• Korean Journal of Mathematics
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• v.6 no.2
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• pp.291-298
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• 1998

The $L^p-L^q$ mapping properties of convolution operators with measures supported on curves in $\mathbb{R}^3$ have been studied by many authors. Oberlin provided examples of nondegenerate compact space curves whose arclength measures enjoy $L^p$-improving properties. This was later extended by Pan who showed that such properties hold for all nondegenerate compact space curves. In this paper, we will prove that the operator norm of the convolution operator with the arclength measure supported on a nondegenerate compact space curve depends only on certain quantities of the underlying curve.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.5
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• pp.112-119
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• 2001

A variety of input shaper has been proposed to reduce the residual vibration of flexible structures. Multi-hump input shaper is known to be robust for parameter variations. However, existing approach should solve the more complicated nonlinear simultaneous equations to improve the robustness of the input shaper with the additional constraints. In this paper, by proposing a graphical approach which uses convolution of shaper, the multi-hump convolution input shaper could be designed even if the constraints are added for further robustness. With a mass-damper-spring model, the better performance is obtained using the proposed new multi-hump convolution input shaper.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.43-51
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• 2006

A fluid transient analysis on the Koreasat 1 & 2 pipeline system is conducted through numerical parametric studies in which unsteady friction results are compared with quasi-steady friction results and show relatively accurate prediction of the response curve with the unsteady friction. The code developed and used in this analysis has finished verification through comparing with the original Zielke model, the full and recursive convolution model and quasi-steady model as a reference. The unsteady friction is calculated by the recursive convolution Zielke model in which a complete evolution history of velocity field is no longer required so that it makes the fluid transient analysis on the complicated system possible. The results show that the application of quasi-steady friction to model cannot predict the entire response curve properly except the first peak amplitude but the application of unsteady friction to model can predict reasonably the response curve, therefore it is to know the characteristics of the propulsion system.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.320-323
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• 2006

A fluid transient analysis on the Koreasat 1 & 2 pipeline system is conducted through numerical parametric studies in which unsteady friction results are compared with quasi-steady friction results and show relatively accurate prediction of the response curve with the unsteady friction. The code developed and used in this analysis has finished verification through comparing with the original Zielke model, the full and recursive convolution model and quasi-steady model as a reference. The unsteady friction is calculated by the recursive convolution Zielke model in which a complete evolution history of velocity field is no longer required so that it makes the fluid transient analysis on the complicated system possible. The results show that the application of quasi-steady friction to model cannot predict the entire response curve properly except the first peak amplitude but application of unsteady friction to model can predict reasonably he response curve, therefore it is to know the characteristics of the propulsion system.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.6
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• pp.540-546
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• 2013

This paper presents a trajectory planning algorithm for TMR (Two-wheeled Mobile Robots). The trajectory is developed in joint space and considers the physical limits of a TMR. First, we present a process for generating a smooth curve through a Bezier curve. The trajectory for the center of the TMR following the Bezier curve is developed through a convolution operator taking into consideration its physical limits. The trajectory along the Bezier curve is regenerated using time-dependent parameters which correspond to the distance driven by the velocity of the center of the TMR in a sampling time. The velocity commands in the Cartesian space are converted to actuator commands for two wheels. In case that the actuator commands exceed the maximum velocity, the trajectory is redeveloped with compensated center velocity. We also suggest a smooth trajectory planning algorithm in joint space for the two segmented paths. Finally, the effectiveness of the algorithm is shown through numerical examples and application to a simulator.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.67-73
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• 2002

The flexibility of long reach manipulators presents a difficult control problem when accurate end-point position is required. Input shaping by convolving system commands with impulse sequences has been shown to be an effective method of reducing residual vibrations in flexible systems. However, existing shapers have been considered robustness fur only frequency uncertainty. However, this paper presents new multi-hump convolution(CV) input shaper that could accommodate with the simultaneous variation of natural frequency and damping ratio. Comparisons with previously proposed input shapers are presented to illustrate the qualities of the new input shaper. These new shapers will be shown to have better robustness fur the variation of frequency and damping ratio.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.127-133
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• 2001

The flexibility of long reach manipulators presents a difficult control problem when accurate end-point position is required. Input shaping by convolving system commands with impulse sequences has been shown to be an effective method of reducing residual vibrations in flexible systems. However, existing shapers has been considered robustness for only frequency uncertainty. However, this paper presents new multi-hump convolution(CV) input shaper that could accommodate with the simultaneous variation of natural frequency and damping ratio. Comparisons with previously proposed input shapers are presented to illustrate the qualities of the new input shaper. These new shapers will be shown to have better robustness for the variation of frequency and damping ratio.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.10
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• pp.997-1005
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• 2010

Most motion control systems consist of a desired trajectory generator, a motion controller such as a conventional PID controller, and a plant to be controlled. The desired trajectory generator as well as the motion controller is very important to achieve a good tracking performance. Especially, if the desired trajectory is generated actively utilizing the maximum velocity, acceleration, jerk and snap as given system specifications, the tracking performance would be better. For this, we make use of the properties of convolution operator in order to generate a smooth (S-curve) trajectory satisfying the system specifications. Also, the proposed trajectory generation method is extended to more general cases with arbitrary initial and terminal conditions. In addition, the suggested trajectory generator can be easily realized for real-time implementation. Finally, the effectiveness of the suggested method is shown through numerical simulations.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.731-742
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• 2001

A Gaussian smoothing algorithm obtained from a cascade of convolutions with a seven-point kernel is described. We prove that the change of local sums after applying our algorithm to sinusoidal signals is reduced to about two thirds of the change by the binomial coefficients. Hence, our seven point kernel is better than the binomial coefficients when trend curves are needed to be generated. We also prove that if our Gaussian convolution is applied to sinusoidal functions, the amplitude of higher frequencies reduces faster than the lower frequencies and hence that it is a low pass filter.