The goal of this research is to achieve very intelligent telerobotic controllers which are capable of receiving high-level commands from the human operator and implementing them in an adaptive manner in the object/task/manipulator workspace. Initiatives by the authors at Integrated Systems, Inc. to identify and develop the key technologies necessary to create such a flexible, highly programmable, telerobotic controller are presented. The focus of the discussion is on the modeling of insertion tasks in three dimensions and nonlinear implicit force feedback control laws which incorporate tool/workspace constraints. Preliminary experiments with dual arm beam assembly in 2-D are presented

Elia, C. F.

Walker, R. A.

Ward, L. S.

English

NASA Technical Reports Server

/,!i_/_i¸ : _ .......
Task Oriented Nonlinear Control Laws for Telerobotic
Assembly Operations ..... z ?
R.A. Walker,t L.S. Ward,* and C.F. Ella* .... >_ : _ .... •
Integrated,Systems, Inc. _ •i ,
Palo Alto, CA 94301
Abatract
The goal of this research is to achieve very intelligent telerobotlc controllers which are capable of receiving high-
level commands from the human operator and implementing them in an adaptive mamner in the object/task/manipulator
workspace, q2kk.4t_._esents .initiatives by the authors at Integrated Systems, Inc. to identify and develop the key
technologies necessary to create s_uch a flexible, highly programmable, telerobotlc controller. The focus of the discussion is
on the modeling of insertion tasks in three dimensions and nonlinear implicit force feedback control laws which incorporate
tool/workspace constraints. Preliminary experiments with dual arm beam assembly in 2D ar¢_ presented.
I. Introduction
In the future, telerobotic manipulators will be used to enable increased space assembly, servicing, and repair. Specific
goals, as determined by NASA, are:
1) "to decrease mission operations manpower by 75 percent,
2) to replace 50 percent of extravehicular aci.ivity (EVA) with telerobotics, and
3) to enable remo:e (e.g. geosynchronons earth orbit and polar orbit) assembly, servicing, and repair through :ele-
robotics" {l I.
In order to _ati_fy the above requirements for telerobotics, significant improvements in manipulator control wiJl be
necessary. Telerobotic assembly requires powerful Jocally autonomous control laws for l)t_k completion in the pre_¢,,ce of
disturbances and sensor errors 2) control of position and force for trajectory guidance 3) task completio.: .¢ithout continuo,,s
operator supervision. The last is especially important for long distance tasks (such as Mars exploration) where the time delays
involved in receiving sensory information or relaying earth-based control signals make traditional teleoperation unsuitable.
Furthermore, an interface for expert system planners and/or human interaction will be necessary so that the system is flexible
to various levels of human supervision.
Previous work in the general ar,.a of robotics has focused on a decompositoa of robot control into trajectory planhing
and servocontrol to the preplanned wire in statespace. A logical extension of this work approaches the problem with real-time
expert systems to formulate the planned trajectory "in-the-loop". Expert systems "in-the-loop" will be much more powerful
with more-sophisticated control algorithms a.s a foundation. Namely, analytic, optimization bazed, "trajector'/ feedback",
nonlinear control laws whose performance index and time phasing are controlled by a combination of expert _ystems and the
human operator.
The effort described below involves fundamental nonlinear control laws valuable in dual arm coordination. These
approaches to dextrous, coordinated motion were evaluated in a new highly flexible simulation environment {-%The authors
have modeled ,wo 2DOF planar robots, performing a beam assembly task. Two dimensonal plots and figures illustrate by
comparative results the sensitivity of performance to the control law structure. Reasonable long term research conclusions
will be
a) which control approaches are most reasonable
b) what level of actuator/sensor performance is required to do meaningful experiments well with these control laws,
and
1" Manager, Aircraft and Robotics Control Systems Division
* Members of Technical Staff
185
https://ntrs.nasa.gov/search.jsp?R=19890017143 2020-03-20T02:08:07+00:00Z
c) what are the controller architecture issues to implement such control laws.
We first describe the modeling, then various control structures followed by a discussion of the experimental results.
