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Chenut, X; Paul, Friedemann; Samin, Jean-Claude

doi:10.1023/a:1019555013391

Cited by 28 publications

(5 citation statements)

References 11 publications

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“…In general, the objective function J p; rð0Þ ð Þ contains numerous local minima; the best mathematical model (5) is obtained when the parameters p correspond to the global minimum of the objective function (6). In order to find the global minimum, we first modify the objective function by introducing a homotopy transformation J p; rð0Þ; k ð Þ¼ 1 2…”

Section: Mathematical Detailsmentioning

confidence: 99%

“…Unfortunately, it is not possible to apply the linear least-square methods unless the parameters to be identified can be completely decoupled from each other. Barycentric parameters [6][7][8], which are functions of parameter groups, can be defined in such cases so that, upon substitution, the equations of motion become linear in these new parameters. The barycentric parameters can then be identified using linear regression.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

Vyasarayani

McPhee

2011

Journal of Computational and Nonlinear Dynamics

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The identification of parameters in multibody systems governed by ordinary differential equations, given noisy experimental data for only a subset of the system states, is considered in this work. The underlying optimization problem is solved using a combination of the Gauss–Newton and single-shooting methods. A homotopy transformation motivated by the theory of state observers is proposed to avoid the well-known issue of converging to a local minimum. By ensuring that the response predicted by the mathematical model is very close to the experimental data at every stage of the optimization procedure, the homotopy transformation guides the algorithm toward the global minimum. To demonstrate the efficacy of the algorithm, parameters are identified for pendulum-cart and double-pendulum systems using only one noisy state measurement in each case. The proposed approach is also compared with the linear regression method.

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Section: Mathematical Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

Vyasarayani

McPhee

2011

Journal of Computational and Nonlinear Dynamics

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“…Then, using the Newton/Euler recursive algorithm, the dynamic equations of (only) these joints are symbolically generated to obtain (5). The ROBOTRAN reaction model has been successfully used to identify dynamic parameters of robots, by establishing the relationship between [a set of] exciting trajectories and the reaction forces and torques: the main advantage with respect to an inverse dynamics approach relates to the absence of the joint friction forces which cancel each other out in (5) by the action/reaction principle (Chenut et al, 2002).…”

Section: Reaction Dynamicsmentioning

confidence: 99%

ROBOTRAN: a powerful symbolic gnerator of multibody models

2013

Self Cite

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Abstract. The computational efficiency of symbolic generation was at the root of the emergence of symbolic multibody programs in the eighties. At present, it remains an attractive feature of it since the exponential increase in modern computer performances naturally provides the opportunity to investigate larger systems and more sophisticated models for which real-time computation is a real asset.Nowadays, in the context of mechatronic multibody systems, another interesting feature of the symbolic approach appears when dealing with enlarged multibody models, i.e. including electrical actuators, hydraulic devices, pneumatic suspensions, etc. and requiring specific analyses like control and optimization. Indeed, since symbolic multibody programs clearly distinguish the modeling phase from the analysis process, extracting the symbolic model, as well as some precious ingredients like analytical sensitivities, in order to export it towards any suitable environment (for control or optimization purposes) is quite straightforward. Symbolic multibody model portability is thus very attractive for the analysis of mechatronic applications.In this context, the main features and recent developments of the ROBOTRAN software developed at the Université catholique de Louvain (Belgium) are reviewed in this paper and illustrated via three multibody applications which highlight its capabilities for dealing with very large systems and coping with multiphysics issues.

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“…Identification techniques have been developped in robotics by representing the inertia characteristics by a 10 components vector [1]. But when applying a least squares method to the Newton-Euler motion equations in order to identify this 10 components vector, one has to be careful: the positivity of the mass and of the inertia matrix should not be forgotten.…”

Section: Introductionmentioning

confidence: 99%

Matrix formulation of the motion equations of a rigid body and identification of the ten inertia characteristics

Atchonouglo

Dumitriu

Monnet

et al. 2008

Proc Appl Math and Mech

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The motion equations of a rigid body involve ten inertial characteristics: the mass, the mass center position and the inertia matrix. In order to identify these ten inertia characteristics, we propose an approach unifying them in a 4 × 4 positive definite symmetric matrix. The translation vector and the rotation matrix of the rigid body are also gathered in a 4 × 4 matrix. Therefore the motion equations are formulated as an equality between 4 × 4 skew-symmetric matrices: one representing the sum of external forces and torques, the second representing the dynamic force and torque. The identification is performed by a projected conjugate gradient algorithm developped in the 10-Dimensional linear space of 4 × 4 symmetric matrices.

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Untitled

Cited by 28 publications

References 11 publications

Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

ROBOTRAN: a powerful symbolic gnerator of multibody models

Matrix formulation of the motion equations of a rigid body and identification of the ten inertia characteristics

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