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Jerzy E Kurek - One of the best experts on this subject based on the ideXlab platform.

David E Orin - One of the best experts on this subject based on the ideXlab platform.

  • IROS - Centroidal Momentum Matrix of a humanoid robot: Structure and properties
    2008 IEEE RSJ International Conference on Intelligent Robots and Systems, 2008
    Co-Authors: David E Orin, Ambarish Goswami
    Abstract:

    The centroidal momentum of a humanoid robot is the sum of the individual link momenta, after projecting each to the robotpsilas Center of Mass (CoM). Centroidal momentum is a linear function of the robotpsilas generalized velocities and the centroidal momentum Matrix is the Matrix form of this function. This Matrix has been called both a Jacobian Matrix and an Inertia Matrix by others. We show that it is actually a product of a Jacobian and an Inertia Matrix.

  • parallel algorithms for computation of the manipulator Inertia Matrix
    The International Journal of Robotics Research, 1991
    Co-Authors: Masoud Aminjavaheri, David E Orin
    Abstract:

    This article presents the development of an O(log{sub 2} N) parallel algorithm for the manipulator Inertia Matrix. It is based on an efficient serial algorithm that uses the composite rigid-body method. Recursive doubling is used to reformulate the linear recurrence equations that are required to compute the diagonal elements of the Matrix. It results in O(log{sub 2} N) levels of computation. Computation of the off-diagonal elements involves N linear recurrences of varying size, and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log{sub 2} N) algorithm is presented in both equation and graphic forms that clearly show the parallelism inherent in the algorithm. The relationship between the number of processors required and the order of the computation is also given for several versions of parallel algorithms for the Inertia Matrix.

  • alternate formulations for the manipulator Inertia Matrix
    The International Journal of Robotics Research, 1991
    Co-Authors: Kathryn W Lilly, David E Orin
    Abstract:

    Four compact methods for computing the manipulator joint space Inertia Matrix are derived and compared. The derivation of the first, the Structurally Recursive Method, is based on the successive addition of single links to the free end of a serial manipulator. A general joint model allows multiple-degree-of-freedom joints to connect the links if desired, and the manipulator Jacobian Matrix is a simultaneous result at no extra cost. the computational complexity of this new method is O(N{sup 3}) for an N-link manipulator with revolute and/or prismatic joints. Derivation of the other methods follows from expanding the equations obtained in the structural recursion and examining the resulting terms. The second method, the Inertia Projection Method, defines a finite summation for each Matrix component that has a form similar to that found in other work. this method is also O(N{sup 3}), and once again, the Jacobian Matrix is computed simultaneously. Through judicious use of the composite rigid body Inertia concept, a third new and efficient algorithm, the Modified Composite Rigid Body Method, is developed with a computational complexity of O(N{sup 2}). Additional manipulation leads to the O(N{sup 2}) Spatial Composite Rigid Body Methods, which is the most efficient for all N {ge} 6more » but eliminates the simultaneous Jacobian computation. These four methods are compared with existing algorithms for computing the Inertia Matrix with respect to their computational complexities. The significance of the simultaneous Jacobian computation is demonstrated by a brief examination of the operational space Inertia Matrix.« less

  • efficient o n computation of the operational space Inertia Matrix
    International Conference on Robotics and Automation, 1990
    Co-Authors: K W Lilly, David E Orin
    Abstract:

    The development of a recursive algorithm for the operational space Inertia Matrix, the Inertia propagation method, which reduces the computational complexity to O(N) for any manipulator is presented. The algorithm is based on a single recursion which begins at the base of the manipulator and progresses out to the last link. Spatial articulated transformations are utilized in the recursion procedure. The algorithm is the most efficient method known for N>or=6. The numerical accuracy of the algorithm is tested for a PUMA 560 robot with a fixed base. The results demonstrate the accuracy of the Inertia propagation method for such a configuration. >

  • ICRA - Efficient O(N) computation of the operational space Inertia Matrix
    Proceedings. IEEE International Conference on Robotics and Automation, 1990
    Co-Authors: K W Lilly, David E Orin
    Abstract:

