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Structured Motion Planning in the Local Configuration Space

Published online by Cambridge University Press:  09 March 2009

A. M. S. Zalzala  and
A. S. Morris
A. M. S. Zalzala
Affiliation:
Robotics Research Group, Department of Control Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (UK)
A. S. Morris
Affiliation:
Robotics Research Group, Department of Control Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (UK)
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Summary

The minimum-time motion of robot manipulators is solved by defining a suitable time history for the arm end-effector to traverse. As the planning is performed in the configuration space, the uniqueness of the proposed algorithm emerges from the combination of both cubic and quadratic polynomial splines. Furthermore, the highly efficient time optimisation procedure could be applied to local segments of each joint trajectory, leading to a significant reduction of the travelling time. In addition, the ability to perform a search in the work space is granted, exploiting all possible options for an optimum motion. The method proposed considers all realistic physical limitations inherent in the manipulator design, in addition to any geometric constraints imposed on the path. Simulation programs have been written, and results are reported for the Unimation PUMA 560 robot manipulator.

Keywords

Minimum-time motionRobotsOptimisationConfiguration spaceMotion planning
Type
Article
Information
Robotica , Volume 9 , Issue 1 , January 1991 , pp. 81 - 92
Copyright
Copyright © Cambridge University Press 1991

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References

1.Paul, R.P., Robot Manipulators: Mathematics, Programming and Control (MIT Press, Cambridge, MA, 1981).Google Scholar
2.Lee, C.S.G., Fu, K.S. and Gonzales, R.C., “Planning of Manipulator Trajectories” In Tutorial on Robotics (IEEE Computer Society Press, Washington, 1986) pp. 155–65.Google Scholar
3.Fu, K.S., Gonzalez, R.C. and Lee, C.S.G., Robotics: Control, Sensing, Vision and Intelligence (McGraw Hill, New York, 1987).Google Scholar
4.Paul, R.P., “Manipulator Cartesian Path Control” IEEE Trans. Syst., Man, Cyber. SMC-9, 702–11 (1979).Google Scholar
5.Luh, J.Y.S. and Lin, C.S., “Optimum Path Planning for Mechanical Manipulators” Trans. ASME, J. of Dyn. Syst., Meas. and Control 102, 142–51 (1981).Google Scholar
6.Taylor, R.H., “Planning and Execution of Straight Line Manipulator Trajectories” IBM J. of Res. and Dev. 23, No. 4, 253–264 (1979).CrossRefGoogle Scholar
7.Taylor, R.H., “Planning and Execution of Straight Line Manipulator Trajectories” Research Report (RC-6647) IBM Thomas J. Watson Research Centre, New York (1977).Google Scholar
8.Orin, D.E., “Pipelined Approach to Inverse Plant Plus Jacobian Control of Robot Manipulators” Proc. IEEE Int. Conf. Robotics and Automation (IEEE,Atlanta, GA, 1984) pp. 169–175.Google Scholar
9.Bazerghi, A., Goldenberg, A.A. and Apkarian, J., “An Exact Kinematic Model of PUMA 600 Manipulator” IEEE Trans. Syst., Man, Cyber. SMC-14, 483–87 (1984).Google Scholar
10.Burden, R.L., Faires, J.D. and Reynolds, A.C., Numerical Analysis (PWS Pub., Boston, MA, 1974).Google Scholar
11.Finkel, R.A., “Constructing and Debugging Manipulator Programms” Ph.D. Dissertation Stanford University (1976).Google Scholar
12.Paul, R.P., “Modeling, Trajectory Calculation and Servoing of a Computer Controlled Arm” Ph.D. Dissertation Stanford University (1972).CrossRefGoogle Scholar
13.Lewis, R.A., “Autunomous Manipulation on a Robot: Summary of Manipulator Software Functions” Tech. Memo 33–679 J.P.L., CA (1974).Google Scholar
14.Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical Recipes (Cambridge University Press, Cambridge, 1986).Google Scholar
15.De-Boor, C., A Practical Guide to Splines (Springer-Verlag, New York, 1978).CrossRefGoogle Scholar
16.Vandergraft, J.S., Introduction to Numerical Computations (Academic Press, London, 1978).Google Scholar
17.Lin, C.S., Chang, P.R. and Luh, J.Y.S., “Formulation and Optimization of Cubic Polynomial Joint Trajectories For Industrial Robots” IEEE Trans. Automatic Control AC-28, 1066–74 (1983).CrossRefGoogle Scholar
18.Lin, C.S. and Chang, P.R., “Approximate Optimum Paths of Robot Manipulators Under Realistic Physical Constraints” Proc. IEEE Int. Conf. on Robotics and Automation (IEEE,St. Louis, MO, 1985) pp. 737–42.Google Scholar
19.Jeon, H.T. and Eslami, M., “On Minimum-Time Joint-Trajectory Planning For Industrial Manipulators With Cubic Polynomial and Input Torque Constraints” Proc. IEEE 25th Conf. on Decision and Control (IEEE,Athens, 1986) pp. 435–40.CrossRefGoogle Scholar
20.Khalil, W., “Trajectories Calculations in the Joint Space of Robots” In Advanced Software in Robotics, ed. Danthine, A. and Geradin, M. (Elsevier Science Pub. B. V., North-Holland, 1984).Google Scholar
