Abstract
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.
Highlights
A set of numerical results and an evaluation of the performance of the method proposed in the paper are provided to demonstrate the application of the Udwadia-Kalaba Equations in conjunction with the Underactuation Equivalence Principle to nonlinear control problems
Multibody dynamics is a branch of analytical mechanics devoted to the study of the dynamic behavior of articulated systems composed of rigid or flexible bodies constrained by mechanical joints
This paper is concerned with forward and inverse dynamic problems of wheeled mobile robots having an underactuated structure and is part of a wider research plan inspired by the vision of the authors
Summary
Background information is provided first. Subsequently, the problem of interest for this investigation is formulated and a brief literature survey is reported. Dynamic models can be used for the development of new control algorithms suitable for solving several engineering problems [19–24]. This process is effective in the field of robotics for controlling mobile robots that represent the main object of the present research work [25–30]. The general form of the fundamental problem of constrained motion is recalled and, subsequently, these equations are rewritten in an analytical form suitable for solving inverse dynamics problems. The combined use of the Udwadia-Kalaba Equations with the Underactuation Equivalence Principle necessary for the development of nonlinear control laws suitable for controlling underactuated nonholonomic mechanical systems is analyzed. In the central problem of constrained dynamics, the main goal is to predict the dynamical evolution of a mechanical system subjected to a given set of algebraic constraint equations [86–88]
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