A Multi-Element generalized Polynomial Chaos approach to analysis of mobile robot dynamics under uncertainty

Kewlani, Gaurav; Iagnemma, Karl

doi:10.1109/iros.2009.5354420

Cited by 15 publications

(14 citation statements)

References 17 publications

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“…GPC is then used to locally approximate the stochastic process in each element and so a global approximation is built. The efficiency of this technique has been tested in some applications such as the solution of differential equations with random coefficients [54] and the analysis of the dynamic behavior of mobile robots [55]. The improvement in the accuracy of statistic estimations obtained with the multi-element based approach, compared with the GPC method, is illustrated in both applications.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Nechak¹,

Berger²,

Aubry³

2012

Journal of Vibration and Acoustics

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The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

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Section: Introductionmentioning

confidence: 99%

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Nechak¹,

Berger²,

Aubry³

2012

Journal of Vibration and Acoustics

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“…Relatively recent work has applied gPC to both classical and optimal control system design [63,85,86]. Also, MEgPC has been used applied to uncertainty quantification in power systems [87] and mobile robots [88].…”

Section: 27mentioning

confidence: 99%

Motion Planning of Uncertain Ordinary Differential Equation Systems

Hays

Sandu

Sandu³

et al. 2014

Journal of Computational and Nonlinear Dynamics

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“…Because multiple uncertain sources are considered in the system, the mean and the variance of the sensor response could be reconstructed from the uncertain states with circuit laws as [10]. The interval zt representing the possible values of an arbitrary measured variable is defined through its boundaries as:…”

Section: Pct Based Sensor Failure Diagnosismentioning

confidence: 99%

Sensor Failure Detection and Diagnosis via Polynomial Chaos Theory—Part I: Theoretical Background

Zhang

Yao

et al. 2013

Lecture Notes in Electrical Engineering

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Sensors are widely used in engineering applications to provide measurements to the control and protection centers. In order to achieve higher level reliability of the whole system in engineering applications, polynomial chaos theory (PCT) is applied for sensor failure detection and diagnosis (SFDD) considering parameter uncertainties. The proposed approach allows for independent model development by propagation of uncertainty through systems. First, a review of the SFDD methods both at home and abroad is given. Then, the standard process for PCT expansion, together with the proposed new SFDD algorithm is presented. Simulation verification with a DC/DC boost converter has also been done, and the results show good consistency with the theoretical analysis.

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A Multi-Element generalized Polynomial Chaos approach to analysis of mobile robot dynamics under uncertainty

Cited by 15 publications

References 17 publications

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Motion Planning of Uncertain Ordinary Differential Equation Systems

Sensor Failure Detection and Diagnosis via Polynomial Chaos Theory—Part I: Theoretical Background

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