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.
Skip Nav Destination
e-mail: ghorbel@rice.edu
Article navigation
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
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Control of a Directional Downhole Drilling System Using a State Barrier Avoidance Based Method
J. Dyn. Sys., Meas., Control (May 2025)
Dynamic control of cardboard-blank picking by using reinforcement learning
J. Dyn. Sys., Meas., Control
Offline and online exergy-based strategies for hybrid electric vehicles
J. Dyn. Sys., Meas., Control
In-Situ Calibration of Six-Axis Force/Torque Transducers on a Six-Legged Robot
J. Dyn. Sys., Meas., Control (May 2025)
Related Articles
Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction
J. Dyn. Sys., Meas., Control (March,2004)
Synchronizing Tracking Control for Flexible Joint Robots via Estimated State Feedback
J. Dyn. Sys., Meas., Control (March,2004)
Solution of the Forward Dynamics of a Single-loop Linkage Using Power Series
J. Dyn. Sys., Meas., Control (November,2011)
Decentralized Control of Rigid Robots Driven by Current-Fed Induction Motors
J. Dyn. Sys., Meas., Control (December,2002)
Related Proceedings Papers
Related Chapters
Motion Prediction with Gaussian Process Dynamical Models
International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
Fundamentals of Finite Element and Finite Volume Methods
Compact Heat Exchangers: Analysis, Design and Optimization using FEM and CFD Approach
Pseudoinverse Method and Singularities Discussed
Robot Manipulator Redundancy Resolution