• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.170-176
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• 1998

In this paper, the column space and null space of the Jacobian matrix were obtained by using the pseudo-inverse method and projection matrix. The equations of motion of the system were replaced by independent acceleration components using the null space matrix. The proposed method has the following advantages. (1) It is simple to derive the null space. (2) The efficiency is improved by getting rid of constrained force terms. (3) Neither null space updating nor coordinate partitioning method is required. The suggested algorithm is applied to a three-dimensional vehicle model to show the efficiency.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.497-504
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• 2006

This paper presents a new technique that derives the dynamic acceleration bounds of multiple cooperating robot systems from given individual torque limits of robots. A set of linear algebraic homogeneous equation is derived from the dynamic equations of multiple robots with friction contacts. The mobility of the robot system is analyzed by the decomposition of the null space of the linear algebraic equation. The acceleration bounds of multiple robot systems are obtained from the joint torque constraints of robots by the medium of the decomposed null space. As the joint constraints of the robots are given in the infinite norm sense, the resultant acceleration bounds of the systems are described as polytopes. Several case studies are presented to validate the proposed method in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1664-1670
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• 1991

For kinematically redundant manipulators, conventional dynamic control methods of local torque optimization showed the instability which resulted in physically unachievable torque requirements. In order to guarantee stability of the null space vector method which resolves redundancy at the acceleration level, Maciejewski[1] analyzed the kinetic behavior of homogeneous solution component and proposed the condition to identify regions of stability and instability for this method. 'In this paper, a modified null space vector method is first presented based on the Maciejewski's condition which is a function of a manipulator's configuration. Secondly, a new control method which is based on the concept of aspects is proposed. It was shown by computer simulations that the modified null space vector method and the proposed method have a common property that a preferred aspect is preserved during the execution of a task. It was also illustrated that both methods demonstrate a drastic reduction of torque loadings at the joints in the tracking motion of a long trajectory when compared with the null space vector method, and thus guarantee the stability of joint torque.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.2
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• pp.208-212
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• 2013

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.

• International Journal of Automotive Technology
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• v.2 no.3
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• pp.117-122
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• 2001

For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3253-3269
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• 1994

In this paper a new concept, named the Extended Operational Space Formulation, has been proposed for the effective analysis and real-time control of the robot manipulators with kinematic redundancy. The extended operational space consists of operational space and optimal null space. The operational space is used to describe robot end-effector motion; whereas the optimal null space, defined as the target space of the self motion manifold, is used to express the self motion for the secondary tasks. Based upon the proposed formulation, the kinematics, statics, and dynamics of redundant robots have been analyzed, and an efficient control algorithm has been proposed. Using this algorithm, one can optimize a performance measure while tracking a desired end-effector trajectory with a better computational efficiency than the conventional methods. The effective ness of the proposed method has been demonstrated with simulations.

• Journal of the Korea Society of Computer and Information
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• v.23 no.2
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• pp.17-26
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• 2018

In this paper, we propose a gait type classification method based on pressure sensor which reflects various terrain and velocity variations. In order to obtain stable gait classification performance, we divide the whole gait data into several steps by detecting the swing phase, and normalize each step. Then, we extract robust features for both topographic variation and speed variation by using the Null-LDA(Null-Space Linear Discriminant Analysis) method. The experimental results show that the proposed method gives a good performance of gait type classification even though there is a change in the gait velocity and the terrain.

• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1554-1567
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• 2005

When multiple robotics systems with several sub-chains grasp a common object, the inherent force redundancy provides a chance of utilizing internal loading. Analysis of grasping space based internal loading is proposed in this work since this method facilitates understanding the physical meaning of internal loadings in some applications, as compared to usual operational space based approach. Investigation of the internal loading for a triple manipulator has been few as ,compared to a dual manipulator. In this paper, types of the internal loading for dual and triple manipulator systems are investigated by using the reduced row echelon method to analyze the null space of those systems. No internal loading condition is derived and several load distribution schemes are compared through simulation. Furthermore, it is shown that the proposed scheme based on grasping space is applicable to analysis of special cases such as three-fingered and three-legged robots having a point contact with the grasped object or ground.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.117-119
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• 2005

For large structural eigen-analysis, the whole structure is divided into some partitioned structures and through synthesis of partitioned structural model the eigen-data of structure can be obtained. In that case, eigenvalue problem consists of semidefinite mass matrix form because of displacement constraint condition. In this work the eigenvalue problem is considered by means of several method, determinant search and null space reduction method.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.71-78
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all variables, which are coupled by the constraints. The position velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The Perturbed constraint equations are then simultaneously solved for variations of all variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent variables variations.