Work during the recording period proceeded along the lines of the proposal, i.e., three aspects of high speed motion planning and control of flexible structures were explored: fine motion control, gross motion planning and control, and automation using light weight arms. In addition, modeling the large manipulator arm to be used in experiments and theory has lead to some contributions in that area. These aspects are reported below. Conference, workshop and journal submissions, and presentations related to this work were seven in number, and are listed. Copies of written papers and abstracts are included

Book, Wayne J.

English

NASA Technical Reports Server

HIGH SPEED, PRECISION MOTION STRATEGIES 
FOR LIGHTWEIGHT STRUCTURES 
Semi annual Progress Report 
November 15, 1986 t o  May 14, 1987 
Wayne J .  Book, Principal Investigator 
The George W. Woodruff School 
of Mechanical Engineering 
Georgia Inst i tute  of Technology 
Atlanta, GA 30332 
NASA Grant NAG 1-623 
( E25- 5 17) 
Technical Officer: Donald Soloway 
https://ntrs.nasa.gov/search.jsp?R=19870018578 2020-03-20T10:09:34+00:00Z
SUMMARY 
The work dur ing  the period covered by this report proceeded along the 
l ines  of the proposal, including work on three aspects of the high speed 
motion planning and control o f  flexible structures:  f i ne  motion control,  gross 
motion planning and control, and automation using l igh t  weight arms. In 
addition, work on modeling of the large manipulator arm t o  be used i n  
experiments and theory has lead t o  some contributions i n  t ha t  area. These 
aspects w i  11 be found somewhat distributed through the modules reported below. 
Conference, workshop and journal submissions and presentations related 
d i rec t ly  t o  this support totaled seven, and are l i s t e d  i n  the references. 
Copies of the written papers o r  abstracts are  attached. 
Four students are  involved i n  this work. S. Cetinkunt will f inish his 
Ph.D. degree i n  a matter o f  months, He i s  considering a University research 
and teaching career. D. Lee and J. Kwon are  preparing t h e i r  Ph.D. Thesis 
proposals, and J. Huggins i s  completing his Master's Thesis this Fall ,  and 
will be taking the Ph.0. Qualifying Exam. T h i s  grant has previously supported 
G. Hastings, who is  now on the faculty a t  Clemson U. and continuing research 
i n  the same general areas. 
GROSS MOTION PLANNING AND CONTROL 
Sabri Centinkunt 
Research i n  this area seeks t o  develop advanced s t ra teg ies  for  "high 
speed, high precision motion planning and control of lightweight manipulators" 
w i t h  the following properties: 
1. Wide range of motion speeds should be possible w i t h i n  the prespecified 
precision. 
2. Precision motion via 
control, 
a) Joint space tracking accuracy, b) 
3. Robustness with respxt to a) payload variations, b) S 
F1 exi bl e vi bration 
nsor noises due to 
environment and hardware disturbances, c) system nonl ineari ties that will 
become dominant at high speed motions. 
In searching for high performance motion planning and control strategies for 
lightweight arms, a logical first step is to look at the performance o f  rigid 
model based strategies and identify their short comings. The following well- 
known rigid model based control strategies are studied when applied to flexible 
arm models, with typical trajectory planning algorithms, i .e. trapozoidal 
prof i 1 es : 
1. 
2. 
3. 
4. Adaptive Model Following Control 
Notice that these control strategies do not consider the arm flexibilities, 
and yet they are applied to real systems which exhibit structural flexibilities. 
Computed Torque Method (CTM) , 
Decoupled Joint Controller, plus gravity compensation (DJC + g), 
Independent Joint Controller, plus gravity compensation (IJC + g), 
The results o f  our studies on the performance of these controllers are 
summarized bel ow: 
1, Maximum speed of  motion, achievable by (CTM, DJC+g, and IJC+g), is limited 
by the arm flexibility to the 1/3 of lowest clamped-cantilever frequency of arm. 
AMFC can achieve speeds twice as high by adaptively compensating nonl inearities 
under parameter uncertainty. 
2, Precision Performance: 
a) Joint tracking performance is closely related to the speed of motion and arm 
flexibility. For slow motions (relative to arm flexibility) joint space 
tracking performance is very good. When high speed motion is attempted, this 
performance deteriorates. 
b) F1 exi bl e v i  bration control performance of rigid model based control 1 e rs  give 
surprising resul ts .  All of the controllers successfully damp out the h i g h  
frequency vibrations. However, low frequency vibrations do pe r s i s t  and cause 
large deflections. A t  this point, i t  i s  c lear  tha t  the major problem for  more 
advanced control s t ra teg ies  i s  to  control low frequency vibrations as oppose to  
