• Title/Summary/Keyword: Inverse Jacobian

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Dynamic Equations of Robots and Sensitivity Analysis (로봇 운동방정식과 감도해석)

  • Song, Sung-Jae;Lee, Jang-Moo
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.6
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    • pp.105-111
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    • 1995
  • The inverse dynamic equations for 5 link robot including a closed chain have been derived. The closed chain is virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints by the Jacobian matrix which represents the configuration of the closed chain. The topology of tree structrued open chain robot is described by a FATHER array. The FATHER array of a link indicates the link tha tis connected in the direction of base link. Based on the inverse dynamic equations, the torque sensitivity models of the 5 link robot have been developed. The sensitivity models characterize the sensitivity of the driving torque with respect to the link parameters. All the procedures are illustrated through the 2 link robot.

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Position Control of a Redundant Flexible Manipulator (여유자유도 유연 매니퓰레이터의 위치제어)

  • 김진수
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.10 no.3
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    • pp.83-89
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    • 2001
  • In this paper, we discuss the vibration suppression control of spatial redundant flexible manipulators through pseudo-inversed of Jacobian. In order to verify our method, the experiments are performed for PTP(Point To Point) motion of spa-tial flexible manipulators(1) with no redundancy(2) with one redundant DOF(degree of freedom). Finally, a comparison between these results is presented to show the performance of out approach.

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Kinematic Analysis and Optimal Design of 3-PPR Planar Parallel Manipulator

  • Park, Kee-Bong
    • Journal of Mechanical Science and Technology
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    • v.17 no.4
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    • pp.528-537
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    • 2003
  • This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic Joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure Is carried out using Min-Max theory. Finally. one example using the optimal design is presented.

The study on the Intelligent Control of Robot using Fuzzy Inverse Kinematics Mapping (Fuzzy Inverse Kinematics Mapping을 이용한 로봇의 지능제어에 관한 연구)

  • 김관형;이상배
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1996.10a
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    • pp.166-171
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    • 1996
  • Generally, when we control the robot, we should calculate exactly Inverse Kinematics. However, Inverse Kinematics calculation is complex and it takes much time for the manipulator to control in real-time. Therefore, the calculation of Inverse Kinematics can result in significant control delay in real time. In this paper, we will present that Inverse Kinematics can be calculated through Fuzzy Logic Mapping, Based on an exact solution through fuzzy reasoning instead of Inverse Kinematics calculation Also, the result provides sufficient precision and transient tracking error can be controlled based on a fuzzy adaptive scheme proposed in this paper. Based on the Denavit-Hartenberg parameters specification, after the Jacobian matrix of arbitrary manipulator is calculated, we will construct Fuzzy Inverse Kinematics Mapping(FIKM) using fuzzy logic and represent a good control efficiency through simulation of 2-DOF manipulator.

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A Study on the load Flow Calculation for preserving off Diagonal Element in Jacobian Matrix (Jacobian 행렬의 비 대각 요소를 보존시킬 수 있는 조류계산에 관한 연구)

  • 이종기;최병곤;박정도;류헌수;문영현
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.9
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    • pp.1081-1087
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    • 1999
  • Load Flow calulation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning. operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to slove load flow equation and to modify above defects. And it preserve P-Q bus part of Jacobian matrix to shorten computing time. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical results and the same numbers of iteration obtained by Newton-Raphson method. The effect of computing time reduction showed about 28% , 30% , at each case of 39 bus, 118 bus system.

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Visual servoing based on neuro-fuzzy model

  • Jun, Hyo-Byung;Sim, Kwee-Bo
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.712-715
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    • 1997
  • In image jacobian based visual servoing, generally, inverse jacobian should be calculated by complicated coordinate transformations. These are required excessive computation and the singularity of the image jacobian should be considered. This paper presents a visual servoing to control the pose of the robotic manipulator for tracking and grasping 3-D moving object whose pose and motion parameters are unknown. Because the object is in motion tracking and grasping must be done on-line and the controller must have continuous learning ability. In order to estimate parameters of a moving object we use the kalman filter. And for tracking and grasping a moving object we use a fuzzy inference based reinforcement learning algorithm of dynamic recurrent neural networks. Computer simulation results are presented to demonstrate the performance of this visual servoing

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Dynamics Analysis and Control of Five Bar Parallel Robot (5-bar 병렬 로봇의 동역학 해석 및 제어)

  • Chung, Young-Hoon;Lee, Jae-Won;Joo, Hae-Ho
    • Proceedings of the KSME Conference
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    • 2000.04a
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    • pp.529-535
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    • 2000
  • This paper propose the method to obtain the inverse kinematics and the Jacobian of the 5-bar parallel robot and apply the nonlinear controller to the 5-bar parallel robot with the dynamic analyses using the Jacobian of the Passive joints with respect to the active ones and singular value decomposition(SVD). It also experimentally shows that we can do high-speed and accuracy tasks using nonlinear control method. And it explains the relation between the property of the position control and manipulability using a new performance index.

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A Geometrical Approach to the Characteristic Analysis of Parallel Mechanism for Planar Task (평면 작업용 병렬 메카니즘의 특성 해석을 위한 기하학적 접근)

  • Song, Nak-Yoon;Cho, Hwang
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.9
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    • pp.158-166
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    • 1998
  • This paper presents a geometrical approach to the characteristic analysis of parallel mechanism with free joints intended for use as a planar task robot. Solution of the forward and inverse kinematic problems are described. Because the mechanism has only three degree-of-freedom output, constraint equations must be generated to describe the inter-relationship between actuated joints and free joints so as to describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. and it is used for the solution of the forward kinematic equations by Newton-Raphson technique. Another Jacobian matrix was derived to describe the interrelationship between actuated joints and moving platform. The stiffness, velocity transmission ratio, force transmission ratio and dexterity of the mechanism are then determined based on this another Jacobian matrix. The geometrical construction of the mechanism for the best performance was investigated using the characteristic analysis.

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A Study on a Load Flow calculation for Preserved Jacobian Matrix's elements except diagonal terms (Jacobian 행렬의 비 대각 요소를 보존시킬 수 있는 조류계산에 관한 연구)

  • Moon, Yong-Hyun;Lee, Jong-Gi;Choi, Byoung-Kon;Park, Jeong-Do;Ryu, Hun-Su
    • Proceedings of the KIEE Conference
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    • 1998.11a
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    • pp.311-315
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    • 1998
  • Load Flow calculation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning, operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to solve load flow equation and to modify above defects. And it preserve certain part of Jacobian matrix to shorten the time of calculation. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical result and the number of iteration got by Newton-Raphson method. The effect of time reduction showed about 28%, 30%, at each case of 39 bus, 118 bus system.

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The Development of an Inverse Kinematic Solution for Periodic Motion of a Redundant Manipulator (여유자유도 로봇의 주기적 운동제어를 위한 역기구학 해의 개발)

  • 정용섭;최용제
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.1
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    • pp.142-149
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    • 1995
  • This paper presents a new kinematic control strategy for serial redundant manipulators which gives repeatability in the joint space when the end-effector undergoes some general cyclic motions. Theoretical development has been accomplished by deriving a new inverse kinematic equation that is based on springs being conceptually located in the joints of the manipulator. Although some inverse kinematic equations for serial redundant manipulators have been derived by many researchers, the new strategy is the first to include the free angles of torsional springs and the free lengths of the translational springs. This is important because it ensures repeatability in the joint space of a serial redundant manipulator whose end-effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie Bracket Condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joints.