Modeling and control of closed kinematic chains: A singular perturbation approach

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dc.contributor.advisorGhorbel, Fathi H.
dc.creatorWang, Zhiyong
dc.date.accessioned2009-06-04T08:36:08Z
dc.date.available2009-06-04T08:36:08Z
dc.date.issued2005
dc.description.abstractClosed kinematic chains (CKCs) are constrained multibody systems that contain closed kinematic loops. Nowadays, CKCs are used in a variety of applications ranging from flight simulators to medical instruments, and are becoming increasingly popular in the machine-tool industry and haptic interfaces due to their better performance in terms of accuracy, rigidity and payload capacity as compared to open-chain mechanisms. This document intends to present a novel methodology for the modeling and control of general CKCs. The dynamics of CKCs are characterized by index-3 differential algebraic equations (DAEs). Dynamic models in the form of DAEs pose difficulties in model-based control because most existing control design techniques are devised for explicit state space models. The control methodology presented in this document is based on a singular perturbation formulation (SPF), which has attractive properties including the minimum dimension of its slow dynamics and the large validity domain that contains the entire singularity-free workspace of the CKCs. The key issue of the model approximation error is addressed under different stability conditions. Explicit error bounds are derived and sufficient conditions for the exponential convergence of the approximation errors are established. For the control of CKCs, our approach transfers the control of the original DAE system to the control of an artificially created singularly perturbed system. Compared to control methods which directly solve the nonlinear algebraic constraint equations, the proposed method uses an ODE solver to obtain the dependent coordinates, hence eliminating the need for Newton type iterations and is amenable to real-time implementation. The closed loop system, when controlled by typical open kinematic chain schemes, achieves asymptotic trajectory tracking. The efficacy of the approach is illustrated by simulating the dynamics of a CKC mechanism, the Rice Planar Delta Robot, and then by validating the simulation results with experimental data. Thus, this work establishes a framework in which the control of CKCs can be systematically addressed.
dc.format.extent141 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS M.E. 2005 WANG
dc.identifier.citationWang, Zhiyong. "Modeling and control of closed kinematic chains: A singular perturbation approach." (2005) Diss., Rice University. <a href="https://hdl.handle.net/1911/18835">https://hdl.handle.net/1911/18835</a>.
dc.identifier.urihttps://hdl.handle.net/1911/18835
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMechanical engineering
dc.subjectArtificial intelligence
dc.titleModeling and control of closed kinematic chains: A singular perturbation approach
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMechanical Engineering
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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