Abstract
The main objectives of this chapter are (a) to devise an algorithm for the real-time computed-torque control and (b) to derive the system of second-order ordinary differential equations (ODE) governing the motion of an n-axis manipulator. We will focus on serial manipulators, the dynamics of a much broader class of robotic mechanical systems, namely, parallel manipulators and mobile robots, being the subject of Chap. 12. Moreover, we will study mechanical systems with rigid links and rigid joints and will put aside systems with flexible elements, which pertain to a more specialized realm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See Exercise 9 for an extension of this relation to a system of n rigid bodies.
- 2.
\(\boldsymbol{\iota }\) is the Greek letter iota and denotes a vector; according to our notation, its components are ι 1, ι 2, and ι 3.
- 3.
The relations below are made apparent with the aid of Fig. 4.6.
- 4.
Only rows involving floating-point operations are counted here.
References
Angeles, J., 1988, Rational Kinematics, Springer-Verlag, New York.
Angeles, J. and Lee, S., 1988, “The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement”, ASME J. Applied Mechanics 55, pp. 243–244.
Angeles, J. and Ma, O., 1988, “Dynamic simulation of n-axis serial robotic manipulators using a natural orthogonal complement”, The Int. J. Robotics Res. 7, no. 5, pp. 32–47.
Angeles, J., Ma, O., and Rojas, A.A., 1989, “An algorithm for the inverse dynamics of n-axis general manipulators using Kane’s formulation of dynamical equations”, Computers and Mathematics with Applications 17, no. 12, pp. 1545–1561.
Balafoutis, C.A. and Patel, R.V., 1991, Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach, Kluwer Academic Publishers, Dordrecht.
Bryson, Jr., A.E. and Ho, Y-C., 1975, Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere Publishing Corporation, Washington, DC.
Craig, J.J., 1989, Introduction to Robotics: Mechanics and Control, 2nd Edition, Addison-Wesley Publishing Company, Reading, MA.
Currie, I.G., 1993, Fundamental Mechanics of Fluids, 2nd Edition, McGraw-Hill Book Company, New York.
Dahlquist, G. and Björck, Å., 1974, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ.
Etter, D.M., 1997, Engineering Problem Solving with Matlab, Prentice-Hall, Upper Saddle River, NJ.
Featherstone, R., 1983, “Position and velocity transformations between robot end-effector coordinates and joint angles”, The Int. J. Robotics Res. 2, no. 2, pp. 35–45.
Featherstone, R., 1987, Robot Dynamics Algorithms, Kluwer Academic Publishers, Dordrecht.
Gear, C.W., 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.
Golub, G.H. and Van Loan, C.F., 1989, Matrix Computations, The Johns Hopkins University Press, Baltimore.
Hollerbach, J.M., 1980, “A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamic formulation complexity”, IEEE Trans. Systems, Man, and Cybernetics SMC-10, no. 11, pp. 730–736.
Hollerbach, J.M. and Sahar, G., 1983, “Wrist-partitioned inverse kinematic accelerations and manipulator dynamics”, The Int. J. Robotics Res. 2, no. 4, pp. 61–76.
Kahaner, D., Moler, C., and Nash, S., 1989, Numerical Methods and Software, Prentice-Hall, Englewood Cliffs, NJ.
Kahn, M. E. 1969. “The near-minimum time control of open-loop articulated kinematic chains”, AI Memo 177, Artificial Intelligence Laboratory, Stanford University, Stanford. Also see Kahn, M.E., and Roth, B., 1971, “The near-minimum-time control of open-loop articulated kinematic chains”, ASME J. Dyn. Systs., Meas., and Control, 91, pp. 164–172.
Kane, T.R., 1961, “Dynamics of nonholonomic systems”, ASME J. Applied Mechanics 83, pp. 574–578.
Kane, T.R. and Levinson, D.A., 1983, “The use of Kane’s dynamical equations in robotics”, The Int. J. Robotics Res. 2, no. 3, pp. 3–21.
Khalil, W., Kleinfinger, J.F., and Gautier, M., 1986, “Reducing the computational burden of the dynamical models of robots”, Proc. IEEE Int. Conf. on Robotics & Automation,, San Francisco, pp. 525–531.
Li, C.-J., 1989, “A new Lagrangian formulation of dynamics of robot manipulators”, ASME J. Dyn. Systs., Meas., and Control, 111, pp. 559–567.
Li, C.-J. and Sankar, 1992, “Fast inverse dynamics computation in real-time robot control”, Mechanism and Machine Theory 1992, no. 27, pp. 741–750.
Luh, J.Y.S., Walker, M.W., and Paul, R.P.C., 1980, “On-line computational scheme for mechanical manipulators”, ASME J. Dyn. Systs., Meas., and Control, 102, pp. 69–76.
Paul, R.P., 1981, Robot Manipulators. Mathematics, Programming, and Control, The MIT Press, Cambridge. MA.
Saha, S.K., 1997, “A decomposition of the manipulator inertia matrix”, IEEE Trans. Robotics & Automation 13, pp. 301–304.
Saha, S.K., 1999, “Analytical expression for the inverted inertia matrix of serial robots”, The Int. J. Robotics Res. 18, no. 1, pp. 116–124.
Saha, S.K., 2008, Introduction to Robotics, The McGraw-Hill Companies, New Delhi.
Shampine, L.F. and Gear, C.W., 1979, “A user’s view of solving stiff ordinary differential equations”, SIAM Review 21, no. 1, pp. 1–17.
Silver, W.M., 1982, “On the equivalence of Lagrangian and Newton-Euler dynamics for manipulators”, The Int. J. Robotics Res. 1, no. 2, pp. 118–128.
Spong, M.W., Hutchinson, S., and Vidyasagar, M., 2006, Robot Modeling and Control, John Wiley & Sons, Inc., Hoboken, NJ.
Uicker, Jr., J.J., 1965. On the Dynamic Analysis of Spatial Linkages Using 4 × 4 Matrices, Ph.D. thesis, Northwestern University, Evanston.
Walker, M.W. and Orin, D.E., 1982, “Efficient dynamic computer simulation of robotic mechanisms”, ASME J. Dyn. Systs., Meas., and Control, 104, pp. 205–211.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Angeles, J. (2014). Dynamics of Serial Robotic Manipulators. In: Fundamentals of Robotic Mechanical Systems. Mechanical Engineering Series, vol 124. Springer, Cham. https://doi.org/10.1007/978-3-319-01851-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-01851-5_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01850-8
Online ISBN: 978-3-319-01851-5
eBook Packages: EngineeringEngineering (R0)