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Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 251 (15 self)
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AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of twoinput systems can be converted into this form. I.
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
"... ..."
Steering nonholonomic systems using sinusoids
 in: Proc. 29th IEEE Conf. Decis. Contr
, 1990
"... In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields ..."
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Cited by 31 (2 self)
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In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their (first order) Lie brackets. Using Brockett's result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. Examples and simulation results are presented. 1
HAMILTON–JACOBI THEORY FOR DEGENERATE LAGRANGIAN SYSTEMS WITH HOLONOMIC AND NONHOLONOMIC CONSTRAINTS
"... Abstract. We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the ..."
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Cited by 4 (4 self)
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Abstract. We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For nondegenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton–Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to nondegenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with nonclosed twoforms. Accordingly, the Dirac–Hamilton– Jacobi equation reduces to a variant of the nonholonomic Hamilton–Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac–Hamilton–Jacobi equation can be used to exactly integrate the equations of motion.
Adaptive Stabilization of a Mechanical System with Nonholonomic Constraints
"... The motion control problem is considered for the nonholonomic systems with unknown dynamic parameters. The proposed control algorithm is based on a method of recursive aim inequalities which allows us to solve the problem of the adaptive stabilization in the presence of uniformly bounded disturbance ..."
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Cited by 1 (1 self)
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The motion control problem is considered for the nonholonomic systems with unknown dynamic parameters. The proposed control algorithm is based on a method of recursive aim inequalities which allows us to solve the problem of the adaptive stabilization in the presence of uniformly bounded disturbances affecting the system. Unlike other works, the presented algorithm of the parameters estimation is given in a form of a differential equation instead of a discretetime algorithm. 1 Introduction This paper addresses adaptive control of mechanical systems with linear homogeneous constraints. Assume that the system under consideration is defined on the connected Riemannian ndimensional real smooth configuration manifold M with local coordinates q = (q 1 ; . . . ; q n ). Linear homogeneous constraints are defined by a kdimensional smooth regular codistribution \Delta ? = span f! 1 ; . . . ; ! k g ae T M and given in the local coordinates as ! j (q) q = 0; j = 1; . . . ; k; (1:1) where ...
Preface
, 2009
"... 1 The research of HC was partly done during a sabbatical stay in Control and Dynamical ..."
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1 The research of HC was partly done during a sabbatical stay in Control and Dynamical
Developments in Nonholonomic . . .
, 1995
"... n this article, we provide a summary of recent developments I in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide ..."
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n this article, we provide a summary of recent developments I in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole.