• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.283-295
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• 1997

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using $2^N$ algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

• Journal of the Korea Society of Computer and Information
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• v.26 no.12
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• pp.29-43
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• 2021

In this paper, a new approach to solve the constrained dynamic programming is proposed by using the constraint programming. While the conventional dynamic programming scheme has the state space augmented with states on constraints, this approach, without state augmentation, represents states of constraints as domains in a contraining programming solver. It has a hybrid computational mechanism in its computation by combining solving the Bellman equation in the dynamic programming framework and exploiting the propagation and inference methods of the constraint programming. In order to portray the differences of the two approaches, this paper solves a simple version of the long-term car rental financing problem. In the conventional scheme, data structures for state on constraints are designed, and a simple inference borrowed from the constraint programming is used to the reduction of violation of constraints because no inference risks failure of a solution. In the hybrid approach, the architecture of interface of the dynamic programming solution method and the constraint programming solution method is shown. It finally discusses the advantages of the proposed method with the conventional method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.74-78
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• 2001

In this study, a multi-step optimization technique combined with a simple genetic algorithm is introduce to the structural design optimization of a high speed machining center. In this case, the design problem is to find out the best design variables which minimize the static compliance, the dynamic compliance, and the weight of the machine structure and meet some design constraints simultaneously. Dimensional thicknesses of the thirteen structural members along the static force loop of the machine structure are adopted as design variables. The first optimization step is a static design optimization, in which the static compliance and the weight are minimized under some dimensional and safety constraints. The second step is a dynamic design optimization, where the dynamic compliance and the weight are minimized under the same constraints. After optimization, the weight of the moving body was reduced to 9.1% of the initial design respectively. Both static and dynamic compliances of the optimum design are also in the feasible range even thought they were slightly increased than before.

• Steel and Composite Structures
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• v.45 no.5
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• pp.697-713
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• 2022

In the context of the finite elements method, the dynamic behavior of porous functionally graded double wishbone vehicle suspension structural system incorporating joints flexibility constraints under road bump excitation is studied and analyzed. The functionally graded material properties distribution through the thickness direction is simulated by the power law including the porosity effect. To explore the porosity effects, both classical and adopted porosity models are considered based on even porosity distribution pattern. The dynamic equations of motion are derived based on the Hamiltonian principle. Closed forms of the inertia and material stiffness components are derived. Based on the plane frame isoparametric Timoshenko beam element, the dynamic finite elements equations are developed incorporating joint flexibilities constraints. The Newmark's implicit direct integration methodology is utilized to obtain the transient vibration time response under road bump excitation. The presented procedure is validated by comparing the computational model results with the available numerical solutions and an excellent agreement is observed. Obtained results show that the decrease of porosity percentage and material graduation tends to decrease the deflection as well as the resulting stresses of the control arms thus improving the dynamic performance and increasing the service lifetime of the control arms.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.11
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• pp.36-45
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• 1992

A numerical trajectory planning method for path-constrained trajectory planning is proposed which ensures collision-free and time-optimal motions for two robotic manipulators with limited actuator torques and velocities. For each robot, physical constraints of the robots such as limited torques or limited rotational velocities of the actuators are converted to the constraints on velocity and acceleration along the path, which is described by a scalar variable denoting the traveled distance from starting point. Collision region is determined on the coordination space according to the kinematic structures and the geometry of the paths of the robots. An Extended Coordination Space is then constructed` an element of the space determines the postures and the velocities of the robots, and all the constraints described before are transformed to some constraints on the behaviour of the coordination-velocity curves in the space. A dynamic programming technique is them provided with on the discretized Extended Coordination Space to derive a collision-free and time-optimal trajectory pair. Numerical example is included.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.2 no.1
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• pp.51-62
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• 2008

This paper proposes a second-order implicit constraint enforcement method which yields enhanced controllability compared to a first-order implicit constraints enforcement method. Although the proposed method requires solving a linear system twice, it yields superior accuracy from the constraints error perspective and guarantees the precise and natural movement of objects, in contrast to the first-order method. Thus, the proposed method is the most suitable for exact prediction simulations. This paper describes the numerical formulation of second-order implicit constraints enforcement. To prove its superiority, the proposed method is compared with the firstorder method using a simple two-link simulation. In this paper, there is a reasonable discussion about the comparison of constraints error and the analysis of dynamic behavior using kinetic energy and potential energy.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.9
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• pp.133-144
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• 2000

The dynamic walking planning and the inverse dynamics of the biped robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian corrdinates then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot the holonomic constraints are added or deleted on the equations of motion. the number of these constraints can be changed by types of walking patterns with three modes. In order for the dynamic walking to be stabilizable optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.548-555
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• 2000

The dynamic walking and the inverse dynamics of the biped walking robot is investigated in this paper. The biped robot is modeled with 14 degrees of freedom rigid bodies considering the walking pattern and kinematic construction of humanoid. The method of the computer aided multibody dynamics is applied to the dynamic analysis. The equations of motion of biped are initially represented as terms of the Cartesian coordinates, then they are converted to the minimum number of equations of motion in terms of the joint coordinates using the velocity transformation matrix. For the consideration of the relationships between the ground and foot, the holonomic constraints are added or deleted on the equations of motion. The number of these constraints can be changed by types of walking pattern with three modes. In order for the dynamic walking to be stabilizable, optimized trunk positions are iteratively determined by satisfying the system ZMP(Zero Moment Point) and ground conditions.

• Structural Engineering and Mechanics
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• v.73 no.4
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• pp.397-405
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• 2020

In this study size optimization of large-scale dome structures with dynamic constraints is presented. In the optimal design of these structure, the Jaya algorithm is used to find minimal size of design variables. The design variables are the cross-sectional areas of the steel truss bar elements. To take into account the constraints which are the first five natural frequencies of the structures, the finite element analysis is coded in Matlab programs using eigen values of the stiffness matrix of the dome structures. The Jaya algorithm and the finite elements codes are combined by the help of the Matlab - GUI (Graphical User Interface) programming to carry out the optimization process for the dome structures. To show the efficiency and the advances of the Jaya algorithm, 1180 bar dome structure and the 1410 bar dome structure were tested by taking into the frequency constraints. The optimal results obtained by the proposed algorithm are compared with those given in the literature to demonstrate the performance of the Jaya algorithm. At the end of the study, it is concluded that the proposed algorithm can be effectively used in the optimal design of large-scale dome structures.

• Korean Management Science Review
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• v.33 no.1
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• pp.77-87
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• 2016

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-separable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky investment decrease as the borrowing constraints become stronger.