Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T12:46:03.206Z Has data issue: false hasContentIssue false

Computer Automated Symbolic Modeling of Dynamics of Robotic Manipulators with Flexible Links

Published online by Cambridge University Press:  09 March 2009

Sabri Cetinkunt
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680 (USA)
B. Ittop
Affiliation:
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60680 (USA)

Summary

Dynamic equations of chain structured robotic manipulators with compliant links and joints are developed in a non-recursive symbolic form. A program is developed in REDUCE to automate the symbolic expansion of these equations for any given chain structured manipulator. The symbolic non-recursive form of dynamic model is particularly suitable for controller synthesis and real-time control implementations. The link flexibility is included in the formulation using assumed mode shapes. The mode shapes and the parameters that are functions of the mode shapes are kept in symbolic form so that once a symbolic model is generated, different types of mode shapes can be studied using the same model. Because of the structural similarity between the developed equations and the well known rigid manipulator equations, the computer automated symbolic expansion capability presented here are likely to be utilized widely by many other researchers in the area who are already familiar with rigid manipulator problems.

Type
Article
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hastings, G.G. and Book, W.J.. “Verification of a Linear Dynamic Model for Flexible Robotic Manipulators” IEEE Control Systems Magazine, IEEE Control Systems Society (04, 1987).Google Scholar
2.Canon, R.H. Jr and Schmitz, E., “Initial Experiments on the End-Point Control of a Flexible One-Link RobotInt. J. Robotics Research, 3, No. 3, 6275 (1984).CrossRefGoogle Scholar
3.Spong, M.W., “Modeling and Control of Elastic Joint Robots”, Trans. of ASME, J. of Dyn. Sys. Mea. and Control 109, 310319 (12, 1987).Google Scholar
4.Naganathan, G. and Soni, A.H., “Coupling Effects of Kinematics and Flexibility in Manipulators”, Int. J. Robotics Research 6, No. 1, 7584 (1987); 6, No. 1, 75–84 (1987).CrossRefGoogle Scholar
5.Rosenthal, D.E. and Sherman, M.A., “High Performance Multibody Simulations Via Symbolic EquationsJ. Astronautical Sciences, 34, No. 3, 223239 (1986).Google Scholar
6.Leu, M.C. and Hemati, N., “Automated Symbolic Derivation Of Dynamic Equations of Motion for Robotic Manipulators”, J. Dynamic Systems, Measurernent, and Control 108, 172179 (1986).Google Scholar
7.Neuman, C.P. and Murray, J.J., “The Complete Dynamic Model and Customized Algorithms of the Puma RobotIEEE Trans. on System, Man, and Cybernetics, SMC-17, No. 4, 635644 (1987).Google Scholar
8.Book, W.J., “Recursive Lagrangian Dynamics of Flexible Manipulator Arms”. Int. J. Robotic Research 3, No. 3, 87101 (1984).CrossRefGoogle Scholar
9.Cetinkunt, S. and Book, W.J., “Symbolic Modeling and Dynamic Simulation of Robotic Manipulators with Compliant Links and JointsRobotics & ComputerIntegrated Mamifacturing 5, No. 4, 301310 (1989).CrossRefGoogle Scholar
10.Luh, J.Y.S. and Lin, C.S., “Scheduling of Parallel computation for a Computer-Controlled Mechanical ManipulatorIEEE Trans. on Systems, Man, and Cybernatics SMC-12, No. 2, 214234 (1982).Google Scholar
11.Ittoop, B., “Computer Automated Symbolic Modeling of Dynamics of Robotic manipulator with Compliant Links and Joints” M.S. Thesis (University of Illinois, Chicago, 1989).Google Scholar
12.Book, W.J., Naizza-Netto, O. and Whitney, D.E., “Feedback Control of Two Beam, Two Joint Systems with Distributed Flexibility” ASME J. Dynamic Systems, Measurement, and Control, 97G (12, 1975).CrossRefGoogle Scholar
13.Shahinpoor, M. and Meghdari, A.. “Combined flexuraljoint stiffness matrix and elastic deformation of a servo-controlled two-link robot manipulatorRobotica, 4, No. 4. 237242 (1986).CrossRefGoogle Scholar
14.Jumarie, G., “Tracking Control of Flexible Robot Manipulators with Active Inertia LinksRobotica 8, No. 1, 7380 (1990).CrossRefGoogle Scholar