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Research Papers

The Use of the Adjoint Method for Solving Typical Optimization Problems in Multibody Dynamics

[+] Author and Article Information
Karin Nachbagauer

Faculty of Engineering
and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria
e-mail: karin.nachbagauer@fh-wels.at

Stefan Oberpeilsteiner

Faculty of Engineering
and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria
e-mail: stefan.oberpeilsteiner@fh-wels.at

Karim Sherif

Faculty of Engineering
and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria
e-mail: karim.sherif@fh-wels.at

Wolfgang Steiner

Faculty of Engineering
and Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria
e-mail: wolfgang.steiner@fh-wels.at

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 22, 2014; final manuscript received August 19, 2014; published online April 9, 2015. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 10(6), 061011 (Nov 01, 2015) (10 pages) Paper No: CND-14-1135; doi: 10.1115/1.4028417 History: Received May 22, 2014; Revised August 19, 2014; Online April 09, 2015

The present paper illustrates the potential of the adjoint method for a wide range of optimization problems in multibody dynamics such as inverse dynamics and parameter identification. Although the equations and matrices included show a complicated structure, the additional effort when combining the standard forward solver to the adjoint backward solver is kept in limits. Therefore, the adjoint method shows an efficient way to incorporate inverse dynamics to engineering multibody applications, e.g., trajectory tracking or parameter identification in the field of robotics. The present paper studies examples for both, parameter identification and optimal control, and shows the potential of the adjoint method in solving classical optimization problems in multibody dynamics.

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Figures

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Fig. 1

Geometry description of the planar, rigidly modeled overhead crane

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Fig. 2

The point mass has to follow a linear trajectory from a specified starting point to a fixed end point

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Fig. 3

Time history of identified force F and torque M after 300 iterations and initial settings for the first iteration for Ex. 5.1. The initial input for the force is set to F0 = 0 N for the first iteration. The initial input for the torque is defined as the static torque M0 = 98.1 N m.

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Fig. 4

The convergence analysis of the cost functional for Ex. 5.1 shows that the optimization process reduces the costs to a factor of 10−7 within 300 iterations

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Fig. 5

A single rigid body is studied for which the moments of inertia parameters describing the inertia tensor are not known. Point S follows a specified motion, and the velocity of point P is measured in order to identify the entries of the inertia tensor.

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Fig. 6

The convergence analysis of the cost functional for Ex. 5.2 shows that the optimization process reduces the costs already tremendously within the first 100 iterations. It has to be mentioned that only the costs of every second iteration are depicted here.

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Fig. 7

Exemplary, the convergence analysis of the moment of inertia I11 considered in Ex. 5.2 is shown here for 126 iterations. Only the costs of every second iteration are depicted here.

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Fig. 8

A triple inverse pendulum is studied for which the excitation force F is identified which leads to a swing up maneuver into the rest position with φ1=φ2=φ3=π. (a) Geometric description of the inverse pendulum and (b) definition of the necessary parameters for the numerical simulation.

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Fig. 9

Simulation results of the swing up maneuver of the inverse triple pendulum at six time steps: t = 0.0, 0.7, 1.4, 2.3, and 3.0 s

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Fig. 10

Time history of identified force F for the inverse triple pendulum in Ex. 5.3 after 353 iterations. The initial input for the force is set to F0 = 0 N for the first iteration.

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Fig. 11

The costs according to the end point error considered in Ex. 5.3 decrease to the limit of the value 1.5 after 353 iterations

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Fig. 12

Time history of the three angles φ1,φ2, and φ3 in the revolute joints considered in Ex. 5.3 after 353 iterations, where the optimization is stopped since the costs according to the end point error decrease below a prescribed limit value

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