Research Papers

Dynamic Optimization of Multibody System Using Multithread Calculations and a Modification of Variable Metric Method

[+] Author and Article Information
Kornel Warwas

Department of Computer
Science and Engineering,
University of Bielsko-Biała,
Bielsko-Biala 43-300, Poland

Szymon Tengler

Department of Mechanics,
University of Bielsko-Biała,
Bielsko-Biala 43-300, Poland

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 3, 2016; final manuscript received June 1, 2017; published online July 13, 2017. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 12(5), 051031 (Jul 13, 2017) (9 pages) Paper No: CND-16-1474; doi: 10.1115/1.4037104 History: Received October 03, 2016; Revised June 01, 2017

The paper presents dynamic optimization methods used to calculate the optimal braking torques applied to wheels of an articulated vehicle in the lane following/changing maneuver in order to prevent a vehicle rollover. In the case of unforeseen obstacles, the nominal trajectory of the articulated vehicle has to be modified, in order to avoid collisions. Computing the objective function requires an integration of the equation of motions of the vehicle in each optimization step. Since it is rather time-consuming, a modification of the classical gradient method—variable metric method (VMM)—was proposed by implementing parallel computing on many cores of computing unit processors. Results of optimization calculations providing stable motion of a vehicle while performing a maneuver and a description and results of parallel computing are presented in this paper.

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Fig. 1

A model of the articulated vehicle: 1—the tractor, 2—the fifth wheel, and 3—the semitrailer

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Fig. 2

Lane changing and lane following maneuver during cornering

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Fig. 3

(a) A sequential way of computing the gradient vector and (b) a division of the gradient vector into the elements calculated parallel on many processor cores

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Fig. 4

The multibody system prepared for tests: (a) a general view and (b) location of the Correvit sensor

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Fig. 5

Course of the steering angle of the front wheel for the maneuver of jerking the steering wheel

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Fig. 6

Comparison of the yaw velocity of (a) the tractor and (b) the semitrailer obtained from (1) the road tests and (2) the presented model

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Fig. 7

Numbering of the articulated vehicle wheels

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Fig. 8

A course of the steering angle of the articulated vehicle

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Fig. 9

Courses of the articulated vehicle: (a) the tractor trajectory, (b) the roll angle, (c) the vertical displacement, and (d) optimal braking torques

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Fig. 10

The courses of the articulated vehicle velocity (a) longitudinal and (b) lateral

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Fig. 11

The courses of the total velocity of the articulated vehicle tractor

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Fig. 12

The average time of execution for one call of the objective function for architecture: (a) i5 and (b) i7

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Fig. 13

An increase in efficiency by implementing parallel processing for architecture: (a) i5 and (b) i7



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