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A closed-loop inverse kinematic scheme for on-line joint-based robot control*

Published online by Cambridge University Press:  09 March 2009

Bruno Siciliano
Bruno Siciliano
Affiliation:
Dipartimento di Informatica e Sistemistica, Università degli Study “Federico II” di Napoli, Via Claudio 21, 80125 Napoli (Italy)
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Summary

A computationally fast inverse kinematic scheme is derived which solves robot's end-effector (EE) trajectories in terms of joint trajectories. The inverse kinematic problem (IKP) is cast as a control problem for a simple dynamic system. The resulting closed-loop algorithms are shown to guarantee satisfactory tracking performance. Differently from previous first-order schemes which only solve for joint positions and velocities, we propose here new second order tracking schemes which allow the on-line generation of joint position + velocity + acceleration (PVA) reference trajectories for any computed torque-like controller in sensor-based robot applications. The algorithms do explicitly solve the IKP for both EE position and orientation. Simulation results for a six-degree-of-freedom PUMA-like geometry demonstrate the effectiveness of the scheme, even near singularities.

Keywords

Kinematic schemeClosed-loop algorithmsOn-line controlRobots
Type
Article
Information
Robotica , Volume 8 , Issue 3 , July 1990 , pp. 231 - 243
Copyright
Copyright © Cambridge University Press 1990

