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Nonlinear Control of Mechanical Systems: A Lagrangian Perspective
, 1997
"... . Recent advances in geometric mechanics, motivated in large part by applications in control theory, have introduced new tools for understanding and utilizing the structure present in mechanical systems. In particular, the use of geometric methods for analyzing Lagrangian systems with both symmetr ..."
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Cited by 27 (4 self)
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. Recent advances in geometric mechanics, motivated in large part by applications in control theory, have introduced new tools for understanding and utilizing the structure present in mechanical systems. In particular, the use of geometric methods for analyzing Lagrangian systems with both symmetries and nonintegrable (or nonholonomic) constraints has led to a unified formulation of the dynamics that has important implications for a wide class of mechanical control systems. This paper presents a survey of recent results in this area, focusing on the relationships between geometric phases, controllability, and curvature, and the role of trajectory generation in nonlinear controller synthesis. Examples are drawn from robotics and flight control systems, with an emphasis on motion control problems. Key Words. Geometric mechanics, nonlinear control, Lagrangian dynamics, motion control. 1. INTRODUCTION Mechanical systems form an important class of nonlinear control systems that h...
Geometric mechanics, Lagrangian reduction and nonholonomic systems
 in Mathematics Unlimited2001 and Beyond
, 2001
"... This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with constraints typified by rolling without slipping. Reduction theory for mechanical systems with symmetry has ..."
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Cited by 24 (5 self)
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This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with constraints typified by rolling without slipping. Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré and others. The modern vision of mechanics includes, besides the traditional mechanics of particles and rigid bodies, field theories such as electromagnetism, fluid mechanics, plasma physics, solid mechanics as well as quantum mechanics, and relativistic theories, including gravity. Symmetries in mechanics ranges from obvious translational and rotational symmetries to less obvious particle relabeling symmetries in fluids and plasmas, to subtle symmetries underlying integrable systems. Reduction theory concerns the removal of symmetries and utilizing their associated conservation laws. Reduction theory has been extremely useful in a wide variety of areas, from a deeper understanding of many
Control and Coordination of Locomotion and Manipulation of a Wheeled Mobile Manipulator
, 1994
"... In this thesis, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation ..."
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Cited by 24 (1 self)
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In this thesis, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation capability offered by fixedbase manipulators and the mobility offered by mobile platforms. While mobile manipulators offer a tremendous potential for flexible material handling and other tasks, at the same time they bring about a number of challenging issues rather than simply increase the structural complexity. First, combining a manipulator and a platform creates redundancy. Second, a wheeled mobile platform is subject to nonholonomic constraints. Third, there exists dynamic interaction between the manipulator and the mobile platform. Fourth, manipulators and mobile platforms have different bandwidths. Mobile platforms typically have slower dynamic response than manipulators. The objectiv...
The EnergyMomentum Method for the Stability of Nonholonomic Systems
, 1998
"... In this paper we analyze the stability of relative equilibria of nonholonomic systems (that is, mechanical systems with nonintegrable constraints such as rolling constraints). In the absence of external dissipation, such systems conserve energy, but nonetheless can exhibit both neutrally stable and ..."
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Cited by 22 (7 self)
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In this paper we analyze the stability of relative equilibria of nonholonomic systems (that is, mechanical systems with nonintegrable constraints such as rolling constraints). In the absence of external dissipation, such systems conserve energy, but nonetheless can exhibit both neutrally stable and asymptotically stable, as well as linearly unstable relative equilibria. To carry out the stability analysis, we use a generalization of the energymomentum method combined with the LyapunovMalkin Theorem and the center manifold theorem. While this approach is consistent with the energymomentum method for holonomic systems, it extends it in substantial ways. The theory is illustrated with several examples, including the the rolling disk, the roller racer, and the rattleback top. 1 Introduction The main goal of this paper is to analyze the stability of relative equilibria for nonholonomic mechanical systems with symmetry using an energymomentum analysis for nonholonomic systems that is ana...
Kinematics and Dynamics of UnderActuated Manipulators
 in IEEE International Conference onRobotics and Automation
, 1991
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NONIDEAL CONSTRAINTS AND LAGRANGIAN DYNAMICS
"... ABSTRACT: This paper deals with mechanical systems subjected to a general class of nonideal equality constraints. It provides the explicit equations of motion for such systems when subjected to such nonideal, holonomic and/or nonholonomic, constraints. It bases Lagrangian dynamics on a new and more ..."
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Cited by 11 (6 self)
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ABSTRACT: This paper deals with mechanical systems subjected to a general class of nonideal equality constraints. It provides the explicit equations of motion for such systems when subjected to such nonideal, holonomic and/or nonholonomic, constraints. It bases Lagrangian dynamics on a new and more general principle, of which D’Alembert’s principle then becomes a special case applicable only when the constraints become ideal. By expanding its perview, it allows Lagrangian dynamics to be directly applicable to many situations of practical importance where nonideal constraints arise, such as when there is sliding Coulomb friction.
Fundamental Principles of Lagrangian Dynamics: Mechanical Systems with Nonideal, Holonomic, and Nonholonomic Constraints
, 2000
"... This paper deals with the foundations of analytical dynamics. It obtains the explicit equations of motion for mechanical systems that are subjected to nonideal holonomic and nonholonomic equality constraints. It provides an easy incorporation of such nonideal constraints into the framework of Lagr ..."
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Cited by 7 (4 self)
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This paper deals with the foundations of analytical dynamics. It obtains the explicit equations of motion for mechanical systems that are subjected to nonideal holonomic and nonholonomic equality constraints. It provides an easy incorporation of such nonideal constraints into the framework of Lagrangian dynamics. It bases its approach on a fundamental principle that includes nonideal constraints and that reduces to D’Alembert’s Principle in the special case when all the constraints become ideal. Based on this, the problem of determining the equations of motion for the constrained system is reformulated as a constrained minimization problem. This yields a new fundamental minimum principle of analytical dynamics that reduces to Gauss’s Principle when the constraints become ideal. The solution of this minimization problem then yields the explicit equations of motion for systems with nonideal constraints. An illustrative example showing the use of this general equation for a system with sliding Coulomb friction is given. � 2000 Academic Press Key Words: nonideal constraints; holonomic and nonholonomic equality constraints; fundamental principle of Lagrangian dynamics; new minimum principle of analytical dynamics; explicit equations of motion for nonideal constraints; sliding friction. 1.