• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.11
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• pp.1353-1360
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• 2012

The Jacobian and singularity analysis of parallel robots is necessary to analyze robot motion. The derivations of the Jacobian matrix and singularity configuration are complicated and have no geometrical earning in the velocity form of the Jacobian matrix. In this study, the screw theory is used to derive the Jacobian of parallel robots. The statics form of the Jacobian has a geometrical meaning. In addition, singularity analysis can be performed by using the geometrical values. Furthermore, this study shows that the screw theory is applicable to redundantly actuated robots as well as non-redundant robots.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2148-2153
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• 2005

For a legged robot such as a humanoid, balancing its body during a given motion is natural but the most important problem. Recently, a motion given to a humanoid is more and more complicated, and thus the balancing problem becomes much more critical. This paper suggests a real-time motion generation algorithm that guarantees a humanoid to be balanced during the motion. A desired motion of each arm and/or leg is planned by the conventional motion planning method without considering the balancing problem. In order to balance a humanoid, all the given motions are embedded into the COG Jacobian. The COG Jacobian is modified to include the desired motions and, in consequence, dimension of the COG Jacobian is drastically reduced. With the motion-embedded COG Jacobian, balancing and performing a task is completed simultaneously, without changing any other parameters related to the control or planning. Validity and efficiency of the proposed motion-embedded COG Jacobian is simulated in the paper.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.4
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• pp.337-344
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• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.10
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• pp.45-52
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• 2001

This paper presents a study on the position tracking control of a robot system on the uncertain elastic base. The elastic bathe is a nonholonomic system but it can be changed into holonomic system, which is much easier to analyze, by modeling an elastic base as a virtual robot that has passive joints. Also, Jacobian operators, which represent the overall robot system including base movement, are defined and applied to the changed model. However, because base movements are not known, the exact Jacobian operators can＇t be estimated. The control algorithm proposed is that uses only Jacobians of a real robot as approximate Jacobian operators. Therefore the approximate Jacobian operators compensate the measured errors from external sensors. The proposed control strategy is evaluated by the simulation and experiment of a single-axis robot system on the elastic base.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.473-489
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• 2001

The notion of difference for two convex compact sets in Rⁿ, proposed by Rubinov et al, is generalized to R/sub mxn/. A formula of the difference for the two sets, which are convex hulls of a finite number of points, is developed. In the light of this difference, the relation between Clarke generalized Jacobian and quasidifferential, in the sense of Demyanov and Rubinov, for a nonsnooth function, is established. Based on the relation, the method of estimating Clarke generalized Jacobian via quasidifferential for a certain class of function, is presented.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.211-219
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• 2010

Let P be a Jacobian polynomial such as deg P = $deg_y$ P. Suppose the Jacobian polynomial P satisfies the intersection condition satisfying $dim_C$ C[x, y]/$P_y$> = deg P - 1, we can prove that the Keller map which has P as one of coordinate polynomial always has its inverse.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.8 s.173
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• pp.34-41
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• 2005

Generally, it is not easy to get a suitable controller for multi variable systems. If the modeling equation of the system can be found, it is possible to get LQR control as an optimal solution. This paper suggests an LQR learning method to design LQR controller without the modeling equation. The proposed algorithm uses the same cost function with error and input energy as LQR is used, and the LQR controller is trained to reduce the function. In this training process, the Jacobian matrix that informs the converging direction of the controller Is used. Jacobian means the relationship of output variations for input variations and can be approximately found by the simple experiments. In the simulations of a hydrofoil catamaran with multi variables, it can be confirmed that the training of LQR controller is possible by using the approximate Jacobian matrix instead of the modeling equation and this controller is not worse than the traditional LQR controller.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.780-788
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• 2004

To avoid the unit inconsistency problem in the conventional Jacobian matrix, new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points was presented (Kim and Ryu, 2003). This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived unit consistent Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1500-1505
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• 2003

In order to avoid the unit inconsistency problem in the conventional Jacobian matrix, previously we presented new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points based on the velocity relationship [1]. This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived dimensionally homogeneous Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.2
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• pp.112-119
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• 2003

Generally, PID controller is not suitable to control multi variable system because it is very difficult to tune the PID gains. However, this paper shows that it is not hard to tune the PID gains if we can find a Jacobian matrix of the system. The Jacobian matrix expresses the ratio of output variations according to input variations. It is possible to adjust the input values in order to reduce the output error using the Jacobian. When the colt function is composed of error related terms, the gradient approach can tune the PID gains to minimize the function. In simulation, a hydrofoil catamaran with two inputs and two outputs is applied as a multi variable system. We can easily get the multi variable PID controller by the proposed teaming method. When the controller is compared with LQR controller, the performance is as good as that of LQR controller with a modeling equation.