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References

1.Vukobratović, M. and Kirćanski, M., Scientific Fundamentals of Robotics 3: Kinematics and Trajectory Synthesis of Manipulation Robots (Springer-Verlag, Berlin, Heidelberg, FRG, 1986).CrossRefGoogle Scholar
2.Pieper, D.L., “The Kinematics of Manipulators Under Computer Control” Ph.D. dissertation, Stanford University (1968).Google Scholar
3.Paul, R.P., Robot Manipulators: Mathematics, Programming, and Control (Cambridge, MA, MIT Press, 1981).Google Scholar
4.Goldenberg, A.A., Benhabib, B. and Fenton, R.G., “A complete generalized solution to the inverse kinematics of robots” IEEE J Robotics and Automation RA-1, No. 1, 14–20 (1985).CrossRefGoogle Scholar
5.Angeles, J., “On the Numerical solution of the inverse kinematic problem” Intern. J. Robotics Resarch 4, No. 2, 21–37 (1985).CrossRefGoogle Scholar
6.Lenarčič, J., “An efficient numerical approach for calculating the inverse kinematics for robot manipulators” Robotica 3, 21–26 (1985).CrossRefGoogle Scholar
7.Tsai, L.-W. and Morgan, A.P., “Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods” ASME J. Mechanism, Transmission, and Automation in Design 107, No. 2, 189–200 (1985).CrossRefGoogle Scholar
8.Manseur, R. and Doty, K.L., “A fast algorithm for inverse kinematic analysis of robot manipulators” Intern. J. Robotics Research 7, No. 3, 52–63 (1988).CrossRefGoogle Scholar
9.Whitney, D.E., “Resolved motion rate control of manipulators and human prostheses” IEEE Trans. Man–Machine Systems MMS-10, No. 2, 47–53 (1969).CrossRefGoogle Scholar
10.Featherstone, R., “Position and velocity transformations between robot end-effector coordinates and joint angles” Intern. J. Robotics Research 2, No. 2, 35–45 (1983).CrossRefGoogle Scholar
11.Hollerbach, J.M. and Sahar, G., “Wrist-partitioned, inverse kinematic acceleration and manipulator dynamics” Inter. J. Robotics Research 2, No. 4, 61–76 (1983).CrossRefGoogle Scholar
12.Balestrino, A., De Maria, G. and Sciavicco, L., “Robust control of robotic manipulators” Preprints of the 9th IFAC World Congress 6, Budapest, Hungary, 80–85 (07, 1984).Google Scholar
14.Siciliano, B., “Solution Algorithms to the Inverse Kinematic Problem for Manipulation Robots” (in Italian) Ph.D. dissertation, University of Naples (1986).Google Scholar
15.Balestrino, A., De Maria, G., Sciavicco, L. and Siciliano, B., “An algorithmic approach to coordinate transformation for robotic manipulators” Advanced Robotics 2, No. 4, 327–344 (1987).CrossRefGoogle Scholar
16.Sciavicco, L. and Siciliano, B., “Coordinate transformation: A solution algorithm for one class of robots” IEEE Trans. Systems, Man, and Cybernetics SMC-16, No. 4, 550–559 (1986).CrossRefGoogle Scholar
17.Sciavicco, L. and Siciliano, B., “An inverse kinematic solution algorithm for dexterous redundant manipulators” Proceedings of the 3rd International Conference on Advanced Robotics,Versailles, France,247–256 (10, 1987).Google Scholar
18.Sciavicco, L., Siciliano, B. and Chiacchio, P., “On the use of redundancy in robot kinematic control” Proceedings of the 1988 American Control Conference,Atlanta, GA,1370–1375 (06, 1988).CrossRefGoogle Scholar
19.Sciavicco, L. and Siciliano, B., “A solution algorithm to the inverse kinematic problem for redundant manipulators” IEEE J. Robotics and Automation RA-4, No. 4, 303–310 (1988).Google Scholar
20.Sciavicco, L. and Siciliano, B., “On the solution of inverse kinematics of redundant manipulators” Preprints of the NATO Advanced Research Workshop: Robots with Redundancy, Salò, Italy (06/07, 1988) to be published by Springer-Verlag.Google Scholar
21.Chiacchio, P. and Siciliano, B., “Achieving singularity robustness: An inverse kinematic solution algorithm for robot control” IEE Control Engineering Series 36 Robot Control: Theory and Application 16, 149–156 (Peter Peregrinus Ltd., London, UK, 1988).Google Scholar
22.Asada, H. and Slotine, J.-J.E., Robot Analysis and Control (Wiley-Interscience, New York, NY, 1986).Google Scholar
23.Das, H., Slotine, J.-J.E. and Sheridan, T.B., “Inverse kinematic algorithms for redundant systems” Proceedings of the 1988 IEEE International Conference on Robotics and Automation,Philadelphia, PA,43–48 (04, 1988).Google Scholar
24.Tsai, Y.T. and Orin, D.E., “A strictly convergent real-time solution for inverse kinematics of robot manipulators” J. Robotic Systems 4, No. 4, 477–501 (1987).CrossRefGoogle Scholar
25.Wolovich, W.A. and Flueckiger, K.F., “Inverse kinematic-based control” Proceedings of the Workshop on Space Telerobotics, Pasadena, CA, 165–175 (01, 1987).Google Scholar
26.Slotine, J.-J.E. and Yoerger, D.R., “A rule-based inverse kinematics algorithm for redundant manipulators” Intern. J. Robotics and Automation 2, No. 2, 86–89 (1987).Google Scholar
27.Vaccaro, R.J. and Hill, S.D., “A joint-space command generator for Cartesian control of robotic manipulators” IEEE J. Robotics and Automation RA-4, No. 1, 70–76 (1988).CrossRefGoogle Scholar
28., S.D. and Vaccaro, R.J., “Cartesian control of robotic manipulators with joint compliance” Robotica 5, 207–215 (1987).CrossRefGoogle Scholar
29.Luh, J.Y.S., Walker, M.W. and Paul, R.P.C., “Resolved-acceleration control of mechanical manipulators” IEEE Trans. Automatic Control AC-25, No. 3, 468–474 (1980).CrossRefGoogle Scholar
30.Sciavicco, L. and Siciliano, B., “A computational technique for solving robot end-effector trajectories into joint trajectories” Proceedings of the 1988 American Control Conference,Atlanta, GA,535–536 (06, 1988).CrossRefGoogle Scholar
31.Siciliano, B., “Closed-loop computational schemes of robot inverse kinematics” Proceedings of the International Meeting: Advances in Robot Kinematics,Ljubljana, Yugoslavia, 113–121 (09, 1988).Google Scholar
32.Novaković, Z.R., “A solution of the inverse kinematics problem using the sliding mode” Report No. 5153, Institut Jožef Stefan, Ljubljana, Yugoslavia (03, 1988).Google Scholar
33.Slotine, J.-J.E. and Sastry, S.S., “Tracking control of nonlinear systems using sliding surfaces with application to robot manipulators” Intern. J. Control 38, No. 2, 465–492 (1983).CrossRefGoogle Scholar
34.Chiacchio, P. and Siciliano, B., “A closed-loop Jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant writs” J. Robotic Systems 6, No. 5, 601–630 (1989).CrossRefGoogle Scholar
35.Coiffet, P., Robot Technology Series 1: Modelling and Control (Kogan Page, London, UK, 1983).Google Scholar
36.Yuan, J.S.-C., “Closed-loop manipulator control using quaternion feedback,” IEEE J. Robotics and Automation RA-4, No. 4, 434–440 (1988).CrossRefGoogle Scholar
37.Khatib, O., “A unified approach for motion and force control of robot manipulators: The operational space formulation” IEEE J. Robotics and Automation RA-3, No. 1, 43–53 (1987).CrossRefGoogle Scholar
38.Hogan, N., “Impedance control: An approach to manipulation: Part II—Implementation” ASME J. Dynamic Systems, Measurement, and Control 107, No. 1, 8–16 (1985).CrossRefGoogle Scholar
39.Litvin, F.L., Yi, Z., Castelli, V. Parenti and Innocenti, C., “Singularities, configurations, and displacement functions for manipulators,” Intern. J. Robotics Research 5, No. 2, 52–65 (1986).CrossRefGoogle Scholar
40.Nakamura, Y., Hanafusa, H. and Yoshikawa, T., “Task-priority based redundancy control of robot manipulators,” Intern. J. Robotics Research 6, No. 2, 3–15 (1987).CrossRefGoogle Scholar