
reference frame) -- first, by one robot arm and then by multiple robot arms.
3. Symbols/Strings
alpha
base
crf
hnd
i,j,k
matrix from # to ## -
turf
a real number that locates a point along a llne between two selected robot grippers
or tools
base axis system
control reference frame for operator inputs
ha_d axis system
integers
.rmatrlx frcm# to #@ ) vector from ## to # 7
moving reference frame
https://ntrs.nasa.gov/search.jsp?R=19890017155 2020-03-20T02:07:28+00:00Z
nobJ
r mtrtx_frou # to t#
robot (t)
robot(t ).#
rye1_#
sta
tool
tvel t
vecter_frou f. to ##
vec ter..c ros i;_produc t_q_t
vectOr tnput_q t
world
number of robot anus
object axts system
rotational transfomatton matrtx froe axts system # to ax|s system ##; 3X3 mtr|x
tn upper left corner of the homogeneous transforemtton metr|x froe e to #t (t.e.,
mtrtx..from # to F#)
robot are associated wtth Integer 1
attribute t (such as axts system or velocity) of robot(t)
rotational veloctty tn exls system #
statton axts system, ihtch ts known with respect to the world axts system
tool axts system
translational veloctty tn axts system t
vector from # to It
vector q tn axts sys_n t resulting from cross-product operation
operator vector Input q tn axts systm F
world axts system
Note: In equations, an astertsk (*) denotes molttpllcatton, and x
4. Ax|s System
signifies a vector cross product.
Axts systems allow quantities tn the robot's environment to be geometrically related.
systems associated wttha gtven robot(t) are:
Pertinent axts
(1) Base axts system (robot(t).base),whtch ts located at the base of robot(t). If the base moves, whtch
does not happen tn thts paper, the homogeneous transformetton from world to robot(|).base ts updated
to reflect thts movement. •
(2) Control reference frame (robot(t).crf), whtch ts an ax|s system on or off'robot(t) that |s selected by
the operator for hts veloctt_ tnput to d|rect the movtng reference frame. Th|s frame may cotnctde wtth
the mevtng reference frame or any other convenient axts system. Default of rehet(t).crf |s
robot(t).toel.
(3) Hand axts system (robot(t).hnd), whtch ts a mevtng axts system representing the hand of robot(t).
(4) Movtng reference frame (robot(t).mrf), whtch ts a definable axts system that ts moved by the robot hand
w|th respect to a control reference frame. Default of robot(1).mrf ts robot(t).tool.
(5) Object axts system (robot(t).obJ), ihtch refers to an object assoc|ated wtth robot(t). Default of
robot(l).obJ |srobot(t).tool.
(6) Star|on axts system (rebot(t).sta), whtch |s known w|th respect to the world axts system and does not
move w|th joint-angle changes |n robot(t). Default robot(t).sta ts the world ax|s system.
(7) Tool axts system (robot(t).tool), whtch ts located on a tool attached or held |n the hand of robot(t).
Default robot(t).tool ts robot(t).hnd.
(8) World axis system (world), In whtch the positions of each base and statton ax|s system are known. Mhen
movement only tnvolves a stngle robot am, default world |s the base axts system of that robot ann.
Moreover, each Jotnt tn the robot arm has an associated Jotnt ax|s system. The ftrst three Joints are
sometimes referred to as the base or watst, shoulder, and elbow Jolnts. The latter three Jotnts constitute the
robot wrtst. Other axts system not used In thts paper are those associated wtth cameras, sensors, and goals.
S. Stngle Robot Am Contrel
In general (ftg. 1), an operator coamands a veloctty (expressed tn a control reference frame
(robot(t).crf)) to dtrect the movement of a movtng reference frame (robot(t).mrf). The mevtng reference frame
ts actually moved by the robot hand (robot(|).hand). The requ|red veloctty of the robot hand ts subsequently
calculated as a consequence of the commandedveloctty for th|s movement.
302
reference frame to the mvtng reference frame tsfhe holiogeneous transfomatton matrix from the control
computed as
matrtx from robot ( ! ). crf_to..robot ( t ) ,turf
• metrtx from_world_to_robot(t ).turf
* metrt x from robot( t ) • crf..to_worl d ( 1 )
where the matrices on the right stale of equation (1) are available when the moving and control reference frames
are selected.
The operator issues velocit_y commands in the control reference frame to direct the moving reference frame.