    The development of a recursive algorithm for the operational space Inertia Matrix, the Inertia propagation method, which reduces the computational complexity to O(N) for any manipulator is presented. The algorithm is based on a single recursion which begins at the base of the manipulator and progresses out to the last link. Spatial articulated transformations are utilized in the recursion procedure. The algorithm is the most efficient method known for N>or=6. The numerical accuracy of the algorithm is tested for a PUMA 560 robot with a fixed base. The results demonstrate the accuracy of the Inertia propagation method for such a configuration. >

Jakub Mozaryn - One of the best experts on this subject based on the ideXlab platform.

Subir Kumar Saha - One of the best experts on this subject based on the ideXlab platform.

  • A new perspective towards decomposition of the generalized Inertia Matrix of multibody systems
    Multibody System Dynamics, 2018
    Co-Authors: Suril V. Shah, Subir Kumar Saha, J. K. Dutt
    Abstract:

    This paper presents a new perspective into the decomposition of the Generalized Inertia Matrix (GIM) of multibody systems with open kinematic architecture, serial or tree-type. Links and kinematic pairs are the two constituting elements of multibody systems. In this work, we propose to decompose a multi-branch multibody system into several kinematic modules. Each module is a set of serially connected links like a serial-chain system. Such a description allows one to obtain a block decomposition U ¯ D ¯ U ¯ T $\bar{\mathbf{U}}\bar{\mathbf{D}}\bar{\mathbf{U}}^{T}$ of the GIM where U ¯ $\bar{\mathbf{U}}$ and D ¯ $\bar{\mathbf{D}}$ are the block upper-triangular and diagonal matrices, respectively. The results provide a recursive inverse of the GIM on module-level. Many new perspectives leading to macroscopic purview of the complex multibody systems are provided. Empowered with the proposed decomposition, an inter- and intra-modular efficient and numerically stable recursive dynamics algorithm for forward dynamics and simulation was possible. While recursive expressions are derived for a four degree-of-freedom gripper, numerical results are shown for a spatial biped.

  • Correlation between diagonal ratio and condition number of the generalized Inertia Matrix of a serial-chain
    Archive of Mechanical Engineering, 2013
    Co-Authors: Suril V. Shah, Subir Kumar Saha
    Abstract:

    The condition number of the Generalized Inertia Matrix (GIM) of a serial chain can be used to measure its ill-conditioning. However, computation of the condition number is computationally very expensive. Therefore, this paper investigates alternative means to estimate the condition number, in particular, for a very long serial-chain. For this, the diagonal elements of the GIM are examined. It is found that the ratio of the largest and smallest diagonal elements of the GIM, when scaled using an initial estimate of the condition number, closely resembles the condition number. This significantly simplifies the process of detecting ill-conditioning of the GIM, which may help to decide on stability of the system at hand

  • simulation of industrial manipulators based on the udu t decomposition of Inertia Matrix
    Multibody System Dynamics, 2003
    Co-Authors: Subir Kumar Saha
    Abstract:

    The UDUT – U and D are respectively the upper triangular and diagonal matrices – decomposition of the generalized Inertia Matrix of an n-link serial manipulator, introduced elsewhere, is used here for the simulation of industrial manipulators which are mainly of serial type. The decomposition is based on the application of the Gaussian elimination rules to the recursive expressions of the elements of the Inertia Matrix that are obtained using the Decoupled Natural Orthogonal Complement matrices. The decomposition resulted in an efficient order n, i.e., O(n), recursive forward dynamics algorithm that calculates the joint accelerations. These accelerations are then integrated numerically to perform simulation. Using this methodology, a computer algorithm for the simulation of any n degrees of freedom (DOF) industrial manipulator comprising of revolute and/or prismatic joints is developed. As illustrations, simulation results of three manipulators, namely, a three-DOF planar manipulator, and the six-DOF Stanford arm and PUMA robot, are reported in this paper.

