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Dynamics of redundant robots – inverse solutions

Published online by Cambridge University Press:  09 March 2009

Ronald L. Huston  and
Timothy P. King
Ronald L. Huston
Affiliation:
Department of Mechanical and Industrial Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0072 (USA)
Timothy P. King
Affiliation:
Department of Mechanical and Industrial Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0072 (USA)
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Abstract

SUMMARY

The dynamics of “simple, redundant robots” are developed. A “redundant” robot is a robot whose degrees of freedom are greater than those needed to perform a given kinetmatic task. A “simple” robot is a robot with all joints being revolute joints with axes perpendicular or parallel to the arm segments. A general formulation, and a solution algorithm, for the “inverse kinematics problem” for such systems, is presented. The solution is obtained using orthogonal complement arrays which in turn are obtained from a “zero-eigenvalues” algorithm. The paper concludes with an assertion that this solution, called the “natural dynamics solution,” is optimal in that it requires the least energy to drive the robot.

Keywords

DynamicsRedunantRobotsInverseSolutions
Type
Articles
Information
Robotica , Volume 4 , Issue 4 , October 1986 , pp. 263 - 267
Copyright
Copyright © Cambridge University Press 1986

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References

1.Benati, M., Morasso, P. and Tagliasco, V., “The Inverse Kinematic Problem for Anthropomorphic Manipulator Arms” Trans. ASME, J. Dyn. Syst. Measurement Contr. 104(1), 110–113 (03 1982).Google Scholar
2.Featherstone, R., “Position and Velocity Transformations Between Robot End-effector Coordinates and Joint Angles” Int. J. Robotics Res. 2(2), 35–45 (1983).CrossRefGoogle Scholar
3.Featherstone, R., “Calculation of Robot Joint Rates and Actuator Torques from End Effector Velocities and Applied Forces” Mechanism and Machine Theory 18(3), 193–198 (1983).CrossRefGoogle Scholar
4.Hollerback, J.M. and Sahar, G., “Wrist-partitioned, Inverse-kinematic Accelerations and Manipulator Dynamics” Int. J. Robotics Res. 2(4), 61–76 (1983).CrossRefGoogle Scholar
5.Pennock, G.R. and Yang, A.T., “Application of Dual- number Matrices to the Inverse Kinematics Problem for Robot Manipulators” Trans. ASME, I. Mech., Trans., and Aut. in Des. (1984).Google Scholar
6.Oh, S.-Y., Origin, D. and Bach, M., “An Inverse Kinematic Solution for Kinematically Redundant Robot Manipulators” J. Robotic Sys. 1(3), 235–249 (1984).CrossRefGoogle Scholar
7.Pieper, D.L., “Kinematics of Manipulators Under Computer Control” Ph.D. Dissertation, Standford University (10, 1968).Google Scholar
8.Bobrow, J.E., Dubowsky, S. and Gibson, J.S., “Time-optimal Control of Robotic Manipulators Along Specific Paths” Int. J. Robotics Res. 4(3), 3–17 (1985).CrossRefGoogle Scholar
9.Kane, T.R. and Levinson, D.A., “Formulation of Equations of Motion for Complex Spacecraft” AIAA J. Quid. and Cont. 3, 99–112 (1980).Google Scholar
10.Kane, T.R. and Levinson, D.A., “The Use of Kane's Dynamical Equations in Robotics Research” Int. I. Robotics Res. 2(3), 3–21 (1983).CrossRefGoogle Scholar
11.Huston, R.L. and Kelly, F.A., “The Development of Equations of Motion of Single-arm Robots,” IEEE Trans. Sys. Man and Cybernetics SMCf-12(3), 259–266 (05/06, 1982).CrossRefGoogle Scholar
12.Huston, R.L., Passerello, C.E. and Harlow, M.W., “Dynamics of Multirigid-body Systems” ASME Trans. I. Appl. Mech. 45, 889–894 (1978).CrossRefGoogle Scholar
13.Huston, R.L. and Passerello, C.E., “On Lagrange's Form of d' Alembert's Principle” Matrix and Tensor Quart. 23, 109–112 (1973).Google Scholar
14.Hemami, H. and Weimer, F.C., “Modelling of Nonholonomic Dynamic Systems with Applications” ASME Trans. I. Appl. Mech. 28, 177–182 (1981).CrossRefGoogle Scholar
15.Walton, W.C. Jr and Steeves, E.C., “A New Matrix Theorem and Its Application for Establishing Independent Coordinates for Complex Dynamical Systems with Constraints” NASA Technical Report TR R-326 (1969).Google Scholar
16.Kamman, J.W. and Huston, R.L., “Constrained Multibody System Dynamics – An Automated Approach” Computers and Structures 18(6), 999–1003.CrossRefGoogle Scholar
17.Kamman, J.W. and Huston, R.L., “Dynamics of Constrained Multibody Systems” Trans. ASME J. Appl. Mech. 51(4), 889–904 (1984).CrossRefGoogle Scholar
18.Huston, R.L., “A Discussion on Constraint Equations in Multibody Systems” Mech. Res. Comm. 9(4), 251–256 (1982).CrossRefGoogle Scholar
19.Kane, T.R., Dynamics (Holt, New York, 1968).Google Scholar
20.Bailey, C.D., “A New Look at Hamilton's Principle Foundations of Phys. 5(3), 433–451 (1975).CrossRefGoogle Scholar