In the moving reference frame of robot(t), the translational veloctty (tvel) and the rotational veloctty (rye1)
that correspond to these coamlnds are
vector._robot(t ).rye1 _turf - r mtrtx._from_robot(t ).crfto_rebot(( ).lm-f
* vector_tnputrobot(t ),rvel.crf (2)
vector robot( t ). tvel turf • r__trt x from robot( t ). cr f_to_robot ( 1 ) .turf
* vector_Input .robot(t ).tvel crf
+ vector__cross product robot(t ).tvel mrf (3)
where
vector_c ros s_roduct_rebot (I ).tve1_mr f
- - vector tnnut i,,nhne(41 _,vn I P-_
X vector from_robot( t ) .turf to_robot ( t ). crf (4)
In response to an operator rotational velocity input tn the control reference frame, equation (4) makes the
origin of the moving reference frame translate tn a ¢trcular motion about the commanded rotational veloctty
vector. If it is desired that the moving reference frame only change tts orientation and not translate tn
response to a rotational velocity command, then equaton (4) ts not used.
The homogeneous transformation matrix from the moving reference frame to the robot hand ts computed as
matrt x_fromrobot ( i ). turf to .robot ( t ). hnd
= matrix from world to robot(i).hnd
m
* matrix..fromrobot(l ).mrf to_.world (5)
where the elements of the first homogeneous transformation matrix on the left slde of equation (5) Is a known
function of the robot joint variables.
To cause the moving reference frame to move with the commanded velocities, the hand axls system must move
with the velocities:
vector_robot (I ).rvel_hnd - r_matrl xJrom_rebot (I ).mrf..to._robot(I ).hnd
* vector._Input_robot(l ).rvel__mrf (6)
vectorjobot(i ).tvel_hnd - r_matrlx_from_.robot(i ).turf to_robot(l ).hnd
* vec tor_l nput__robot (I).tvel_mr f
+ vectorcross joroduct__robot{I ).tvel_hnd (7 )
where
vector_cross_product_robot( I).tvelhnd
= - vector_Input robot(l }.rvel_mrf
x vector_from_.robot (I ).hndto__robot (i ).turf (8)
Equation (8) Is necessary because the robot hand must also translate to produce a pure rotation In the ...-o.vi.-.g
reference frame.
303
The rotational and translational velocities in equations (6) and (7) are expeditiously treated as operator
inputs (rye1 hnd and tvel hnd) tn the hand axis system and used in previously programmed resolved-rate
equations tha'_ take veloct_" comMnds in the robot hand axts system and transform them into Joint rates in the
robot am to accomplish the commanded movement (fig. 2). Resolved-rate control is tmplemntod once the
homgeneous transformation mtrtces from the world to the control reference frame and from the world to the
moving reference framo are known.
An operator ts free to choose the control reference frame and the moving reference frame, Fop example, he
may specify these frames by u_tng menu selection, keyboard inputs, or a combination of ltght pen (location) and
turnball (orientation) on a graphics system. (The latter way has not yet been tmplemnted tn ISRL).
6. Multiple Robot Am Control
The Intention in this paper ts to communicate a method for coordinating multtple robot arm as they
collectively move an object. The solution here (fig. 3) is simply to choose a commoncontrol reference frame
and a comon moving reference frame for each of the robot arms; that ts.
robot(t).crf " crf
robot(t).mrf - mrf
An object axis system, tf considered commonto the robot arms, is noted as
robot(t).obj - obJ
(g)
(;o)
(11)
Then, resolved-rate control is applted to each robot ann with. respect to the co,non control reference frame.
Each am moves by resolved-rate control as though it were carrying out the commanded motions by ttself. Two
particular cases of reference frames are Identified here by the following homogeneous transformation matrix
equal t tt _s :
Case I: matrix from crf to world = matrlx._fromobJ to world
matrix from turfto world - matrlx__fromobJ to world
Case 2: matrix from crf to world - matrlx_from sta to world
matrix from mrf to world - matrix from obJ to world
The first case corresponds to the movement of an object with respect to velocities issued in its own axis
system; whe:-eas,the second case corresponds to an object that is moved with velocities that are specified in a
station axis system. A particular set of object axis systems are formulated.
7. Object Axis System on Line Between Grasp Points of Two Selected Robot Arms
An object grasped by robot arms can be maneuvered with respect to an object axis system located at a point
(automatically computed) on a llne between the grasp points (tool axis systems)of two selected robot arms.