  • analytical expression for the inverted Inertia Matrix of serial robots
    The International Journal of Robotics Research, 1999
    Co-Authors: Subir Kumar Saha
    Abstract:

    This paper presents the analytical derivation of the Inertia Matrix and its inverse for an open-loop, serial-chain mbot. The derivation allows one to write a recursiveforward-dynamics algorithmforsimulation purposes whose computational complexity is of order a, i.e., O(n) n being the degrees offreedom of the robot under study The proposed methodology is based on the Gaussian elimination of the Inertia Matrix, in contrast to, say, Kalmanftltering; which is proposed elsewhere. The derivation is illustrated with a three-degrees-of-freedom planar robot.

  • a decomposition of the manipulator Inertia Matrix
    International Conference on Robotics and Automation, 1997
    Co-Authors: Subir Kumar Saha
    Abstract:

    A decomposition of the manipulator Inertia Matrix is essential, for example, in forward dynamics, where the joint accelerations are solved from the dynamical equations of motion. To do this, unlike a numerical algorithm, an analytical approach is suggested in this paper. The approach is based on the symbolic Gaussian elimination of the Inertia Matrix that reveal recursive relations among the elements of the resulting matrices. As a result, the decomposition can be done with the complexity of order n, O(n), where n being the degrees of freedom of the manipulator, as opposed to an O(n/sup 3/) scheme, required in the numerical approach. In turn, O(n) inverse and forward dynamics algorithms can be developed. As an illustration, an O(n) forward dynamics algorithm is presented.

Roy Featherstone - One of the best experts on this subject based on the ideXlab platform.

  • Forward Dynamics — Inertia Matrix Methods
    Rigid Body Dynamics Algorithms, 2020
    Co-Authors: Roy Featherstone
    Abstract:

    Forward dynamics is the problem of finding the acceleration of a rigid-body system in response to given applied forces. It is used mainly for simulation; and it is sometimes called ‘direct dynamics’, or simply ‘dynamics’. In this chapter and the next, we examine the forward dynamics of kinematic trees. The dynamics of closed-loop systems is covered in Chapter 8.

  • efficient factorization of the joint space Inertia Matrix for branched kinematic trees
    The International Journal of Robotics Research, 2005
    Co-Authors: Roy Featherstone
    Abstract:

    This paper describes new factorization algorithms that exploit branch-induced sparsity in the joint-space Inertia Matrix (JSIM) of a kinematic tree. It also presents new formulae that show how the cost of calculating and factorizing the JSIM vary with the topology of the tree. These formulae show that the cost of calculating forward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same size. Branches can also reduce complexity; some examples are presented of kinematic trees for which the complexity of calculating and factorizing the JSIM are less than O(n2) and O(n3) , respectively. Finally, a cost comparison is made between an O(n) algorithm and an O(n3) algorithm, the latter incorporating one of the new factorization algorithms. It is shown that the O(n3) algorithm is only 15% slower than the O(n) algorithm when applied to a 30-degrees-of-freedom humanoid, but is 2.6 times slower when applied to an equivalent unbranched chain. This is due mainly to the O(n3) algorithm running about 2.2 times faster on the humanoid than on the chain.

  • an empirical study of the joint space Inertia Matrix
    The International Journal of Robotics Research, 2004
    Co-Authors: Roy Featherstone
    Abstract:

    The joint-space Inertia Matrix of a robot mechanism can be highly ill-conditioned. This phenomenon is not merely a numerical artifact: it is symptomatic of an underlying property of the mechanism itself that can make it more dicult to simulate or control. This paper investigates the problem by means of an empirical study of the eigenvalues, eigenvectors and condition number of the joint-space Inertia Matrix. It is shown that the condition number is typically large, and that it grows anywhere from O(N) to O(N 4 ) with the number of bodies in the system. Several graphs are presented showing how the condition number varies with conguration, the number of links, variations in link sizes, variations in connectivity, and xed or oating bases. Explanations are oered for some of the observed eects.