• Journal of the Institute of Electronics Engineers of Korea SC
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• v.43 no.5 s.311
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• pp.10-18
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• 2006

We propose a new approach to compute possible acceleration boundary, so is called dynamic manipulability, for multiple robotic systems with frictional contacts between robot end-effectors and object. As the frictional contact condition which requires each contact force to lie within a friction cone is based on the nonlinear inequality formalism is not easy to handle the constraint in manipulability analysis. To include the frictional contact condition into the conventional manipulability analysis we approximate the friction cone to a pyramid which is described by linear inequality constraints. And then achievable acceleration boundaries of manipulated object are calculated conventional linear programming technique under constraints for torque capability of each robot and the approximated contact condition. With the proposed method we find some solution to which conventional approaches did not reach. Also, case studies are Presented to illustrate the correctness of the proposed approach for two robot systems of simple planar robots and PUMA560 robots.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.17-35
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• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.103-107
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• 2009

This paper presents how to minimize the second-order cone programming problem occurring in the 3D reconstruction of multiple views. The $L_{\infty}$-norm minimization is done by a series of the minimization of the maximum infeasibility. Since the problem has many inequality constraints, we have to adopt methods of the interior point algorithm, in which the inequalities are sequentially approximated by log-barrier functions. An initial feasible solution is found easily by the construction of the problem. Actual computing is done by an iterative Newton-style update. When we apply the interior point method to the problem of reconstructing the structure and motion, every Newton update requires to solve a very large system of linear equations. We show that the sparse bundle-adjustment technique can be utilized in the same way during the Newton update, and therefore we obtain a very efficient computation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.159-166
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• 2019

Due to the various engagement situations, it is very difficult to generate the optimal trajectory with several constraints. This paper investigates the sequential convex programming for the impact angle control with the additional constraint of altitude limit. Recently, the SOCP(Second-Order Cone Programming), which is one area of the convex optimization, is widely used to solve variable optimal problems because it is robust to initial values, and resolves problems quickly and reliably. The trajectory optimization problem is reconstructed as convex optimization problem using appropriate linearization and discretization. Finally, simulation results are compared with analytic result and nonlinear optimization result for verification.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.281-292
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• 2007

A pair of symmetric fractional variational programming problems is formulated over cones. Weak, strong, converse and self duality theorems are discussed under pseudoinvexity. Static symmetric dual fractional programs are included as special case and corresponding symmetric duality results are merely stated.

• Journal of Computational Design and Engineering
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• v.3 no.3
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• pp.198-214
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• 2016

Oval substrates are widely used in automobiles to reduce the exhaust emissions in Diesel oxidation Catalyst of CI engine. Because of constraints in space and packaging Oval substrate is preferred rather than round substrate. Obtaining the flow uniformity is very challenging in oval substrate comparing with round substrate. In this present work attempts are made to optimize the inlet cone design to achieve the optimal flow uniformity with the help of CATIA V5 which is 3D design tool and CFX which is 3D CFD tool. Initially length of inlet cone and mass flow rate of exhaust stream are analysed to understand the effects of flow uniformity and pressure drop. Then short straight cones and angled cones are designed. Angled cones have been designed by two methodologies. First methodology is rotating flow inlet plane along the substrate in shorter or longer axis. Second method is shifting the flow inlet plane along the longer axis. Large improvement in flow uniformity is observed when the flow inlet plane is shifted along the direction of longer axis by 10, 20 and 30 mm away from geometrical centre. When the inlet plane is rotated again based on 30 mm shifted geometry, significant improvement at rotation angle of $20^{\circ}$ is observed. The flow uniformity is optimum when second shift is performed based on second rotation. This present work shows that for an oval substrate flow, uniformity index can be optimized when inlet cone is angled by rotation of flow inlet plane along axis of substrate.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• Journal of Radiation Protection and Research
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• v.43 no.3
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• pp.107-113
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• 2018

Background: The purpose of our study was to compare the dosimetric advantages of Flattening filter free (FFF) beams for trigeminal neuralgia patients using 4 mm conical collimators over previously treated patients with 6 MV SRS beam. Materials and Methods: A retrospective study was conducted for 5 TN patients who had been previously treated at our institution using frame-based, LINAC-based stereotactic radiosurgery (SRS) on Novalis Tx using 6 MV SRS beam were replanned on 6X FFF beams on Edge Linear accelerator with same beam angles and dose constraints using 4 mm conical collimator. The total number of monitor units along with the beam on time was compared for both Edge and Novalis Tx by redelivering the plans in QA mode of LINAC to compare the delivery efficiency. Plan quality was evaluated by homogeneity index (HI) and Paddick gradient index (GI) for each plan. We also analyzed the doses to brainstem and organ at risks (OARs). Results and Discussion: A 28% beam-on time reduction was achieved using 6X FFF when compared with 6X SRS beam of Novalis Tx. A sharp dose fall off with gradient index value of $3.4{\pm}0.27$ for 4 mm Varian conical collimator while $4.17{\pm}0.20$ with BrainLab cone. Among the 5 patients treated with a 4 mm cone, average maximum brainstem dose was 10.24 Gy for Edge using 6X FFF and 14.28 Gy for Novalis Tx using 6X SRS beam. Conclusion: The use of FFF beams improves delivery efficiency and conical collimator reduces dose to OAR's for TN radiosurgery. Further investigation is warranted with larger sample patient data.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.49 no.1
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• pp.21-30
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• 2021

Mid-course trajectory of the missiles equipped with seeker should be designed to detect target within FOV of seeker and to maximize the maneuverability at the point of transition to terminal guidance phase. Because the trajectory optimization problems are generally hard to obtain the analytic solutions due to its own nonlinearity with several constraints, the various numerical methods have been presented so far. In this paper, mid-course trajectory optimization problem for boost-glide missiles is calculated by using SOCP (Second-Order Cone Programming) which is one of convex optimization methods. At first, control variable augmentation scheme with a control constraint is suggested to reduce state variables of missile dynamics. And it is reformulated using a normalized time approach to cope with a free final time problem and boost time problem. Then, partial linearization and lossless convexification are used to convexify dynamic equation and control constraint, respectively. Finally, the results of the proposed method are compared with those of state-of-the-art nonlinear optimization method for verification.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.559-567
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• 2000

This paper proposes simple and practical methods in order to overcome complex formulation and heavy computational burden of the forward kinematics of 6 앨 3-6 type parallel manipulators. Three ap-proaches for the forward kinematics are presented : one extra sensor a modified structure and novel numerical method. The proposed methods are applied to the forward kinematics of a new 6 앨 parallel manipulator with special geometry that has three internal links three external links and a moving platform of a cone shape. The proposed methods use three tetrahedrons for finding the position and orientation vector of the moving platform. The main advantages of the appraches using tetrahedrons are to abbreviate the formulation to easily find so-lutions of the forward kinematics and to be able to practically control of the manipulator in real time.