The generalized inertia matrix and its inverse are used extensively in robotics applications. While construction of the inertia matrix requires Θ(n) time, inverting it traditionally employs algorithms running in time O(n). We describe an algorithm that reduces the asymptotic time complexity of this operation to the theoretical minimum: Θ(n). We also present simple modifications that reduce the ...

In this paper, the UDUT decomposition of the generalized inertia matrix o f an n-link serial manipulator is presented in symbolic form, where U and D, respectively, are the upper triangular and diagonal matrices. To render the decomposition, the elementary upper triangular matrices, associated to a modified Gaussian elimination, are introduced, whereas each element of the inertia matrix is writ...

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 eleme...

This paper proposes a nonlinear adaptive position and attitude tracking controller for satellite proximity operations between a target and a chaser satellite. The controller requires no information about the mass and inertia matrix of the chaser satellite, and takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth’s oblateness, a...

This paper presents the development of an O(log 2 N) parallel algorithm for the manipulator inertia matrix. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which are required to compute the diagonal elements of the matrix. It results in O(log 2 N) levels of computation. Compu...

Given two polynomials with coeecients over Zk], the associated Bezout matrix B(k) with entries over Zk] deenes a parametric family of Bezout matrices with entries over Z. It is intended in this paper to propose a hybrid approach for determining the inertia of B(k) for any value of k in some real interval. This yields an eecient solution to certain root-location problems for bivariate polynomial...

In this paper, we propose a nonlinear adaptive position and attitude tracking controller for satellite proximity operations. This controller requires no information about the mass and inertia matrix of the satellite, and takes into account the gravitational force, the gravitygradient torque, the perturbing force due to Earth’s oblateness, and other constant – but otherwise unknown – disturbance...

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 el...

In this paper, the e ect of shaft rotation on its natural frequency is investigated. Considering rotary inertia and gyroscopic momentum, the fourth order di erential equation representing the exural vibration of the shaft is solved by the new analytical method. The Distributed Lumped Modeling Technique (DLMT) is applied to obtain the transfer matrix for the distributed elements using the propos...