Abstract
We describe new architectures for the efficient computation of redundant manipulator kinematics (direct and inverse). By calculating the core of the problem in hardware, we can make full use of the redundancy by implementing more complex self-motion algorithms. A key component of our architecture is the calculation in the VLSI hardware of the Singular Value Decomposition of the manipulator Jacobian. Recent advances in VLSI have allowed the mapping of complex algorithms to hardware using systolic arrays with advanced computer arithmetic algorithms, such as the coordinate rotation (CORDIC) algorithms. We use CORDIC arithmetic in the novel design of our special-purpose VLSI array, which is used in computation of the Direct Kinematics Solution (DKS), the manipulator Jacobian, as well as the Jacobian Pseudoinverse. Application-specific (subtask-dependent) portions of the inverse kinematics are handled in parallel by a DSP processor which interfaces with the custom hardware and the host machine. The architecture and algorithm development is valid for general redundant manipulators and a wide range of processors currently available and under development commercially.
Similar content being viewed by others
References
Amin-Javaheri, M. and Orin, D. E., Systolic architectures for the manipulator inertia matrix,IEEE Trans. Systems Man, Cybernet. 18(6), 939–951 (1988).
Brent, R. P., Luk, F. T. and Van Loan, C. F., Computation of the singular value decomposition using mesh-connected processors,J. VLSI Comput. Systems 1(3), 242–270 (1985).
Butner, S. E., Wang, Y., Mangaser, A. and Jordan, S., Design and simulation of RIPS: An advanced robot control system, inProc. 1988 IEEE Conf. Robotics and Automation, Philadelphia, PA, 1988, pp. 470–474.
Cavallaro, J. R., Keleher, M. P., Price, R. H. and Thomas, G. S., VLSI implementation of a CORDIC SVD processor,Proc. 8th Biennial University/Government/Industry Microelectronics Symposium, June 1989, pp. 256–260.
Cavallaro, J. R. and Luk, F. T., CORDIC Arithmetic for an SVD processor,J. of Parallel and Distributed Computing 5(3), 271–290 (1988).
Chang, P. R. and Lee, C. S. G., Residue arithmetic VLSI array architecture for manipulator pseudo-inverse Jacobian computation,IEEE Trans. Robot. Automat. 5(5), 569–582 (1989).
Chen, D. C. and Price, R. H., A real-time TMS320C40 based parallel system for high rate digital signal processing, inProc. 1991 IEEE ICASSP, Toronto, Canada, 1991, pp. 1573–1576.
Fijany, A. and Bejczy, A. K., A class of parallel algorithms for computation of the manipulator inertia matrix.IEEE Trans. Robot. Automat. 5(5), 600–615 (1989).
Golub, G. H. and Van Loan, C. F.,Matrix Computations, 2nd edn, Johns Hopkins Univ. Press, Baltimore, MD, 1989.
Graham, J. H., Special computer architectures for robotics: Tutorial and survey.IEEE Trans. Robot. Automat. 5(5), 543–554 (1989).
Harber, R. G., Li, J., Hu, X. and Bass, S. C., The application of bit-serial CORDIC computational units to the design of inverse kinematics processors, inProc. 1988 IEEE Conf. Robotics and Automation, Philadelphia, PA, 1988, pp. 1152–1157.
Hemkumar, N. D., Kota, K. and Cavallaro, J. R., CAPE — VLSI implementation of a systolic processor array: architecture, design and testing,Proc. 9th IEEE Biennial University/Government/Industry Microelectronics Symposium, June 1991, pp. 64–69.
Hsia, T. C., Current, K. W., Mao, Z., Chu, W. S., Liu, J., Lu, G. Z. and Han, W. H., A proposed new VLSI architecture for real-time robot manipulator control,Int. J. Robot. Automat. 6(4), 169–178 (1991).
Jones, D. I. and Fleming, P. J., Control applications of transputers, in P. J. Fleming (ed),Parallel Processing in Control: the Transputer and Other Architectures, Peter Peregrinus Ltd., London, 1988, pp. 101–125.
Kameyama, M., Matsumoto, T., Egami, H. and Higuchi, T., Implementation of a high performance LSI for inverse kinematics computation, inProc. 1989 IEEE Conf. Robotics and Automation, Scottsdale, AZ, 1988, pp. 757–762.
Klema, V. C. and Laub, A. J., The singular value decomposition: Its computation and some applications,IEEE Trans. Automat. Control AC-25(2), 164–176 (1980).
