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Inertia Matrix (inertia + matrix)
Selected AbstractsStructural Properties of Inertia Matrix and Gravity Vector of Dynamics of Rigid ManipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2002ba Ignacy In this paper, with the use of Euler-Lagrange formalism, it has been proven which joint variables can influence entries of the inertia matrix and the gravity vector of dynamics of a manipulator relative to the kinematic structure of the manipulator. Some formulas, alternative to well-known ones, are presented that allow us to compute the inertia matrix and the gravity vector without using a trace operator. These formulas are computationally inexpensive and provide an inspiration for interesting interpretations. Complexity indices are defined that are able to evaluate the complexity of dynamics of manipulators based on their kinematics. A key role of the accumulated pseudoinertia matrix of the manipulator has been shown. © 2002 Wiley Periodicals, Inc. [source] Identification of the inertia matrix of a rotating body based on errors-in-variables modelsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2010Byung-Eul Jun Abstract This paper proposes a procedure for identifying the inertia matrix of a rotating body. The procedure based on Euler's equation governing rotational motion assumes errors-in-variables models in which all measurements, torque as well as angular velocities, are corrupted by noises. In order for consistent estimation, we introduce an extended linear regression model by augmenting the regressors with constants and the parameters with noise-contributed terms. A transformation, based on low-pass filtering, of the extended model cancels out angular acceleration terms in the regressors. Applying the method of least correlation to the model identifies the elements of the inertia matrix. Analysis shows that the estimates converge to the true parameters as the number of samples increases to infinity. Monte Carlo simulations demonstrate the performance of the algorithm and support the analytical consistency. Copyright © 2009 John Wiley & Sons, Ltd. [source] Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot exampleINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2006Arun D. Mahindrakar Abstract Interconnection and damping assignment passivity-based control is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Hamiltonian structure with a desired energy function,that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. A class of underactuation degree one systems for which the partial differential equations can be explicitly solved,making the procedure truly constructive,was recently reported by the authors. In this brief note, largely motivated by the interesting Acrobot example, we pursue this investigation for two degrees-of-freedom systems where a constant inertia matrix can be assigned. We concentrate then our attention on potential energy shaping and give conditions under which an explicit solution of the associated partial differential equation can be obtained. Using these results we show that it is possible to swing-up the Acrobot from some configuration positions in the lower half plane, provided some conditions on the robot parameters are satisfied. Copyright © 2006 John Wiley & Sons, Ltd. [source] A natural redundancy-resolution for 3-D multi-joint reaching under the gravity effectJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2005Masahiro Sekimoto A simple control method for 3-dimensional multi-joint reaching movements under redundancy of degrees of freedom (DOF) is proposed, which need neither introduce any performance index to solve inverse kinematics uniquely nor calculate pseudo-inverse of the Jacobian matrix of task coordinates with respect to joint coordinates. The proposed control signal is composed of linear superposition of three terms: (1) angular-velocity feedback for damping shaping, (2) task-space position error feedback with a single stiffness parameter, and (3) compensation for gravity force on the basis of estimates for uncertain parameters of the potential energy without calculation any inverse joint position to the target in task space. Through a theoretical analysis of the closed-loop dynamics and a variety of computer simulations by using a whole arm model with five DOFs, the importance of synergistic adjustments of damping factors as well as its relation to selection of the stiffness parameter is pointed out. It is shown that if damping factors are chosen synergistically corresponding to the inertia matrix at the initial time and the stiffness parameter then the endpoint converges asymptotically to the target position and reaches it smoothly without incurring any self-motion. © 2005 Wiley Periodicals, Inc. [source] Structural Properties of Inertia Matrix and Gravity Vector of Dynamics of Rigid ManipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2002ba Ignacy In this paper, with the use of Euler-Lagrange formalism, it has been proven which joint variables can influence entries of the inertia matrix and the gravity vector of dynamics of a manipulator relative to the kinematic structure of the manipulator. Some formulas, alternative to well-known ones, are presented that allow us to compute the inertia matrix and the gravity vector without using a trace operator. These formulas are computationally inexpensive and provide an inspiration for interesting interpretations. Complexity indices are defined that are able to evaluate the complexity of dynamics of manipulators based on their kinematics. A key role of the accumulated pseudoinertia matrix of the manipulator has been shown. © 2002 Wiley Periodicals, Inc. [source] | ||||||||||