A classification is obtained of Borel measurable, GL(n) covariant, symmetric matrix valued valuations on the space of n-dimensional convex polytopes. The only ones turn out to be the moment matrix corresponding to the classical Legendre ellipsoid and the matrix corresponding to the ellipsoid recently discovered by Lutwak, Yang, and Zhang. A classical concept from mechanics is the Legendre ellip...

Abstract A robust internal force-based impedance control scheme for coordinating manipulators is introduced. Internal forcebased impedance control enforces a relationship between the velocity of each manipulator and the internal force on the manipulated objects and requires no knowledge of the object dynamic model. Each manipulator's nonlinear dynamics is compensated by a robust auxiliary contr...

| An adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector. The Modiied Rodrigues Parameters (M-RPs) are used as the kinematic variables since they are non-singular for all possible rotations. The desired linear closed-loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be ...

The concept of energy based Lyapunov control is extended to marine vessels with a nonsymmetric system inertia matrix. Acceleration feedback is used as the main tool to symmetrize the nonsymmetric part of the system inertia matrix. The main reason for a nonsymmetric mass distribution is hydrodynamic added mass which depend on the forward speed of the vessel and the frequency of the incoming wave...

Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G asks which inertias can be attained by a matrix in S(G). We give a complete answer to this question for trees in terms of a new family of graph parameters, the ...

In this paper, we propose a nonlinear adaptive position and attitude tracking controller for a rigid body that requires no information about the mass and inertia matrix of the body. Moreover, we provide sufficient conditions on the reference trajectory that guarantee mass and inertia matrix identification. The controller is shown to be almost globally asymptotically stable and can handle large ...

We propose a new inertia-revealing factorization for sparse matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960s for dense, banded, or tridiagonal matrices, but they have been abandoned in favor of faster methods. We show that this scheme can be applied to any sparse matrix and that the fill in the factorization is bounded by the fill i...

This paper addresses the boundedness property of the inertia matrix and the skew-symmetric property of the Coriolis matrix for vehicle-manipulator systems. These properties are widely used in control theory and Lyapunov-based stability proofs and thus important to identify. The skew-symmetric property does not depend on the system at hand, but on the parameterisation of the Coriolis matrix, whi...