• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.237-242
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• 1994

An quintic spline interpolate to a function in $C^{10}$[a, b] and its O($h^6$) error behavior are presented when its fourth derivative satisfies some kind of end conditions. The O($h^6$) relations between its derivatives up to fourth order and the m-th derivatives of the given function are also given at the nodes.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.492-495
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• 2001

In order to utilize a parallel machine tool for CAM system, the development of adequate interpolator is necessary. This paper presents a quintic B-spline interpolator with algorithm of limiting maximum interpolation error. The favored property of near arc-length parametrization in the curve representation is used in the implementation of the reference command generation. Then, this interpolator is applied to cubic parallel manipulator to show its validity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.1133-1137
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• 1995

This paper presents a numerical method of the global search for an optimal geometric path for a manipulator arm amid obstacles. Finite term quintic B-splines are used to describe an arbitrary point-to-point manipulator motion with fixed moving time. The coefficients of the splines span a linear vector space, a point in which uniquely represents the manipulator motion. All feasible geometric paths are searched by adjusting the seed points of the obstacle models in the penetration growth distances. In the numerical implementation using nonlinear programming, the globally optimal geometric path is obtained for a spatial 3-link(3-revolute joints) manipulator amid several hexahedral obstacles without simplifying any dynamic or geometric models.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.12
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• pp.204-213
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• 1999

This paper suggests a numerical method of finding optimal geometric path and minimum-time motion for a manipulator arm. To find the minimum-time motion, the optimal geometric path is searched first, and the minimum-time motion is searched on this optimal path. In the algorithm finding optimal geometric path, the objective function is minimizing the combination of joint velocities, joint-jerks, and actuator forces as well as avoiding several static obstacles, where global search is performed by adjusting the seed points of the obstacle models. In the minimum-time algorithm, the traveling time is expressed by the linear combinations of finite-term quintic B-splines and the coefficients of the splines are obtained by nonlinear programming to minimize the total traveling time subject to the constraints of the velocity-dependent actuator forces. These two search algorithms are basically similar and their convergences are quite stable.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.1
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• pp.78-86
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• 1998

This paper presents a numerical method of the minimum-time trajectory planning for a robot manipulator amid obstacles. Each joint displacement is represented by the linear combination of the finite-term quintic B-splines which are the known functions of the path parameter. The time is represented by the linear function of the same path parameter. Since the geometric path is not fixed and the time is linear to the path parameter, the coefficients of the splines and the time-scale factor span a finite-dimensional vector space, a point in which uniquely represents the manipulator motion. The displacement, the velocity and the acceleration conditions at the starting and the goal positions are transformed into the linear equality constraints on the coefficients of the splines, which reduce the dimension of the vector space. The optimization is performed in the reduced vector space using nonlinear programming. The total moving time is the main performance index which should be minimized. The constraints on the actuator forces and that of the obstacle-avoidance, together with sufficiently large weighting coefficients, are included in the augmented performance index. In the numerical implementation, the minimum-time motion is obtained for a planar 3-1ink manipulator amid several rectangular obstacles without simplifying any dynamic or geometric models.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.10
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• pp.116-126
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• 2001

This paper suggests a numerical method to find optimal geometric path and minimum-time motion for a spatial 6-link manipulator arm (PUMA 560 type). To find a minimum-time motion, the optimal geometric paths minimizing 2 different dynamic performance indices are searched first, and the minimum-time motions are searched on these optimal paths. In the algorithm to find optimal geometric paths, the objective functions (performance indices) are selected to minimize joint velocities, actuator forces or the combinations of them as well as to avoid one static obstacle. In the minimum-time algorithm the traveling time is expressed by the power series including 21 terms. The coefficients of the series are obtained using nonlinear programming to minimize the total traveling time subject to the constraints of velocity-dependent actuator forces.