This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equati...

. Consider a mechanical system consisting of N particles in R subject to some forces. Let xi ∈ R denote the position vector of the ith particle. Then all possible positions of the system are described by N -tuples (x1, . . . , xN ) ∈ (R) . The space (R) is an example of a configuration space. The time evolution of the system is described by a curve (x1(t), . . . , xN (t)) in (R) and is governed...

Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard Euler-Lagrange system restricted to a level set of a momentum map. This provides a Lagrangian parallel to the reduction of symplectic manifolds. The present paper studies the Lagrangian parallel of Poisson reduction for Hamiltonian systems. For the reduc...

The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Legendre transformations we define the Hamiltonian evolution operator which is a...

We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical points of sampled actions. Then we characterize the discretization operators such that, for all quadratic lagrangian, the discrete Euler-Lagrange equations co...

A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover...

The mathematical model of an industrial robot is usually described in the form of Lagrange-Euler equations, Newton-Euler equations or generalized d’Alambert equations. However, these equations require the physical parameters of a robot that are difficult to obtain. In this paper, two methods for calculation of a Lagrange-Euler model of robot using neural networks are presented and compared. The...

Abstract. The mathematical model of industrial robot is well known for example in the form of Lagrange-Euler equations, Newton-Euler equations or generalized d’Alambert equations. However, these equations require the physical parameters of robot like masses, inertia momentums, etc. that are very hard to measure. In the paper, the method for calculation of Lagrange-Euler robot model using neural...

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields ...