Energy-based trajectory tracking and vibration control for multilink highly flexible manipulators

Abstract

In this paper, a discrete model is adopted, as proposed by Hencky for elastica based on rigid bars and lumped rotational springs, to design the control of a lightweight planar manipulator with multiple highly flexible links. This model is particularly suited to deal with nonlinear equations of motion as those associated with multilink robot arms, because it does not include any simplification due to linearization, as in the assumed modes method. The aim of the control is to track a trajectory of the end effector of the robot arm, without the onset of vibrations. To this end, an energy-based method is proposed. Numerical simulations show the effectiveness of the presented approach.

A Lagrangian Hencky-type non-linear model suitable for metamaterials design of shearable and extensible slender deformable bodies alternative to Timoshenko theory

“…Open problems and challenges that could be tackled in the next future include: (i) a careful analysis of the stiffness parameters used to characterize the elastic response of the whole beam in the largedeformation regime, and in general when de Saint-Venant estimate of stiffness parameters does not apply; such parameters should be related to the material constitutive parameters of the material constituting the meso-beams such as the Young and tangential moduli, and to geometrical parameters of the beams cross-section, as the area, the shear correction factor, and the moment of inertia; (ii) the development of functionally graded materials, meaning those materials having stiffness parameters which are varying along the beam axis; an extended campaign of numerical simulations might unveil new and exotic mechanical behaviors, see [48][49][50][51]; (iii) the development of continuum models, as those developed and exploited, e.g., in [52][53][54][55][56][57][58][59][60], aimed at describing for large displacements systems with many discrete elements of the type presented here; besides being useful in unveiling so-called emerging phenomena, continuum models could help in identifying stiffness parameters; (iv) the exploitation of the presented approach to provide a validation and insight into new and existing approaches for the extension of stability theory in classical elastic media to micromorphic, strain-gradient [61,62], and Cosserat media, see, e.g., [12,[63][64][65][66][67][68][69][70]; (v) the extension of the presented approach to problems where dynamics effects are non-negligible, see, e.g., [71][72][73], like those studied in the active control of vibrations [74]; (vi) the validation of continuum approaches to the study of plane and curved structures moulded as, e.g., shells and tubes, see [75][76][77...…”

Lagrangian descriptions of dissipative systems: a review

“…Some 10 years later, Adolph Mayer [29] established the sufficiency of Helmholtz's conditions, even though in the case of one degree of freedom Darboux [30] had already proved it. 4 More contributions to this problem have been given by Arthur Hirsch [31] in 1898, Karl Boehm [32] in 1900, and Leo Königsberger [36] in 1901.…”

“…Of course, dissipation also occurs at a macroscopic level, for example with viscous and frictional forces, or when dissipative effects are modeled by means of internal variables that evolve in an irreversible way (see, e.g. [3][4][5]). However, dissipative systems constitute a wider class of systems than elastic ones: indeed, the possible phenomena related to dissipation may have quite different natures, which result in different mathematical models used in viscoelasticity, plasticity, fracture, creep mechanics, etc.…”

Stepwise analysis of pantographic beams subjected to impulsive loads

“…It must be kept in mind that we are interested in solutions that consider large displacements in the elastic regime. 1 Some interesting recently published papers analyze the dynamics of two-, see [17], and three-dimensional, see [18], beams, as well as the dynamics in the context of robotic arms [19,20].…”