II. Dual Arm ModeIln_._
Modeling and Simulation Tools
The following research was carried out using MATRIXx/AR (Automation and Robotics Modeling and Simulation
Package)f2]. This tool provides a flexible modeling and simulation environment for manipulators, actuators, and control laws.
Figure I is a flowchart for the use of MATRIXx/AR. Model creation is initiated by using the menu-driven Rug (Robotic
User Interface) to specify the geometric, inertial, and functional sp_._iflcatinns of the manipulator. The RUI creates a robotic
database from the given and computed data. Thb data is accemed by command flies which build a kinematic and dynamic
model of the manipulator using the recursive Newton-Euler approach. This model is created in SYSTEM.BUILD[3], a
simu]ation/integration package where linear, nonlinear, and multirate systems and c,:ntrollers can be modeled quickly and
easily in a block diagram format. Figure 2 shows the inverse dynamic model of the PUMA 560 with blocks for the base, arm,
wrist, and end effector. The blocks are nested, so that the block fo:: ,he arm contains blocks for link 1, link 2, and link 3, each
of which contains a dynamic, kinematic, and actuator block. By using input flags, the PUMA block can be used to obtain
kinematic, dynamic, and inverse dynamic information. Suitable control laws can be generated by using ela.ssical and modern
control design techniques available in MATRIXx/AR. The plant and control models are combined in an overall system which
is then simulated. Post-processing animation capabilities are used to visualize the ancce_s or failure of a particular controller.
Manipulator Robot Models
Each of the two roboti." manipulators modeled in this study is a three DOF articulated arm. The arms are made
up of three rigid links connected through one prismatic and two revolute joints. Since the first and second joint axes are
perpendicular, and the second and third are parallel, each arm moves 'm a plane wlth one translational and two rotational
degrees-of-freedom. A schematic of an arm is shown in Figure 3.
The 3-DOF planar manipulators are identical, with the physical characteristics shown in Table I.
Robotic User
Interface
(RUI)
Rnbotic D/B
4r
Is.,:,E,_ou,toI
÷
[ Anlma,ion Capat,,'i ties I
Fig,zreL MATRIXx/AR Drsign Flowchart.
Space Assembly Beam Model
The mating of two long slender beams was chc_en&s a suitable test for the proposed control algorithms. The beams
were sized relative to the arms to simulate a tru_s assembly scenario. The beams, _s well as the manipulators, have a
186
Editing : _UHA (Co_tinuo_u_
Figure 2. Model of PUMA 560.
cylindrical (hollow) shape with the dimensions shown in Table 1.
The dual arm configuration, complete with beams, is shown in its initial position in Figure 4. The arm and beam
on the left with the socket will be referred to u Manipulator 1, and those onthe right with the peg u Manipulator 2. The
Tnble I
3-DOP Planar Manipulator Physical Characteristics.
Link I Link 2 Link 3 Beam
Geometric
Properties
Joint Type Swivel Sliding Hinge n/a
Length (m) .2 .4 .4 I
Cylinder:
Inner Radius (m) .046 .0335 .0335 .023
Outer Radius (m) .050 .0375 .0375 .025
Inertial
Properties
Mass (Kg) .724 1.07 1.07 .905
lnertiM (Kg-m2):
Izz .0017 .0014 .0014 .0005
Iv v .0032 .0149 .0149 .0757
l,s .0032 .0149 .0149 .0757
desired goal involves inserting a prg on the left end of the second beam into the hole in the middle of the first brain.
Dual Arm Constraint Model
Simulating closeddynamic chalns_such as the dual arm manipulators during an assembly ta_k, is a difficult problem.
The collisions which occur c_urlng insertion result in abrupt changes in the motion (velocity) states. These discontinuities
cause problems for the integration package. The problem is dealt with in this research by using a compliant model, since
there is, naturally, compliance in any mechanical mechanism. For this work, the first arm, second arm, and second beam
187
Figure 3. Schematic of Three DOF Arm.
are treated as being rigid. The hole sad the second beam are compliant, generating an oppoaing force linearly proportional
to the amount of deflection caused by the inserting peg upon collision. Since computer CPU time is dependent upon the
"stiff'hesS" of the equations, preliminary tests are run using relatively low spring constants. The results described below are
in this category, with spring gains of 1000 N/re.
IlL Dual Arm Control
This section gives an overview of the various aspect_ of the control approaches investigated on a dual arm experiment.
