On general nonlinear constrained mechanical systems

2019

In this research work, a new method for solving forward and inverse dynamic problems of mechanical systems having an underactuated structure and subjected to holonomic and/or nonholonomic constraints is developed. The method devised in this paper is based on the combination of the Udwadia-Kalaba Equations with the Underactuation Equivalence Principle. First, an analytical method based on the Udwadia-Kalaba Equations is employed in the paper for handling dynamic and control problems of nonlinear nonholonomic mechanical systems in the same computational framework. Subsequently, the Underactuation Equivalence Principle is used for extending the capabilities of the Udwadia-Kalaba Equations from fully actuated mechanical systems to underactuated mechanical systems. The Underactuation Equivalence Principle represents an efficient method recently developed in the field of classical mechanics. The Underactuation Equivalence Principle is used in this paper for mathematically formalizing the underactuation property of a mechanical system considering a particular set of nonholonomic algebraic constraints defined at the acceleration level. On the other hand, in this study, the Udwadia-Kalaba Equations are analytically reformulated in a mathematical form suitable for treating inverse dynamic problems. By doing so, the Udwadia-Kalaba Equations are employed in conjunction with the Underactuation Equivalence Principle for developing a nonlinear control method based on an inverse dynamic approach. As shown in detail in this investigation, the proposed method can be used for analytically solving in an explicit manner the forward and inverse dynamic problems of several nonholonomic mechanical systems. In particular, the tracking control of the unicycle-like mobile robot is considered in this investigation as a benchmark example. Numerical experiments on the dynamic model of the unicycle-like mobile robot confirm the effectiveness of the nonlinear dynamic and control approaches developed in this work.

Section: Udwadia-kalaba Equations In Forward and Inverse Dynamic Probmentioning

confidence: 99%

Forward and Inverse Dynamics of a Unicycle-Like Mobile Robot

2019

“…To this end, several multibody formulation approaches based on the finite element method have been recently developed for modelling flexible continuum bodies that undergo large reference displacements and large deformations [52][53][54][55][56][57][58][59]. In particular, the simple algorithms based on the linearization of the dynamic equations are not suitable for controlling the nonlinear behavior of a flexible multibody mechanical system and more advanced control approaches and numerical procedures are required [60][61][62][63][64][65].…”

Section: Literature Reviewmentioning

confidence: 99%

Use of the Adjoint Method for Controlling the Mechanical Vibrations of Nonlinear Systems

2018

In this work, the analytical derivation and the computer implementation of the adjoint method are described. The adjoint method can be effectively used for solving the optimal control problem associated with a large class of nonlinear mechanical systems. As discussed in this investigation, the adjoint method represents a broad computational framework, rather than a single numerical algorithm, in which the control problem for nonlinear dynamical systems can be effectively formulated and implemented employing a set of advanced analytical methods as well as an array of well-established numerical procedures. A detailed theoretical derivation and a comprehensive description of the numerical algorithm suitable for the computer implementation of the methodology used for performing the adjoint analysis are provided in the paper. For this purpose, two important cases are analyzed in this work, namely the design of a feedforward control scheme and the development of a feedback control architecture. In this investigation, the control problem relative to the mechanical vibrations of a nonlinear oscillator characterized by a generalized Van der Pol damping model is considered in order to illustrate the effectiveness of the computational algorithm based on the adjoint method by means of numerical experiments.

“…In the field of multibody system dynamics, general analysis approaches are required in order to capture the dynamic behavior of a given multibody mechanical system. In general, the analytical techniques used for modelling multibody systems need to facilitate the formulation of the differential dynamic equations and lead to a consistent modelling of the mechanical joints mathematically represented by nonlinear algebraic equations [16][17][18][19][20]. The correct modelling of a multibody system is of paramount importance in several industrial applications such as, for example, in vehicle system dynamics, in aerospace engineering, and, more generally, in the problem of the engineering design of control actuators for mechanical systems formed by rigid and flexible components [21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

On the Computational Methods for Solving the Differential-Algebraic Equations of Motion of Multibody Systems

2018

In this investigation, different computational methods for the analytical development and the computer implementation of the differential-algebraic dynamic equations of rigid multibody systems are examined. The analytical formulations considered in this paper are the Reference Point Coordinate Formulation based on Euler Parameters (RPCF-EP) and the Natural Absolute Coordinate Formulation (NACF). Moreover, the solution approaches of interest for this study are the Augmented Formulation (AF) and the Udwadia-Kalaba Equations (UKE). As shown in this paper, the combination of all the methodologies analyzed in this work leads to general, effective, and efficient multibody algorithms that can be readily implemented in a general-purpose computer code for analyzing the time evolution of mechanical systems constrained by kinematic joints. This study demonstrates that multibody algorithm based on the combination of the NACF with the UKE turned out to be the most effective and efficient computational method. The conclusions drawn in this paper are based on the numerical results obtained for a benchmark multibody system analyzed by means of dynamical simulations.