In this paper, we propose a novel approach to the control of closed kinematic chains (CKCs). This method is based on a recently developed singularly perturbed model for CKCs. Conventionally, the dynamics of CKCs are described by differential-algebraic equations (DAEs). Our approach transfers the control of the original DAE system to the control of an artificially created singularly perturbed system in which the slow dynamics corresponds to the original DAE when the perturbation parameter tends to zero. Compared to control schemes that rely on solving nonlinear algebraic constraint equations, the proposed method uses an ordinary differential equation (ODE) solver to obtain the dependent coordinates, hence, eliminates the need for Newton-type iterations and is amenable to real-time implementation. The composite Lyapunov function method is used to show that the closed-loop system, when controlled by typical open kinematic chain schemes, achieves asymptotic trajectory tracking. Simulations and experimental results on a parallel robot, the Rice planar Delta robot, are also presented to illustrate the efficacy of our method.
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March 2006
Technical Papers
Control of Closed Kinematic Chains Using A Singularly Perturbed Dynamics Model
Zhiyong Wang,
Zhiyong Wang
Department of Mechanical Engineering and Material Science,
Rice University
, Houston, TX, 77005
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Fathi H. Ghorbel
Fathi H. Ghorbel
Department of Mechanical Engineering and Material Science,
e-mail: ghorbel@rice.edu
Rice University
, Houston, TX, 77005
Search for other works by this author on:
Zhiyong Wang
Department of Mechanical Engineering and Material Science,
Rice University
, Houston, TX, 77005
Fathi H. Ghorbel
Department of Mechanical Engineering and Material Science,
Rice University
, Houston, TX, 77005e-mail: ghorbel@rice.edu
J. Dyn. Sys., Meas., Control. Mar 2006, 128(1): 142-151 (10 pages)
Published Online: November 30, 2005
Article history
Received:
April 3, 2005
Revised:
November 30, 2005
Citation
Wang, Z., and Ghorbel, F. H. (November 30, 2005). "Control of Closed Kinematic Chains Using A Singularly Perturbed Dynamics Model." ASME. J. Dyn. Sys., Meas., Control. March 2006; 128(1): 142–151. https://doi.org/10.1115/1.2171440
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