Pseudospectral methods for optimal motion planning of differentially flat systems

The article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess' implicit state variable representation of...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 49; no. 8; pp. 1410 - 1413
Main Authors Ross, I.M., Fahroo, F.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.08.2004
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Applied sciences
Asymptotic stability
Automatic control
Computation
Computer science; control theory; systems
Control systems
Control theory
Control theory. Systems
Dynamical systems
Exact sciences and technology
Lyapunov method
Mathematical analysis
Mathematical models
Matrices
Motion planning
Nonlinear dynamics
Nonlinear systems
Optimal control
Optimization
Optimization methods
Rivers
Time varying systems
Spectral method
Non linear control
Flat system
Gauss method
Two dimensional model
Dynamical system
Crane
Legendre polynomial
Integral method
Quadrature
Gaussian process
Optimal control
Optimal trajectory
System representation
Optimal planning
Dynamic programming
Motion control
Flatness
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Summary:The article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization. We show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to Fliess' implicit state variable representation of dynamical systems. The optimal motion planning problem for differentially flat systems is equivalent to a classic Bolza problem of the calculus of variations. We exploit the notion that derivatives of flat outputs given in terms of Lagrange polynomials at Legendre-Gauss-Lobatto points can be quickly computed using pseudospectral differentiation matrices. Additionally, the Legendre pseudospectral method approximates integrals by Gauss-type quadrature rules. The application of this method to the two-dimensional crane model reveals how differential flatness may be readily exploited.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2004.832972