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15
A Path Space Approach to Nonholonomic Motion Planning in the Presence of Obstacles
 IEEE Trans. Rob. Autom
, 1997
"... Abstract—This paper presents an algorithm for finding a kinematically feasible path for a nonholonomic system in the presence of obstacles. We first consider the path planning problem without obstacles by transforming it into a nonlinear least squares problem in an augmented space which is then iter ..."
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Cited by 18 (4 self)
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Abstract—This paper presents an algorithm for finding a kinematically feasible path for a nonholonomic system in the presence of obstacles. We first consider the path planning problem without obstacles by transforming it into a nonlinear least squares problem in an augmented space which is then iteratively solved. Obstacle avoidance is included as inequality constraints. Exterior penalty functions are used to convert the inequality constraints into equality constraints. Then the same nonlinear least squares approach is applied. We demonstrate the efficacy of the approach by solving some challenging problems, including a tractortrailer and a tractor with a steerable trailer backing in a loading dock. These examples demonstrate the performance of the algorithm in the presence of obstacles and steering and jackknife angle constraints. Index Terms—Mobile robots, nonholonomic motion planning, obstacle avoidance, path planning, tractortrailer. I.
Exponential Stabilization of an Underactuated Surface Vessel
 in Proc. 35th IEEE Conf. on Decision and Control
, 1996
"... The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a co ..."
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Cited by 14 (5 self)
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The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a continuous periodic timevarying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations. 1. Introduction Control of underactuated vehicles, i.e. vehicles where the control vector has lower dimension than the configuration vector, is a field of increasing interest. It has been studied by e.g. Byrnes and Isidori [1] who gave results on stabilizability of a class of underactuated vehicles. Leonard [4, 5] shows how open loop smallamplitude periodic timevarying forcing can be used to control both underactuated spacecraft and underwater vehicles. Morin et al. [8] present smooth timevarying feedb...
Feedback Stabilization Of Nonlinear Systems
 In Mathematical Theory of Networks and Systems. Birkhauser
, 1989
"... This paper surveys some wellknown facts as well as some recent developments on the topic of stabilization of nonlinear systems. 1 Introduction In this paper we consider problems of local and global stabilization of control systems x = f(x; u) ; f(0; 0) = 0 (1) whose states x(t) evolve on IR n a ..."
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Cited by 9 (0 self)
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This paper surveys some wellknown facts as well as some recent developments on the topic of stabilization of nonlinear systems. 1 Introduction In this paper we consider problems of local and global stabilization of control systems x = f(x; u) ; f(0; 0) = 0 (1) whose states x(t) evolve on IR n and with controls taking values on IR m , for some integers n and m. The interest is in finding feedback laws u = k(x) ; k(0) = 0 which make the closedloop system x = F (x) = f(x; k(x)) (2) asymptotically stable about x = 0. Associated problems, such as those dealing with the response to possible input perturbations u = k(x) + v of the feedback law, will be touched upon briefly. We assume that f is smooth (infinitely differentiable) on (x; u), though much less, for instance a Lipschitz condition, is needed for many results. The discussion will emphasize intuitive aspects, but we shall state the main results as clearly as possible. The references cited should be consulted, however, f...
Control of nonholonomic systems
 The Control Handbook
, 1996
"... When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or f ..."
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Cited by 7 (1 self)
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When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or from physical conservation laws such as the conservation of angular
Asymptotic Controllability And Exponential Stabilization Of Nonlinear Control Systems At Singular Points
, 1998
"... We discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points. Using a discounted optimal control approach we construct discrete feedback laws minimizing the Lyapunov exponent of the linearizati ..."
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Cited by 5 (2 self)
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We discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points. Using a discounted optimal control approach we construct discrete feedback laws minimizing the Lyapunov exponent of the linearization. Thus we obtain an equivalence result between uniform exponential controllability and uniform exponential stabilizability by means of a discrete feedback law.