high frequency vibrations. 
3, Robustness of non-adaptive controllers depends on the r a t io  of the speed of 
motion and bandwidth of the closed loop system. Closed loop systems w i t h  h i g h  
bandwidth can to1 e ra te  parameter uncertainty (payload variations).  For h i g h  
speed, high performance manipulation classical  r igid body based control 
s t ra teg ies  are  not appropriate and not robust. Rigid model based AMFC has 
be t t e r  robustness properties. The robustness can be improved by considering the 
f 1 exi bl e body dynamics . 
I n  summary, c lass ical  r igid model based non-adaptive control s t ra teg ies  are 
not sui table  fo r  h i g h  speed, h i g h  precision manipulation. By the basic design 
principles,  speed is  compromised fo r  robustness and precision i s  lo s t  by 
ignoring f l ex ib i l i t y .  
COMBINED CONTROL AND PLANNING STRATEGY 
Sabri Centinkunt 
I t  i s  now c lear  t ha t  f o r  high speed and precision manipulation, control and 
planning methods must account fo r  the arm f l e x i b i l i t i e s .  
A new combined control strategy i s  being studied. Any given desired motion 
i s  considered as consisting of two phases: 1. Gross motion phase, 2. Fine 
Motion phase. In Phase 1, arm moves from one position t o  another w i t h  h i g h  
speed. A t  this phase speed i s  t h e  essential  issue. Towards the end of the 
motion, Phase 2, arm will interact  w i t h  
importance. Clearly, each phase of motion 
objects and accuracy i s  of prime 
has d i f fe ren t  emphasis, "High Speed" 
i s  the main issue i n  Phase 1, whereas 
2. Approach and leads to  a new combined control strategy. 
"precision" i s  i n  the main issue in phase 
In phase 1, arm i s  controlled by a AMFC, which i s  designated based on a 
reduced order model t o  provide high speeds and robustness. In phase 2 ,  fu l l  
s t a t e  feedback control methods are  employed fo r  f a s t ,  accurate positioning and 
vibration control of the arm. A t  this phase arm s t a t i c  deflections are  included 
i n  the position and vibration control. 
Furthermore, i n  the past i t  was believed tha t  the desired j o i n t  space 
t ra jectory effectively determined the f lex ib le  body response under any feedback 
control. Our  analysis shows tha t  the control ler  used i n  the realization of a 
desired trajectory has important influence on the f lex ib le  body dynamics. As a 
resu l t ,  f o r  lightweight arm, planning and control must be studied together, as 
opposed t o  the to ta l ly  separate design stages of r i g i d  manipulators. 
The i n i t i a l  resu l t s  have been very encouraging. The completion of this  
work i s  expected very shortly,  and resu l t s  will be presented i n  the appropriate 
forums. 
MODELING OF CONSTRAINED FLEXIBLE DYNAMICS 
J. Lee 
Unlike a conventional ser ia l  manipulator, a paral le l  l ink driven 
manipulator has an advantages of a high structural  r i g id i ty  without increasing 
weight and lower interaction between links. Research on a closed chain 
mechanism i s  rare because there has not been an e f f i c i en t  computational method. 
In recent years, a reduction method using singular value decomposition that  
eliminates the constraint force explicitly from the equation o f  motion has been 
developed and applied to multibody rigid systems with constraints. This 
reduction method is being used to analyze the dynamics of a flexible manipulator 
with a closed kinematic chain. The mode shapes of a multilink manipulator are 
very difficult to find since exact boundary conditions depend on the 
configuration of the manipulator. The assumed mode shapes of each link were 
verified by comparing the analytical ' method, a finite element method and 
experiment. 
In the coming months, after the dynamics of a flexible manipulator with a 
closed chain is established, a constrained motion such as contour surface 
fol lowing or material hand1 ing aided by an overhead crane wi 1 1  be analyzed using 
this method and compared with unconstrained motion. One o f  the-many recent 
robot control algorithms will be chosen to explore the robots dynamic behavior. 
One purpose of this research is to check that the control scheme is also 
insensitive to an environmental change such as switching between free motion and 
constrained motion. 
SYMBOLIC MODELING OF SERIAL FLEXIBLE MANIPULATORS 
Sabri Cetinkunt 
The modeling needs for this project has lead to a new systematic algorithm 
to symbolically derive the full nonlinear dynamic equations of motion of 
multilink flexible manipulators. Lagrange's equations and the assumed mode 
method are the basis o f  the new algorithm and they are adapted in a way suitable 
for symbolic manipulation by digital computer. Implementation of the algorithm 
on a commercially available symbolic manipulation program has lead to the 