-.8
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F_gure 4. l_,_al Arm Configuration.
3.1 Control Design
The performance of a robotic manipulator in a compliant task, such as peg insertion, greatly depends on the choice of
control used. A one-step control law based on previous research [4] was used for the beam assembly problem described above.
• qP
188
Theadvantaged this scheme over typical hybrid force/position control I- that the control law works for both constrained
and unconstrained motion; thus, the peg does not need to be in close proximity to the hole initially. A brief description of
the control law b presented below.
Nonlinear Control
The equation of the motion of the end effector in cartmian space is given by
where x is • vector of position and orhntation, _s(z, _) contains the Coriolls and centripetal terms, and p(z) contains the
gravity terms. A nonlinear control law can be used to globally linearise equation (1) [5]. The result is s linear system of the
form
_--F¢.
Multiplying (2) on both sides by A(z) and adding _(z,_) + p(z) give_
(_)
A(_)i+_(=,_)+p(=)=A(_)_,÷_(_,_) +V(_)
Letting F = A(z)Fo + #(z, _) + p(_) = A(z)F_ + F,h where F_ = _(z, _) + p(z), the feedback is composed of two components:
a component containing the feedback law designed for the linear system (2), and a nonlinea_ decouplln8 component baaed on
the nonlinear terms of II). It is important to note that exact nonlinear control requires a precise model of"the manipulator.
_,onstralned Motion Control
Control in the presence of constraints was based on research done by lsh- Shalom [6]. The method involves specifying
a task constraint and then using that constraint as the opClmizatlon criterion for a linear quadratic optimal control design.
For example, the constraint on the end effector force and velocity
describes sliding •long • surface.
minimizing the performance index
f.v=O
A linear quadratic controller can be designed to satisfy this constraint. It is based on
J = Ill" ¢11_ = vTH(f) v
and is derived for system (2) with the following result [41:
Fc = -Kz
K = [.Kv K, I
=[0 _.u(fl]
where K v is positionai feedback,K, is velocity feedback, _. is • constant, and
H(/) = I/.f, /_ I,{.I >_0 V/_-R_
Lf,l. /,/. /: J
Note that the force is controlled implicitly through the velocity feedback.
(]nconstrained Motion Control
Control in the absence of constraints can be determined by using linear quadratic optimal control. The solution for
system (2) will provide position and orientation control for the manipulator.
¢*
189
SJ Dual Arm Beam Amemb/y Control Strateg/m
The three control laws described above were combined ud used with the dual arm configuration de_:ribed in chapter
2. Three preliminary control strategies, shown in Table 2, were chosen to determine preliminary conclusions on the Jmportzn_
of implicit force control and relative vs. global cooperative control schemes.
Table 2
Dual Arm Coqtrol Stratetd_ Simulated
#
Control
arml
(SoctetReceptor)
1 NL
slobal servo
NL-force
global servo
NL-force
global/
localaervo-
Strategies
arm 2
(/nsertionPeg)
NI,-force
globalservo
NL-force
global servo
NI,-force
global servo
A global servo means the control is servoing to a point in inertial space. A local servo means that one arm servos
relative to the other arm. Tlle nonlinear aspect is what is often called the coupled torque method, and the force control is
all implicit based on the constraint modeling described above. The next section describes the motivation for these strategies
and experimental simulation results.
IV. Dual Arm Simulation Results
The _rst experiment tests the performance of control J&ws without coordination. The second experiment adds implicit
force control to give a local coordination effect, and the third shows how significant passing information on the other arm's
activity is to a_complish a coordinated assembly task.
Experiment / Objectives and Results
In experiment t both arms were servoed to • globally defined position and orientation. The defined position for
both arms corresponds to the base point of the hole in the beam attatched to arm I. Arm 2 was controlled by the combined
controller as described above. Arm I however, did not have implicit force control. The simulation results are shown for
successive time frames in Figure 5. Note that the initial contact of arm 2 onto arm 1 caused significant deflection, so that
mating was only pcaible,after a second attempt.
Experiment 2 Objectives and Results
