• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1785-1789
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• 1991

Recently, a number of papers on adaptive control scheme of manipulators are proposed. Slotine and Li[1] showed an adaptive control scheme for robot manipulator. The controller was described in closed form. And later Niemeyer and Slotine discussed about a computational implementation of the controller in recursive form[2]. Walker proposed another adaptive control scheme which can be implemented by a recursive-form controller[4]. Closed-form description is used for the analysis or design of adaptive control systems while recursive-form realization is used for implementation of the controller. The relation between the closed-form realization and the recursive-form one seems to be inadequately referred. Hence, it makes sense to consider the relation between the closed-form description and the recursive-form one. In this paper, first, we make a simple derivation of an closed-form dynamics description of a robot arm from its recursive-form description. And then we derive the closed-form realization of Walker's scheme applied to manipulators having no kinematic loop. We clarify the difference between the Walker's scheme and Slotine's and evaluate the convergence under the controllers.

• International Journal of Automotive Technology
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• v.6 no.4
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• pp.375-381
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• 2005

This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.446-450
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• 1987

In this paper, overdetermined method is used for high resolution spectral estimation in case of short data record length. To reduce the computational effort and to obtain recursive form of estimation algorithm, we modify data matrix to have near-Toeplitz structure. Then, new recursive algorithm is derived in the form of fast Kalman algorithm. Two stage procedure is used for the estimation of ARMA parameters. First AR parameters are estimated by using overdetermined modified Yule-walker equation, and then MA parameters are implicitly estimated by estimating numerator spectral coefficients(NS).

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2532-2537
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• 2005

FIR(Finite Impulse Response) filter is well known to be ideal for the finite time state-space model, but it requires much computation due to its inherent non-recursive structure especially when the measurement interval grows to a large extent. And often a fixed-lag smoother based on the finite time interval is needed to monitor the soundness of the system model and the measurement model, but the computation burden of FIR-type smoother imposes much restriction of its usage for real-time application. Conventional recursive forms of FIR estimator[1]-[4] could not be used for real time applications, since they are numerically unstable in their recursive equations. To cope with this problem, we suggest a stable recursive form FIR estimator(SRFIR) and its usefulness is demonstrated for designing the real-time fixed-lag smoother on the finite time window through an example of detection of rate bias in the anti-aircraft gun fire control system.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.927-931
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• 2003

In this paper, a new Recursive Least-Squares(RLS) algorithm based on matrix pseudo-inverses is presented. The aim is to use the proposed new RLS algorithm for not only the over-determined but also the under-determined estimation problem. Compared with previous results, e.g., Jie Zhou et al., the derivation of the proposed recursive form is much easier, and the recursion form is also much simpler. Furthermore, it is shown by simulations that the proposed RLS algorithm is more efficient and numerically stable than the existing algorithms.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.19-25
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• 2012

The purpose of this paper is to derive powers $A^{n}$ using a system of recursive sequences for a given $2{\times}2$ matrix A. Introducing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solving this quadratic equation we can easily obtain an explicit form of $A^{n}$. Our method holds when A is defined not only on the real field but also on the complex field.

• Journal of the Korean Society for Precision Engineering
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• v.33 no.9
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• pp.745-751
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• 2016

This paper presents the acceleration and deceleration control of free-form surfaces. A rapid variation of acceleration (or Deceleration) drives the system into a machine shock, resulting in the inaccuracy of the path control of the NURBS curve. The pattern of acceleration control can be established using the curvature of the NURBS curve. The curvature can be easily calculated from the first and second derivative of the NURBS curve used in Taylor's expansion for NURBS interpolation. However, the derivatives are not used in the recursive method for NURBS interpolation. Hence, we attempted the difference-derivatives for calculating the NURBS curvature. Both, Taylor's expansion and the recursive method, are used jointly for controlling the acceleration in the same interpolation algorithm.

• Journal of Communications and Networks
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• v.9 no.3
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• pp.219-228
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• 2007

In this paper, we present a novel blind adaptive multiuser detector structure and three robust recursive filters to improve the performance in CDMA environments: Sigma point kalman filter (SPKF), particle filter (PF), and Gaussian mixture sigma point particle filter (GMSPPF). Our proposed robust recursive filters have superior performance over a conventional extended Kalman filter (EKF). The proposed multiuser detector algorithms initially use Kalman prediction form to estimated channel parameters, and unknown data symbol be predicted. Second, based on this predicted data symbol, the robust recursive filters (e.g., GMSPPF) is a refined estimation of joint multipaths and time delays. With these estimated multipaths and time delays, data symbol detection is carried out (Kalman correction form). Computer simulations show that the proposed algorithms outperform the conventional blind multiuser detector with the EKF. Also we can see it provides a more viable means for tracking time-varying amplitudes and time delays in CDMA communication systems, compared to that of the EKF for near-far ratio of 20 dB. For this reason, it is believed that the proposed channel estimators can replace well-known filter such as the EKF.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.101-111
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• 2001

Recursive formulas have been effective in solving the equations of motion for large scale constratined mechanical sys-tems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as veloci-ty, acceleration. and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into sev-eral categories. The generalized recursive formula for each category is then developed and applied whenever such a cate-gory of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.167.5-167
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• 2001

Single point attitude determination method provides an optimal attitude minimizing the Wahba loss function. However, for the insufficient number of measurement vectors, the conventional single point methods has no unique solution. Thus, we introduce the sequential method to and an optimal attitude minimizing the windowed loss function. In this paper, this function is de ned as the sum of square errors for all measurement vectors within the axed sliding window. For simple implementation, the proposed algorithm is rewritten as a recursive form. Moreover, the covariance matrix is derived and expressed as a recursive form. Finally, we apply this algorithm to the attitude determination system with three LOS measurement sensors.