The Manipulator Emulator Testbed (MET) is to provide a facility capable of hosting the simulation of various manipulator configurations to support concept studies, evaluation, and other engineering development activities. Specifically, the testbed is intended to support development of the Space Station Remote Manipulator System (SSRMS) and related systems. The objective of this study is to evaluate the math models developed for the MET simulation of a manipulator's rigid body dynamics and the servo systems for each of the driven manipulator joints. Specifically, the math models are examined with regard to their amenability to pipeline and parallel processing. Based on this evaluation and the project objectives, a set of prioritized recommendations are offered for future work

Kelly, Frederick A.

English

NASA Technical Reports Server

MODEL EVALUATION, RECOMMENDATION, AND 
PRIORITIZING OF FUTlTBE WORK FOR THE 
MANIPULATOR EMULATOR TESTBED 
Final Report 
NASA/ASEE Summer Faculty Fellowship Program--1988 
Johnson Space Center 
Prepared By: 
Academic Rank: 
University & Department: 
NASA/JSC 
Directorate: 
Division : 
Branch : 
JSC Colleague: 
Date Submitted: 
Contract Number: 
Frederick A. Kelly, Ph.D. 
Assistant Professor 
Michigan Technological University 
Mechanical Engineering - Engineering 
Mechanics Department 
Houghton, Michigan 49931 
Engineering 
Systems Development and Simulation 
Teleoperator Systems 
Edith C. Taylor 
August 12, 1988 
NGT 44-005-803 
. 
14-1 
https://ntrs.nasa.gov/search.jsp?R=19890010701 2020-03-20T03:48:18+00:00Z
ABSTRACT 
The Manipulator Emulator Testbed (MET) is to provide a facility 
capable of hosting the simulation of various manipulator configurations to 
support concept studies, evaluation, and other engineering development 
activities. Specifically, the testbed is intended to support development 
of the Space Station Remote Manipulator System (SSRMS) and related sys- 
tems. The MET is required to permit that components simulated in software 
may be replaced by future hardware components. 
The objective of this study is to evaluate the math models developed 
for the MET simulation of a manipulator's rigid body dynamics and the 
servo systems for each of the driven manipulator joints. Specifically, 
the math models are examined with regard to their amenability to pipeline 
and parallel processing processing. Based on this evaluation and the 
project objectives, a set of prioritized recommendations are offered for 
future work. 
14-2 
INTRODUCTION 
The Manipulator Emulator Testbed (MET) is to provide a facility in 
It 
which different manipulator configurations may be simulated. The MET will 
be used as a tool to support Space Station manipulator development. 
will be used to develop and evaluate concepts, support design and develop- 
ment studies, and evaluate hardware components and flight software 
modules. The MET is required to be designed such that initial software 
simulated components may be replaced by future hardware elements [l]  - 
[31. 
The MET is currently built around a network of IBM PC-AT computers. 
Each computer operates at an 8-MHz clock rate and is equipped with an 
Intel 80287 math co-processor, 640K bytes of memory, an extended graphics 
adapter (EGA) card, a color monitor, a 30-MB hard disk drive, and a 
high-capacity floppy disk drive. 
Instruments GPIB-PCAA IEEE-488 interface card. The network includes an 
operator control station, data recording and display capability, and 
hardcopy output. A Multibus I1 "Network-in-a-Box" is scheduled to be 
added to the MET in August 1988. 
Each PC is equipped with a National 
The software includes the operating system (iRMK), intercomputer 
communication software from National Instruments, external interface, 
executives, operator support, data recording, and math model modules. 
The math model application software includes (1 )  a multi-link manipulator 
rigid body dynamics model and (2) joint servo models for each of the 
driven manipulator joints. 
simulation of proposed manipulator designs. 
distributed across the PC's such that a hardware component may be 
substituted and consequently the math model removed. 
The MET software is intended to provide a 
The math model software is 
The objective of this study is to evaluate the math models developed 
for the MET simulation of a manipulator's rigid body dynamics and the 
servo systems for each of the driven manipulator joints. Specifically, 
the math models were examined with regard to their amenability t o  pipeline 
and parallel processing. 
objectives, a set of prioritized recommendations are offered for future 
work. 