generation of the equations currently being used in the research on two link 
serial arms. 
EXPERIMENTAL VERIFICATION 
J.  Huggins 
Experiments t o  determine the dynamics of the f lex ib le  arm about a single 
point (linearized, for  small motions) have been performed and the resu l t s  w i t h  
two other analytical methods, a f i n i t e  element method and the assumed modes 
method are  compared. The next experiments t ha t  need t o  be performed are  the 
ones tha t  will analyze the motion of the f lex ib le  arm while undergoing large 
motions (non-linear motions). To do these experiments, the Microvax I1 will be 
used t o  control the motion of the robot arm and t o  acquire and analyze the data. 
To accomplish these l a t t e r  goals, the inverse kinematics of the f lex ib le  
arm have been solved and a software program written t o  use the forward and 
inverse kinematics t o  perform s t ra ight  l i ne  planning. The path planning 
incorporates polynomial smoothing t o  eliminate jerkiness of the motion 
implements the path desired. This software will be general i n  nature so tha t  a 
user can quickly add various control s t ra teg ies  while using the same path 
planning methods. The software will a lso gather vibration data that  can be 
analyzed both i n  the frequency domain and i n  the time domain. 
FINITE ELEMENT MODELING OF THE LARGE FLEXIBLE ARM 
D. Kwon 
In order t o  understand the resu l t s  obtained through experiments and re la te  
them t o  the assumed mode model, a re l iab le  representation of l i nea r  f lexible  
behavior was needed. A commercial f i n i t e  element modeling package, SUPERTAB, 
was used f o r  this  purpose. By changing the f i n i t e  element model t o  closely 
represent the detail  of the experimental setup, o r  t o  represent the assumptions 
of the simplified and linearized assumed mode model, the results of either could 
be closely approximated. This was an important step in verifying the operation 
of each, the assumptions, and understanding the limitations of the assumed mode 
model. 
ANALYSIS OF AUTOMATION USING UNCERTAINTY 
D. Kwon 
The flexibility observed in a light weight arm is one form of dynamic 
uncertainty which is present in automation in may forms. Friction, inaccurate 
construction and fixturing, sensor noise, and thermal expansion are add1 tional 
forms. For any given task to be successfully completed, the uncertainty in the 
robot state must be reduced to an acceptable level, dependant on the tolerance 
of the task. Several means are employed to reduce uncertainty, including 
rigidity and precise construction, end point sensing and feedback, and fixturing 
of the work piece relative to the robot. Although these concepts have been 
implicit in robot system design for many years, little has been done to 
formalize the treatment of the concepts to make them useful for system 
conceptual or detall design. This is now being undertaken with the current 
research which will form the basis of a Ph.D. Thesis. The experimental 
prototype that will be used in exploring these concepts will be the light weight 
arm and, in particular, the bracing strategy for reducing uncertainty. 
REFERENCES 
1. Huggins, J.D., D.S. Kwon, J.W. Lee and W.J. Book, "Alternative Modeling and 
Verification Techniques for a Large F1 exible Arm, 'I Proceedings, Conference 
on ADplied Motion Control '87, June 16-18, 1987, Minneapolis, MN, pp. 157- 
164. 
2. 
3. 
4. 
5. 
6. 
7. 
Cetinkunt, Sabri , and W.J. Book, "Symbolic Modeling of Flexible Robotic 
Manipulators," Submitted to ASME J. Dynamic Systems. Measurement and 
Control , April , 1987. 
Hastings, Gordon and W.J. Book, "Reconstruction and Robust Reduced-Order 
Observation of Modal Vari ab1 es for F1 exi bl e Manipul ators, I' submitted to ASME 
J. Dynamic Systems, Measurement and Control, May, 1987. 
Cetinkunt, S. and W.J. Book, "Symbolic Modeling of Flexible Manipulators," 
proceedinqs of the 1987 IEEE International Robotics and Automation 
Conference, April, 1987, Raleigh, NC, pp. 2074-2080. 
Hastings, Gordon G., J. Dorsey, and W.J. Book, "Application of Balanced 
Real i zations to Estimate Model Order Requi rements for F1 exi bl e 
Manipulators, 'I To be presented at 1987 ASME Winter Annual Meeting, December, 
1987. 
Book, Wayne J. "Symbolic Modeling o f  Flexible Link and Joint Arms with 
Closed Kinematic Chains" Abstract submitted to the Joint CISM--1FToMM 6th 
Symposium on Theory and Practice of Robots and Manipulators, June, 1988, 
Udine, Italy. 
Book, Wayne J., "Modeling and Simulation Applications to Flexible Robots and 
Manipulators," Presentation to be given at the SDIO/NASA Workshop on 
Mu1 tibodv Simulation, Sept. 1-3, 1987, Pasadena, CA. 


High speed precision motion strategies for lightweight structures

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