For example, the operator may locate the origin o_ the object axis system at:
(i) a point midway between two selected robot tools
(2) either robot tool
(3) a specified distance along the llne between the two robot tools
For each robot(1), the homogeneous transformation matrix from its tool to the world axis system is computed
as
matrix from robot(l).tool_.to..world= matrlx_from robot(l).base_to._world
* matrlx_.from_.robot(l).hnd_to__robot(l).base
* matrix from robot(l).tool_to__robot(l).hnd (12)
m
where the transformation matrix from the hand to the base of a robot arm is the result of moving through the
joint axls systems, and the transformation matrix from the tool to the hand is given.
Let the two selected robot arms be labeled as robot(J) and robot(k). Moreover, define the orientation of
the object axis system to be llke that of robot(k). The position vector (needed in matrix from obJ to world)
to locate a point on the llne between the tools of robot(j) and robot(k) is computed as (flg'T4) - - -
vector__from_world_.to__obJ- alpha * (vector_from_world_to_robot(k).tool
- vectorfrom__world_to_robot(J).tool) (13)
30z_
If the operator selects the origin midway between the tools, alpha - 1/2; if the origin is at robot(k).tool,
alpha - O; and if the origin ts at robot(J).tool, alpha - 1. Other values for alpha put the origin at
different locations along the ltne between the two selected rohot tools.
Here, orientation of the object axts system is defined to be like that of the tool of robot(K). Hence, *_e
required rotational matrix is
r_metrix_.fromobJ to world - r_matrlx_from_robot(k).tool__to_world (14)
which is the rotational matrix part of equation (12),with I - k.
8. Object Axis System Located at Mean Grasp Point
The position vector needed to locate the control reference frame at the mean of the robot grasp points is
computed as
vector_from_.world_to_obJ - (i/n)
* (vector_.from_world_to_robot(I).tool
+ vector_from..world_to._robot(2),tool
+ vector from world to robot(n).tool) (15)
Orientation of the object axis system is then defined in some convenie,;tmanner. For example, if the
orientation of the object axis system is llke the tool axis system of robot(k) then
r matrix from obJ to world - r matrix from robot(k).tool_to_.world (16)
Or, if the orientation is llke that of the world axis system then
r matrix from obJ to world - r matrix from world_to_world (17)
where the matrix on the right side of equation (17) is Just the identity rotational matrix.
9. Concluding Remarks
A method of controlling a robot am is for an operator to command the hand to move with a velocity in a
desired direction. The com,_nded velocity (rotational and translational) is then resolved into Joint rates in
the robot arm to actually move the hand as commanded. In the present paper, this simple me'hod, known as
resolved-rate control, is extended from the control of one robot arm to the coordinated cont:ol of multiple
robot arms. The structure supports the general movement of one axis system (moving reference frame) with
respect to another axis system (control reference frame) by one or more robot arms.
The approach in this paper has been applied to two industrial robot arms that grasp a 12-foot long aluminum
tube, representing a structural element for space construction. The bases of the robot arms were separated by
about 6 feet. The operator wlth a slx-axis hand controller successfully translated and rot)ted the tube with
respect to an axis system on the tube. Gross movements of the tube were accomplished with no force/torque
feedback.
TO. References
[i] Daniel E. Whitney, "Resolved Motlon Rate Control of Manipulators and HumallProstheses," IEEE Trans.
Man-Mech. Sys., vol. _S-IO, no. 2, June I%% pp. 47-53.
[2] T.J. Tern, A.K. BeJczy, and ×. Yun, "Coordinated Control of Two Robot Arms," Proceedings 1986 IEEE
International Conference on Robotics and Automation• vol. 2, April 7-I0, 1986, pp. I193-1202.
[3] Tatsuzo Ishlda, "Force Control (n Coordination of Two Arms," Proceedings ,,i:the 5th International Joint
.Conference on Artificial Intelligence. Aug. 1977, pp. 717-722.
[4] Cecil O. Alford and S.M. Belyeu, "Coordinated Control of Two Robot Arms," International Conference _n
Rob,,tlcs,Atlanta, Georgia, March 13-15, 1984, pp. 468-473.
[5] Samad Hayatl, "Hybrid Positlon/Force Control of Multi-Arm Cooperating Robots," Proceedings of the IEEE
International Conference on Robotics _,J Automation, San Francisco, California, Aprll 7-I0, Ig86,
pp. 82-89.
3O5


Coordination of multiple robot arms

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