Based on this evaluation and the project 
MODEL EVALUATION 
A recursive rigid body dynamics formulation was developed for 
real-time simulation on the MET by Nasser [ 4 ] .  Nasser considers it to be 
a generalization of a method due to Armstrong [ 5 ] .  The formulation is 
general in the sense that translational or rotational joint types can be 
modeled. Nasser also claims that the model assumes a topological tree 
configuration, but doesn't describe how this would be done. Procedures 
described in [6]  - [7]  are particularly suitable to extending Nasser's 
method to general topological trees. 
14-3 
The procedure for solving for the reaction force and torques at each 
joint and the joint accelerations given the external forces and moments on 
each link and the actuator forces and moments can be described by 
referring to Figure 1 [4]. 
END EFFECTOR G LOADS 
Figure 1. Open Kinematic Chain 
First, set up the equations of dynamic equilibrium for link N and then 
solve for the reaction forces and moments and the joint acceleration in 
terms of the remaining-variables. The remaining variables include the 
proximal links' joint displacements velocities and accelerations and the 
distal links' applied forces and moments, displacements, and velocities. 
Next, proceed to link N-1 and substitute the expressions for the reactions 
that involve link N-1 joint accelerations into the equations of dynamic 
equilibrium for link N-1. The reaction forces and moments exerted by link 
N-2 on link N-1 and the joint acceleration of link N-1 should then be 
solved for in terms of the remaining variables. This step is repeated 
until link 1 is reached. The joint acceleration for link 1 is then 
obtained in terms of the distal links' external forces and moments, 
actuator forces and moments and state variables, the state of link 1, and 
the base state. Then move distally to link 2 and substitute for the link 
1 joint acceleration t o  find the joint 2 acceleration. This step is 
repeated until link N is reached and all the joint accelerations are 
found . 
A free body diagram for any link i of the open kinematic chain is 
shown in Figure 2. 
14-4 
n. -t-l,l 
C 
Figure 2 .  Link Free Body Diagram 
where 
,l.i 
F1 
-i 
N1 
-i 
fC 
-i 
nc 
-i 
fC 
-i+l 
nc 
-i+1 
f is the reaction force that link i+l exerts on link 1, 
-i+l , i 
n is the reaction moment that link i-1 exerts on link i 
-i+l, i 
f is the reaction force that link i-1 exerts on link i, 
3-1,i 
n 
-i-1, i 
FE 
-i 
is the link i inertia force, 
is the link i inertia torque, 
is the control force exerted on link i at joint i-1, 
is the control torque exerted on link i at joint i-1, 
is the control force exerted on link i+l at joint i, 
is the control torque exerted on link i+l at joint i, 
is the reaction torque that link i-1 exerts on link i, 
is the sum of the external forces acting on link i referred to 
the mass center of link i, 
-. NE 
-. r* 
is the sum of the external moments acting on link i when the 
external forces are 'referred to the mass center of link i, 
is the position vector of the mass center of link i relative to 
the origin of the i-1 frame, 
14-5 
Peg -'
P* -' origin of frame i-1 
is the position vector of the mass center of link i relative to 
the origin of the i frame, 
is the position vector of the origin of frame i relative to the 
A number of researchers have investigated pipeline and parallel 
implementations of the equations of motion for various purposes. 
Lin [8] described a procedure for scheduling the subtasks of a group of 
microprocessors computing the inverse dynamics using the Newton-Euler 
equations of motion. 
link. 
ordered schedule for each of the microprocessors. However, the total 
processing time of solving the minimum-time scheduling problem could not 
be easily reduced to a manageable level. 
Luh and 
One microprocessor is assigned to each manipulator 
A variable branch-and-bound search finds an optional subtask- 
Lathrop [9] proposed two parallel algorithms for solving the inverse 
dynamics problem using a group of special-purpose processors. 
linear Newton-Euler algorithm, which is most closely related to the method 
proposed by Luh and Lin. The other is a logarithmic parallel Newton-Euler 
algorithm based on the "partial sum" technique, which achieves on O(rlog,N1) 
total processing time. However, both methods have two main effects that 
deteriorate the performance of parallel computations. They both require 
potentially massive internal buffering to achieve pipelined computation 
between forward and backward recursions. 
communication and bussing, which frequently cause data to be fetched, and 
as a result data for operand pairs are not properly aligned for parallel 
computations. 
One is a 
They both involve complex inter- 
Lee and Chang [lo] proposed an algorithm for solving the inverse 
dynamics problem of an N-link manipulator using p processors in parallel 
on the Newton-Euler equations of motion. 
technique to achieve a total processing time of O(k,[N/pl + k, rlog,pl) , 
where kl and k, are constants. 
the same as Lathrop. The p-fold parallel algorithm consists of p-parallel 
blocks with pipelined elements within each parallel block. 
from the p-parallel blocks form a homogeneous linear recurrence of size p. 
