This study presents a novel dynamic modelling of a rigid serial manipulator using a compact formula of inertia tensor to simplify dynamic modelling and mathematical transformations. The matrix transformation is used appropriately as a powerful tool for this purpose. The kinetic energy, the potential energy and the inertia matrix of manipulator all are formulated in Denavit-Hartenberg frames (D-...

This paper presents a new method for calculating operational-space inertia matrices, and other related quantities, for branched kinematic trees. It is based on the exploitation of branch-induced sparsity in the joint-space inertia matrix and the task Jacobian. Detailed cost figures are given for the new method, and its efficacy is demonstrated by means of a realistic example based on the ASIMO ...

This article summarizes four formulations of the composite body method for the inertia matrix of a manipulator in the earlier works and presents a new formulation. These five formulations all use the first moments and the inertia tensors of composite bodies about the origin of the local frame. This paper also presents an algorithm for computing these first moments and inertia tensors. This algo...

Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr’s circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjuga...

Let H be a partitioned tridiagonal Hermitian matrix. We characterized the possible inertias of H by a system of linear inequalities involving the orders of the blocks, the inertia of the diagonal blocks and the ranks the lower and upper subdiagonal blocks. From the main result can be derived some propositions on inertia sets of some symmetric sign pattern matrices.

Attitude control of spacecraft remains a challenging nonlinear control problem of intense practical and intellectual importance. Since rotational motion evolves on the set of proper orthogonal matrices, continuous control must account for the presence of multiple equilibria, whereas discontinuous control laws based on quaternions and alternative parameterizations of the rotation matrices lead t...

An original method for the real-time estimation of the roll angle using low-cost sensors in two-wheeled vehicles is proposed. The roll angle greatly affects the dynamics of singletrack vehicles and its estimation is essential in control systems such as ABS, Traction Control, as well as Curve and Collision Warning, or even active suspensions. The proposed method uses a non-linear Kalman filter, ...