SemiGlobal Practical Stabilization and Disturbance Adaptation for an Underactuated Ship
 Proc. 39th Conf. Decision Control
, 2000
"... We consider the problem of stabilizing the position and orientation of a ship to constant desired values, when the ship has only two independentcontrols and also the ship is subject to an environmental force of unknown magnitude. We propose a timevarying feedbackcontrol law and a disturbance adapta ..."
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Cited by 2 (0 self)
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We consider the problem of stabilizing the position and orientation of a ship to constant desired values, when the ship has only two independentcontrols and also the ship is subject to an environmental force of unknown magnitude. We propose a timevarying feedbackcontrol law and a disturbance adaptation law, and show that this provides semiglobal practical asymptotic stability. The control and adaptation laws are derived using a combined integrator backstepping and averaging approach. Simulation results are presented. I. Introduction Position and orientation control of ships are required in many offshore oil field operations, such as drilling, pipelaying, tanking between ships, diving support, etc. The dynamic positioning (DP) control problem consists of finding a feedback control law that asymptotically stabilizes both the position and orientation to desired constant values. We consider the DP control problem for a ship that has no side thruster, but two independent main thrusters...
ON BROCKETT’S NECESSARY CONDITION FOR STABILIZABILITY AND THE TOPOLOGY OF LIAPUNOV Functions On R^N
, 2008
"... In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law asymptotically stabilizing an equilibrium for a given nonlinear control system. The intuitive appeal and the ease with which it can be applied have made this criterion one of the standard tools in the s ..."
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In [2], Roger Brockett derived a necessary condition for the existence of a feedback control law asymptotically stabilizing an equilibrium for a given nonlinear control system. The intuitive appeal and the ease with which it can be applied have made this criterion one of the standard tools in the study of the feedback stabilizability of nonlinear control systems. Brockett’s original proof used an impressive combination of Liapunov theory and algebraic topology, in part to cope with a lacuna in our understanding of the topology of the sublevel sets of Liapunov functions. In [33], F. W. Wilson, Jr. extended the converse theorems of Liapunov theory to compact attractors and proved some fundamental results about the topology of their domain of attraction and the level sets of their Liapunov functions. In particular, Wilson showed that the level sets Mc = V −1 (c) are diffeomorphic to Sn−1 for n ̸ = 4, 5 using the proof of the generalized Poincaré Conjecture of Smale. He observed that the excluded cases would from the validity of the Poincaré Conjecture in dimension 3 and 4 and showed that, for n = 5, the assertion ∂Mc ≃ S4 would imply the Poincaré Conjecture for 4manifolds. Of course, the topological Poincaré Conjecture for S4 was subsequently proved by Freedman in 1980 and with the remarkable recent solution by Perelman of the classical Poincaré Conjecture, Wilson’s Theorem now holds for all n. In this
CONTENTS Contents Preface
"... Published by Cambridge University Pressiii iv For my wife, Tammy, and my sons, Alexander and Ethanv ..."
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Published by Cambridge University Pressiii iv For my wife, Tammy, and my sons, Alexander and Ethanv
Preface to the Second
"... Edition The most significant differences between this edition and the first are as follows: • Additional chapters and sections have been written, dealing with: – nonlinear controllability via Liealgebraic methods, – variational and numerical approaches to nonlinear control, including a brief introd ..."
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Edition The most significant differences between this edition and the first are as follows: • Additional chapters and sections have been written, dealing with: – nonlinear controllability via Liealgebraic methods, – variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, – timeoptimal control of linear systems, – feedback linearization (singleinput case), – nonlinear optimal feedback, – controllability of recurrent nets, and – controllability of linear systems with bounded controls. • The discussion on nonlinear stabilization has been expanded, introducing the basic ideas of controlLyapunov functions, backstepping, and damping control. • The chapter on dynamic programming and linearquadratic problems has been substantially edited, so that the material on linear systems can be read in a fully independent manner from the nonlinear preliminaries. • A fairly large number of errors and typos have been corrected. • A list of symbols has been added. I would like to strongly encourage readers to send me suggestions and comments by