Humans and humanoid robots are often modeled with different types of inverted pendulum models in order to simplify the dynamic analysis of gait, balance and fall. We have earlier introduced the Reaction Mass Pendulum (RMP), an extension of the traditional inverted pendulum models, which explicitly captures the variable rotational inertia and angular momentum of the human or humanoid. In this pa...

In a number of contexts relevant to control problems, including estimation of robot dynamics, covariance, and smart structure mass and stiffness matrices, we need to solve an over-determined set of linear equations AX ≈ B with the constraint that the matrix X be symmetric and positive definite. In the classical least squares method, the measurements of A are assumed to be free of error. Hence, ...

Background and Objectives: Virtual inertia control, as a component of a virtual synchronous generator, is used for the implementation of synchronous generator behaviour in microgrids. In microgrids that include high-capacity distributed generation resources, in addition to virtual inertia, virtual damping can also lead to improvement of frequency stability of the microgrid. The purpose of the c...

An n × n sign pattern matrix A is an inertially arbitrary pattern if for every nonnegative triple (n1, n2, n3) with n1 + n2 + n3 = n, there is a real matrix in the sign pattern class of A having inertia (n1, n2, n3). An n× n sign pattern matrix A is a spectrally arbitrary pattern if for any given real monic polynomial r(x) of degree n, there is a real matrix in the sign pattern class of A with ...

An n × n sign pattern matrix A is an inertially arbitrary pattern if for every nonnegative triple (n1, n2, n3) with n1 + n2 + n3 = n, there is a real matrix in the sign pattern class of A having inertia (n1, n2, n3). An n× n sign pattern matrix A is a spectrally arbitrary pattern if for any given real monic polynomial r(x) of degree n, there is a real matrix in the sign pattern class of A with ...

A solution to the problem of global exponential tracking without velocity measurement of mechanical systems with friction and possibly unbounded inertia matrix is given in the paper. The proposed controller is obtained combining a new full–information passivity–based controller with a new immersion and invariance observer. The resulting closed–loop system has, in some suitably defined coordinat...

The pseudo-SU(3) model is extended to explicitly include the spin and protonneutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given f...

New bounds are derived on the e ective heat conductivity tensor for an anisotropic two-phase composite with interfacial surface resistance between phases. The new upper bound is given in terms of the two-point correlation function, component volume fractions and moment of inertia tensor for the surface of each heterogeneity. The new lower bound is given in terms of the interfacial surface area,...

This paper uses Gauss’ Principle of Least Constraint to derive the “natural” dynamic equations for redundant manipulators. This approach is the fastest way to the result that the operational space inertia matrix of the manipulator is the natural weighting matrix .for the projection used in solving the redundancy problem. Force-controlled robots form a special case of redundant robots, such that...