Experiment 2 was the same as the experiment 1 with the exception that arm 1 was given implicit force control.
As can be seen in Figure 6, the mating was accomplished in the first try. This is due to the cooperative motion of the
manipulators after contact, even though they had no _nformation about each others positions and were se.rvoed to a globally
defined point in space. The presence of the implicit force in arm 1 caused that ann to move in the positive s direction after
being hit by arm 2 (perpendicular to the direction of the external force) rather than in the -x direction as before. Thus, local
relative movement (away from the defined servo point) occured with arm I which allowed the two beams to mate faster and
then travel back togetFer to the global servo point.
Experiment 3 Objectives and ResuP',
Experiment 3 was the same as experiment 2 with the exception that arm I was given information about the z
component of the peg's location (attatched to arm 2). Arm I was thus servoed globally in the x direction and relatively (to
arm 2) in the z direction. As can be seen in Figure 7, faster mating was obtained due to global movement of arm I.
190
Simulation F.xpedment Sum••r,/and Conefuslomm
It should be noted that the above experiments represent preliminary results run under idealized conditions. The
nonlinear control wu exact and the hole was modeled compliantly as a spring system, allowing the manipulator to penetrate
the first beams surface and then apply a point force proportional to the maximum penetration. These simulations were
designed, however, to illustrate the potential benefit of using nonlinear implicit force feedback. Two key observations elm be
made.
First, the presence of implicit force feedback in both arms demonstrated how the two arms were capable of moving
cooperatively without any knowledge of each other. The implicit force feedback Lllowed local movement shout the globally
defined servo point, which resulted in cooperative relative movement for the arms. This is extremely valdable since this can
compensate for sensor inaccuracies in specifying and measuring the global servo point.
Second, as should be obvious, giving one or both arms information about each other, such as positional information,
allows a greater degree of cooperation in the assembly task. Thus, future research will concentrate on using cooperative
schemes, such as dual arm one-sided optimal guidance, to increase the arnount of cooperation between the two arms.
V. Summary
This paper has outlined telerobotic research in progress at Integrated Systems. The emphasis on the work has been
to develop goal directed guidance laws which provide • more powerful framework for telerobotic planners and teleoperator
controllers to interface. Preliminary work has been done to test the concepts by simulation, using flexible automation
modeling and control tools developed at Integrated Systems.
The dual arm control laws tested show that the control strategy is very important for assembly operations and could
be of great benefit to NASA's space bound manipulators. Since there is • major need for telerobots to possess significant
decision-making capabilities before they can be used extensively in remote and hazardous situations, it will be valuable in
the industrial and nuclear environments as well.
References
[t] M.D. Montemerlo, "NASA's Automation and Robotics Technology Development Program," Proc. OF 1986 IEEE
International Conference on Robotics and Automation, San Francisco, CA, April 7-10, 1986.
[2] Reza Langari, Robert A. Walker, Norm Coleman, and Pak Yap, "A Robotics Modeling and Control Law Development
Environment," Proceedings of the AIAA Guidance Control Conference, Williamsburg, VA, August 18-20 1986.
t3] N.K. Gupta, D. Varvell, and R.A. Walker, "SYSTEM_BUILD: A New Interactive Model Building and Simulation
CAE Tool," Proc. of the Society for Computer Simulation, July 22-24, 1985.
[4] Reza Langari and Robert A. Walker, "Nonlinear Feedback Strategies for Control of Robotic Manipulators," ISI
Technical Memorandum 6507-002, March 1986.
[5] E. Freund, "Fast Nonlinear Control with Arbitrary Pole Placement for Industrial Robots and Manipulators," Robotics
Research 1, MIT Press 1982.
16] J. Ish-Shalom, "The C.S. Language Concept: A New Approach to Robot Motion Design, I International Journal of
Robotics Research, Spring 1985, pp. 42-58.
191
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195


Task oriented nonlinear control laws for telerobotic assembly operations

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