The precise control of a manipulator depends on its velocity as well as on its configuration and dynamic properties. This paper presents some observations that can serve as a useful tool for identifying nonlinear ear effects in a manipulator. The tool is based on equations of motion being expressed in terms of inertial quasi-velocities (IQVs). They are rates containing both kinematic and mechanical parameters of the system. The presented approach gives a further insight into the manipulator motion. An analytical example shows the proposed strategy.
1.
Sciavicco
, L.
, and Siciliano
, B.
, 1996, Modeling and Control of Robot Manipulators
, McGraw-Hill
, New York
.2.
Slotine
, J.-J.
, and Li
, W.
, 1991, Applied Nonlinear Control
, Prentice Hall
, Englewood Cliffs, NJ
.3.
Spong
, M. W.
, and Vidyasagar
, M.
, 1989, Robot Dynamics and Control
, Wiley
, New York
.4.
Park
, J. S.
, 1996, “Motion Profile Planning of Repetitive Point-to-Point Control for Maximum Energy Conversion Efficiency Under Acceleration Conditions
,” Mechatronics
0957-4158, 6
, pp. 649
–663
.5.
Tarn
, T.-J.
, Xi
, N.
, and Bejczy
, A. K.
, 1996, “Path-Based Approach to Integrated Planning and Control for Robotic Systems
,” Automatica
0005-1098, 32
, pp. 1675
–1687
.6.
Athans
, M.
, and Falb
, P. L.
, 1966, Optimal Control: An Introduction to the Theory and its Applications
, McGraw-Hill
, New York
.7.
Pons
, J. L.
, Ceres
, R.
, Jimenez
, A. R.
, Calderon
, L.
, and Martin
, J. M.
, 1997, “Nonlinear Performance Index (npi): A Tool for Manipulator Dynamics Improvement
,” J. Intell. Robotic Syst.
0921-0296, 18
, pp. 277
–287
.8.
Hurtado
, J. E.
, and Sinclair
, A. J.
, 2004, “Hamel Coefficients for the Rotational Motion of an N-dimensional Rigid Body
,” Proc. R. Soc. London, Ser. A
1364-5021, 460
(2052
), pp. 3613
–3630
.9.
Jain
, A.
, and Rodriguez
, G.
, 1995, “Diagonalized Lagrangian Robot Dynamics
,” IEEE Trans. Rob. Autom.
1042-296X, 11
, pp. 571
–584
.10.
Junkins
, J. L.
, and Schaub
, H.
, 1997, “An Instantaneous Eigenstructure Quasivelocity Formulation for Nonlinear Multibody Dynamics
,” J. Astronaut. Sci.
0021-9142, 45
, pp. 279
–295
.11.
Loduha
, T. A.
, and Ravani
, B.
, 1995, “On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems
,” Trans. ASME, J. Appl. Mech.
0021-8936, 62
, pp. 216
–222
.12.
Herman
, P.
, 2005, “Sliding Mode Control of Manipulators Using First-Order Equations of Motion With Diagonal Mass Matrix
,” J. Franklin Inst.
0016-0032, 342
, pp. 353
–363
.13.
Kwatny
, H. G.
, and Blankenship
, G. L.
, 2000, Nonlinear Control and Analytical Mechanics
, Birkhäuser
, Boston
.14.
Koditschek
, D.
, 1984, “Natural Motion for Robot Arms
,” Proc. of the 23rd IEEE Conference on Decision and Control
, pp. 733
–735
.15.
Koditschek
, D.
, 1985, “Robot Kinematics and Coordinate Transformations
,” Proc. of the 24th IEEE Conference on Decision and Control
, pp. 1
–4
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.