The parallel algorithm can also be implemented in a systolic pipelined 
architecture, requiring three floating-point operations for each complete 
set of joint torques. 
It was the "recursive doubling" 
When p = N, the algorithm is O(rlog, N1 ), 
The results 
Binder and Herzog [ll] described an algorithm based on the recursive 
Newton-Euler equations of motion where the parallel computations are 
distributed over multiple computing elements, one for each joint. 
Concurrency is achieved by substituting "predicted" values for the actual 
values of variables involved in the recursive equations. The authors 
simulated this method and compared it to other approaches such as 
simplification of the dynamic equations. 
Amin-Javaheri and Orin [12] proposed systolic architectures 
consisting of 1, N, and N(N+1)/2 processors for computing the inertia 
matrix of an N degree of freedom manipulator. 
Processor is being developed as the fundamental component of the 
A VLSI-based Robotics 
14-6 
, 
architecture. The algorithm used is based on recursive computation of the 
inertial parameters of sets of composite rigid bodies and is programmed to 
exploit any inherent parallelism. 
Lee and Chang [13] proposed two parallel algorithms for computing the 
The first algorithm is based on Walker and 
forward dynamics for real-time simulation with N processors for an N 
degree of freedom manipulator. 
Orin's [14] composite rigid-body method. It generates the inertia matrix 
using the parallel Newton-Euler algorithm, the parallel linear recurrence 
algorithm [lo], and the modified row-sweep algorithm, and then inverts the 
inertia matrix to obtain the joint acceleration vector. The time complex- 
ity of this parallel algorithm is of the order O(N2) with O(N) processors. 
Further reduction of the order of time complexity can be achieved by 
implementing the Cholesky factorization procedure on VLSI array processors 
to invert the symmetric, positive-definite, inertia matrix. The second 
parallel algorithm is based on Walker and Orin's [14] conjugate gradient 
method. 
Of the methods just described, only Nasser's method [4] was 
formulated to allow for hardware substitution in a simulation. Currently, 
it is implemented on the MET in a sequential algorithm with one IBM PC-AT. 
The Nasser method appears to be a variation of a method by Featherstone 
[15]. The AT matrix in Nasser's method seems to correspond to the I^ $ 
matrix in Featherstone's method. This would imply that Nasser's method 
has the same nonlinear recurrence that makes Featherstone's method 
impossible to solve with known methods of parallel solution of recurrence 
problems [13]. Kung [16] has shown that any parallel algorithm using any 
number of processors cannot be essentially faster than the obvious 
sequential algorithm for any nonlinear polynomial recurrence problem. If 
not for this, the recursive doubling technique of Kogge and Stone [17] 
could have been used. The method of Nasser does not seem to be particu- 
larly adaptable to pipelining either. The calculation of the A; matrix 
alone requires about 42% of the total computations. 
in the pipeline would have to be idle, waiting for the At to complete. 
The other processors 
The hardware that makes up the MET limits the use of pipelining. 
Instruction pipelining is possible on the Intel 80286 only by prefetching 
instructions. 
application for the new Intel 80960 architecture which allows parallel and 
out-of-order instruction execution of 32-bit operations at 20 MEz [18]. 
As an alternative, the MET would seem to be an ideal 
The Multibus I1 "Network-in-a-Box" promises to greatly speed up 
interprocessor communications with initially three Intel 80386 processors 
on board.' The National Instruments IEEE-488 interface card and software 
are much too slow. 
RECOMMENDATION AND PRIORITIZING OF FUTURE WORK 
My recommendatton of future work for the MET will be listed in order 
of decreasing prior'ity. 
14-7 
1. The Nasser algorithm does not appear to be amenable to pipeline 
or parallel processing. 
sequential algorithm on a fast processor. 
modify the method of Binder and Herzog [ll] and use prediction to estimate 
values, instead of waiting for a complete set of computed values to be 
ready. 
One option would be to run it as a very fast 
Another option would be to 
2. The simulation should include the rigid body dynamics of the base 
Amobile base, where motion relative to either a fixed base or base link. 
with rigid body dynamics should be included in the model. 
3. The servo systems are decoupled in their current design. This 
makes these computations naturally parallel. The rigid body model of 
Nasser could run on a fast processor and broadcast results to N 
processors, one for each of the N servo systems, operating in parallel. 