Lee, C. S. G. and Chang, P. R., A maximum pipelined CORDIC architecture for inverse kinematic position computation,IEEE J. Robot. Automat. RA-3(5), 445–458 (1987).
Lee, C. S. G. and Chen, C. L., Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system,IEEE Trans. Systems Man Cybernet. 20(3), 582–595 (1990).
Leung, S. S. and Shanblatt, M. A., Real-time DKS on a single chip,IEEE Trans. Robot. Automat. 3(4), 281–290 (1987).
Leung, S. S. and Shanblatt, M. A., Computer architecture design for robotics, inProc. 1988 IEEE Conf. Robotics and Automation, Philadelphia, PA, 1988, pp. 453–456.
Li, C. J., Hemami, A. and Sankar, T. S., An efficient computational method of the Jacobian for robot manipulators,Robotica 9, 231–234 (1991).
Maciejewski, A. A. and Reagin, J. M., A parallel algorithm and architecture for the control of kinematically redundant manipulators, inProc. 1992 IEEE Conf. Robotics and Automation, Nice, France, 1992, pp. 488–493.
Nenchev, D. N., Redundancy resolution through local optimization: A review.J. Robotic Systems 6(6), 769–798 (1989).
Orin, D. E., Olson, K. W. and Chao, H. H., Systolic architectures for computation of the Jacobian for robot manipulators, in J. H. Graham (ed),Computer Architectures for Robotics and Automation. Gordon and Breach, London, 1987, pp. 39–67.
Orin, D. E. and Schrader, W. W., Efficient computation of the Jacobian for robot manipulators,Int. J. Robot. Res. 3(4), 66–75 (1984).
Piedra, R. M., A parallel approach for solving matrix multiplication on the TMS320C4x DSP, Technical report, Texas Instruments DSP Application Report, Houston, TX, 1991.
Sadayappan, P., Ling, Y. L. C., Olson, K. W. and Orin, D. E., A restructurable VLSI robotics vector processor architecture for real-time control,IEEE Trans. Robot. Automat. 5(5), 583–599 (1989).
Siciliano, B., Kinematic control of redundant robot manipulators: A tutorial,J. Intelligent and Robotic Systems 3(3), 201–210 (1990).
Smiarowski, A. Jr. and Anderson, J. N., A fast computer architecture for the control of robots,Comput. Elec. Eng. 17(3), 217–235 (1991).
Spong, M. W. and Vidyasagar, M.,Robot Dynamics and Control, Wiley, New York, 1989.
Tourassis, V. D. and Ang, M. H. Jr., A modular architecture for inverse robot kinematics,IEEE Trans. Robot. Automat. 5(5), 555–568 (1989).
Volder, J., The CORDIC trigonometric computing technique,IRE Trans. Elec. Comput. EC-8(3), 330–334 (1959).
Walker, I. D., The use of kinematic redundancy in reducing impact and contact effects in manipulation, inProc. 1990 IEEE Conf. Robotics and Automation, Cincinnati, OH, 1990, pp. 434–439.
Walker, I. D. and Cavallaro, J. R., Parallel VLSI architectures for real-time control of redundant robots, inProc. 1991 American Nuclear Society Meeting on Robotics and Remote Systems, Albuquerque, NM, 1991, pp. 299–310.
Walker, I. D. and Marcus, S. I., Subtask performance by redundancy resolution for redundant robot manipulators,IEEE J. Robot. Automat. 4(3), 350–354 (1988).
Walther, J. S., A unified algorithm for elementary functions,AFIPS Spring Joint Computer Conf., 1971, pp. 379–385.
Wang, Y. and Butner, S. E., A new architecture for robot control, inProc. 1987 IEEE Conf. Robotics and Automation, Raleigh, NC, 1987, pp. 664–670.
Whitney, D. E., Resolved motion rate control of manipulators and human prostheses,IEEE Trans. Man Machine Systems MMS-10(2), 47–53 (1969).
Yeung, T. B. and Lee, C. S. G., Efficient parallel algorithms and VLSI architectures for manipulator Jacobian calculation,IEEE Trans. Systems Man Cybernet. 19(5), 1154–1166 (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Walker, I.D., Cavallaro, J.R. Parallel VLSI architectures for real-time kinematics of redundant robots. J Intell Robot Syst 9, 25–43 (1994). https://doi.org/10.1007/BF01258312
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01258312