Abstract
In this paper parallel computation of manipulator inverse dynamics is investigated. A hierarchical graph-based mapping approach is devised to analyze the inherent parallelism in the Newton-Euler formulation at several computational levels and to derive the features of an abstract architecture for exploitation of parallelism. At each level a parallel algorithm represents the application of a parallel model of computation which transforms the computation into a graph whose structure defines the features of an abstract architecture, i.e., processors and communication structure. Data flow analysis is employed to derive the time lower bound in the computation as well as the sequencing of the abstract architecture. The features of the target architecture are defined by optimization of the abstract architecture to exploit maximum parallelism while minimizing various overheads. A highly parallel MIMD-SIMD architecture is designed and implemented which is capable of efficient exploitation of parallelism at several computational levels. The computation time of the Newton-Euler formulation for a six Degree-Of-Freedom (DOF) general manipulator is measured as 187µs. The increase in the computation time for each additional DOF is 23µs which leads to a computation time of less than 500µs, even for a 12 DOF redundant arm. The architecture also achieves a good performance for other computation problems. For a six DOF general manipulator, the computation time of forward kinematic is measured as 60µs, and forward kinematic and Jacobian as 75µs.
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References
A.K. Bejczy,“Robot Arm Dynamics and Control,” Jet Propulsion Lab., Tech. Memo 33–669, Feb. 1974.
R.P.C. Paul, “Modeling, Trajectory Calculation, and Servoing of a Computer Controlled Arm,” Stanford Univ., AI Memo 177, Sept. 1972.
J.Y.S. Luh, M.W. Walker, and R.P.C. Paul, “Resolved Acceleration Control Mechanical Manipulators,” IEEE Trans. Auto. Control, Vol. AC-25(3), 1980.
E. Freund,“Fast Nonlinear Control with Arbitrary Pole-Placement for Industrial Robots and Manipulators,” Int. J. Robotics Res., Vol. 1 (1), 1982.
A.K. Bejczy, T.J. Tarn, and X. Yun, X.,“Roboust Robot Arm Control with Nonlinear Feedback,” Proc. IFAC Sym., Barcelona, 1985.
O. Khatib, Commande Dynamique dans l’Espace Operationnel des Robots Manipulateurs en Presence d’Obstacles. Ph.D dissertation, ENSAE, 1980.
J.Y.S. Luh, M.W. Walker, and R.C.P. Paul,“On-Line Computation Scheme for Mechanical Manipulators,” Trans. ASME J. Dynamic Syst., Measurement, and Control, Vol. 120, June 1980.
J.M. Hollerbach,“A Recursive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity,” IEEE Trans. Syst., Man, Cybern., Vol. SMC-10(11), Nov. 1980.
A. Fijany, Parallel Algorithms and Architectures in Robotics. Ph.D. dissertation, Univ. of Paris XI ( Orsay ), France, Sept. 1988.
A. Fijany and J.G. Pontnau,“Parallel Computation of the Jacobian for Robot Manipulators,” Proc. IASTED Int. Conf. on Robotics and Automation, Santa Barbara, May 1987.
D.J. Kuck,“Multioperation Machine Computational Complexity”, in Complexity of Sequential and Parallel Numerical Algorithms. J.F. Traub (Ed.), Academic Press, 1973.
J.Y.S. Luh and C.S. Lin,“Scheduling of Parallel Computation for a Computer Controlled Mechanical Manipulators,” IEEE Trans. Syst., Man, and Cybern., Vol. SMC-12(2), March 1982.
H. Kasahara and S. Narita,“Parallel Processing of Robot-Arm Control Computation on a Multimicroprocessor,” IEEE J. Robotics and Automation, Vol. RA-1(2), June 1985.
J. Barhen,“Hypercube Ensembles: An Architecture for Intelligent Robots,” in Computer Architectures for Robotics - and Automation, Ed. J.H. Graham, Gordon and Breach Science Publishers, 1987.
J. Barhen et al,“Optimization of the Computational Load of a Hypercube Supercomputer Onboard a Mobile Robot,” J. Applied Optics, Vol. 26 (23), Dec. 1987.
L.H. Lathrop,“Parallelism in Manipulator Dynamics,” Int. J. Robotics Res., Vol. 4 (2), 1985.
C.S.G. Lee and R.P. Chang,“Efficient Parallel Algorithm for Robot Inverse Dynamics Computation,” IEEE Trans. Syst., Man, Cybern., Vol. SMC-16(4), July 1986.
D.E. Orin et al,“Pipeline/Parallel Algorithms for the Jacobian and Inverse Dynamics Computation,” IEEE Int. Conf. Robotics and Automation, March 1985.
Y-F Zheng and H. Hemami,“Computation of Multibody Sytem Dynamics by a Multiprocessor Scheme,” IEEE Trans. Syst., Man, Cybern., Vol. SMC-16(1), Jan. 1986.
H. Hemami,“A State-Space Model for Interconnected Rigid Bodies,” IEEE Trans. Automatic Control, Vol. AC-27, April 1982.
E.E. Binder and J.H. Herzog,“Distributed Computer Architecture and Fast Parallel Algorithms in Real-Time Robot Control,” IEEE Trans. Syst., Man, Cybern., Vol. SMC-16(4), July 1986.
R. Nigam and C.S.G. Lee,“A Multiprocessor-Based Controller for the Control of Mechanical Manipulators,” IEEE J. Robotics and Automation, Vol. 1 (4), Dec. 1985.
L.H. Jamieson,“Characterizing Parallel Algorithms,” in The Characteristics of Parallel Algorithms, L.H. Jamieson et al ( Eds. ), The MIT Press, 1987.
K. Hwang,“Advanced Parallel Processing with Supercomputer Architectures,” Proc. of The IEEE, Vol. 75 (10), Oct. 1987.
R.W. Hockney and C.R. Jesshope, Parallel Computers. Adam Hilger, 1981.
K. Hwang and F.A. Briggs, Computer Architecture and Parallel Processing. McGraw-Hill, 1984.
L. Snyder, L.H. Jamieson, D.B. Gannon, and H.J. Siegel (Eds.), Algorithmically Specialized Parallel Computers. Academic Press, 1985.
WTL 1232/1233 Floating Point Multiplier and ALU. Weitek Co., Sunnyvale, CA, July 1986.
Blasco, R.W., et al,“SN 54/745516 Co-Processor Supercharges 68000 Arithmetic,” Application Note (AN-114), Monolothic Memories Inc., Sunnyvale, CA, 1984.
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Fijany, A., Bejczy, A.K. (1989). Parallel Algorithms and Architectures for Manipulator Inverse Dynamics. In: Waldron, K.J. (eds) Advanced Robotics: 1989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83957-3_15
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DOI: https://doi.org/10.1007/978-3-642-83957-3_15
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