4. Flexible links should be added to the model. For open 
topological trees, this should be straight forward since the complete 
force system acting on each link is known. A beam element model of a 
flexible manipulator is described in Kelly and Huston [19]. 
5. Constrained motion should be modeled so that closed loops can be 
simulated. Rigid links should be simulated first and then flexible links. 
14-8 
REFERENCES 
1. Van Valkenburg, J. A.: Manipulator Emulator Testbed Development 
Project Plan. LEMSCO-23536, January 1987. 
2. Schindeler, R. E.: Manipulator Emulator Testbed Verification Plan. 
LEMSCO-24095, October 1987. 
3. Rob, K. K.: Manipulator Emulator Testbed Verification Report. 
LEMSCO-24113, May 1988. 
4. Nasser, M. G.: Recursive Newton-Euler Formulation of Manipulator 
Dynamics. LEMSCO-24673, February 1988. 
5. Armstrong, W. W.: 
an N-Link Manipulator. 
Theory of Machines and Mechanisms, Volume 2, Montreal, July 1979, pp. 
1343-1346. 
Recursive Solution to the Equations of Motion of 
Proceedings of the 5th World Congress on the 
6. Huston, R. L., Passerello, C. E., and Harlow, M. W.: Dynamics of 
Multirigid-Body Systems. Trans. SME, J. Applied Mechanics, Volume 45, 
December 1978, pp. 889-894. 
7. Kelly, F. A.: On the Dynamics of Flexible Multibody Systems. Ph.D. 
Dissertation, University of Cincinnati, June 1982. 
8. Luh, J. Y. S., and Lin, C.  S.: Scheduling of Parallel Computation 
for a -Computer-Controlled Mechanical Manipulator. IEEE Trans. on Systems , 
Man, and Cybernetics, Volume SMC-12, No. 2, MarchIApril 1982. 
9. Lathrop, R. 8.: Parallelism in Manipulator Dynamics. The 
International Journal of Robotics Research, Volume 4, No. 2, Summer 1985, 
pp. 80-102. 
10. Lee, C.  S. G., and Chang, P. R.: Efficient Parallel Algorithm for 
Robot Inverse Dynamics Computation. IEEE Trans. on Systems, Man, and 
Cybernetics, Vol. MC-16, No. 4, July/August 1986, pp. 532-542. 
11. Binder, E. E., and Herzog, J. H.: Distributed Computer Architecture 
and Fast Parallel Algorithms in Real-Time Robot Control. Ibid., pp. 
543-549. 
12. Amin-Javaheri, M., and Orin, D. E.: A Systolic Architecture for 
Computation of the Manipulator Inertia Matrix. 
IEEE International Conference on Robotics and Automation, Vol. 2, pp. 
647-653. 
Proceedings of the 1987 
13. Lee, C. S. G., and Chang, P. R.: Efficient Parallel Algorithms for 
Robot Forward Dynamics Computation. IEEE Trans. on Systems, Man, and 
Cybernetics, Volume 18, No. 2, March/April 1988. 
14-9 
14. Walker, M. W., and Orin, D. E.: Efficient Dynamic Computer 
Simulation of Robot Mechanisms. Trans. ASME J. Dynamic Systems, 
Measurement and Control, Volume 104, September 1982, pp. 205-211. 
15. Featherstone, R.: The Calculation of Robot Dynamics Using 
Articulated-Body Inertia. 
Volume 2, No. 1, Spring 1983, pp. 13-30. 
The International Journal of Robotics Research, 
16. Kung, H. T.: New Algorithms and Lower Bounds for the Parallel 
Evaluation of Certain Rational Expressions and Recurrences. 
the Association for Computing Machinery, Volume 23, No. 2, April 1976, pp. 
252-261. 
Journal of 
17. Kogge, P. M., and Stone, H. S.: A Parallel Algorithm for the 
Efficient Solution of a General Class of Recurrence Equations. IEEE 
Trans. on Computers, Volume C-22, No. 8, August 1973, pp. 786-793. 
18. Ryan, D. P.: Intel's 80960: An Architecture Optimized for Embedded 
Control. IEEE Micro, June 1988, pp. 63-76. 
19. Kelly, F. A., and Huston, R. L.: Statics and Dynamics of a Flexible 
Manipulator. Proceedings of the 5th ASME International Computers in 
Engineering Conference, Boston, MA, 1985. 
V 
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Model evaluation, recommendation and prioritizing of future work for the manipulator emulator testbed

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