21.Castain, R.H. and Paul, R.P., “An On-Line Dynamic Trajectory Generator” Int. J. Robotics Research 3, No. 1, 68–72 (1984).CrossRefGoogle Scholar
22.Thompson, S.E. and Patel, R.V., “Formulation of Joint Trajectories for Industrial Robots Using B-Splines” IEEE Trans. Industrial Electronics IE-34, 192–199 (1987).CrossRefGoogle Scholar
23.Luh, J.Y.S. and Lin, C.S., “Approximate Joint Trajectories For Control of Industrial Robots Along Cartesian Paths” IEEE Trans. Syst., Man, Cyber. SMC-14, 444–450 (1984).Google Scholar
24.Sahar, G. and Hollerbach, J.M., “Planning of Minimumtime Trajectories for Robot Arms” Int. J. Robotics Research 5, No. 3, 90–100 (1986).CrossRefGoogle Scholar
25.Rajan, V.T., “Planning of Minimum-time Trajectories for Robot Arms” In Proc. IEEE Int. Conf. Robotics and Automation (IEEE,St. Louis, MO, 1985) pp. 759–64.Google Scholar
26.McKay, N.D. and Shin, K.G., “Minimum-Time Trajectory Planning for Industrial Robots with General Torque Constraints” In Proc. IEEE Int. Conf. on Robotics and Automation (IEEE,San Francisco, CA, 1986), 412–17.Google Scholar
27.Ozaki, H., Yamamoto, M. and Mohri, A., “Optimal and Near-Optimal Manipulator Joint Trajectories With a Preplanned Path” IN Proc. IEEE 26th Conf. on Decision and Control (IEEE,Los Angeles, CA, 1987) pp. 1029–34.CrossRefGoogle Scholar
28.Kim, B.K. and Shin, K.G., “Minimum-Time Path Planning of Robot Arms and Their Dynamics” IEEE Trans. Syst., Man, Cyber. SMC-15, 213–23 (1985).Google Scholar
29.Brady, J.M., Hollerbach, J.M..Johnson, T.L., Lozano-Perez, T. and Mason, M.T., Robot Motion:Planning and Control (MIT Press, Cambridge, MA, 1982).Google Scholar
30.Snyder, W.E., Industrial Robots: Computer Interfacing and Control (Prentice-Hall, London, 1985).Google Scholar
31.Lee, C.S.G. and Ziegler, M., “A Geometric Approach in Solving The Inverse Kinematics of PUMA Robot” IEEE Trans. Aerospace and Electronic Systems AES-20, No. 6, 695–706 (1984).CrossRefGoogle Scholar
32.Paul, R.P., Shimano, B. and Mayer, G.E., “Kinematic Control Equations for Simple Manipulators” IEEE Trans. Syst., Man, Cyber. SMC-11, 449–55 (1981).Google Scholar
33.Chand, S. and Doty, K.L., “On-Line Polynomial Trajectories for Robot Manipulators” Int. J. of Robotics Research 4, No. 2, 38–48 (1985).CrossRefGoogle Scholar
34.Luh, J.Y.S., Walker, M.W. and Paul, R.P.C., “On-Line Computational Scheme for Mechanical Manipulators” Trans. ASME, J. of Dyn. Syst., Meas. and Control 102, 69–76 (1980).Google Scholar
35.Hollerbach, J.M., “Dynamic Scaling of Manipulator Trajectories” Trans. ASME, J. of Dyn. Syst., Meas. and Control 106, 102–6 (1984).Google Scholar
36.Hildebrand, F.B., Introduction to Numerical Analysis (McGraw Hill, New York, 1956).Google Scholar
37.Bobrow, J.E., Dubowsky, S. and Gibson, J.S., “Time-Optimal Control of Robotic Manipulators Along Specified Paths” Int. J. Robotics Research 3, No. 3, 3–17 (1985).CrossRefGoogle Scholar
38.Hollerbach, J. M., “A Recrusive Lagrangian Formulation of Manipulator Dynamics and a Comparative Study of Dynamics Formulation Complexity” IEEE Trans. Syst., Man, Cyber. SMC-10, 730–36 (1980).Google Scholar
39.Leahy, M.B. Jr, Nugent, L.M., Valavanis, K.P. and Saridis, G.N., “Efficient Dynamics for a PUMA 600” In Proc. IEEE Int. Conf. on Robotics and Automation (IEEE,San Francisco, CA, 1986) pp. 519–24.Google Scholar
40.Armstrong, B., Khatib, O. and Burdick, J., “The Explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm” In Proc. 1986 IEEE Int. Conf. on Robotics and Automation, 1 (IEEE,San Francisco, CA, 1986) pp. 510–18.Google Scholar
41.Zalzala, A.M.S. and Morris, A.S., “An On-Line Distributed Minimum-Time Trajectory Generator for Intelligent Robot Manipulators” Research Report #358 (Department of Control Engineering, University of Sheffield, United Kingdom, 1989).Google Scholar
42.Zalzala, A.M.S. and Morris, A.S., “An On-Line Minimum-Time Trajectory Generator for Intelligent Robot Manipulators” In Proc. IMC Sixth Conference on Advanced Manufacturing Technology (City University,Dublin, Ireland, 1989) pp. 1114–31.Google Scholar
43.Zalzala, A. M. S. and Morris, A. S., “Real-Time Robot Motion: The VLSI Implementation Via Transputers” Research Report #364 (Department of Control Engineering, University of Sheffield, United Kingdom, 1989).Google Scholar
44.Zalzala, A.M.S. and Morris, A.S., “A Fast Trajectory Tracker for Intelligent Robot Manipulators” Proc. Int. Conf. Applications of Transputers. (to appear).Google Scholar
45.Zalzala, A.M.S. and Morris, A.S., “A Distributed Pipelined Architecture of the Recursive Lagrangian Equations of Motion for Robot Manipulators with VLSI Implementation” Research Report #353 (Department of Control Engineering, University of Sheffield, United Kingdom, 1989).Google Scholar