Control and stabilization of nonholonomic dynamic systems

Bloch, Anthony M.; Reyhanoglu, Mahmut; McClamroch, N. Harris

doi:10.1109/9.173144

Cited by 735 publications

(365 citation statements)

References 22 publications

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“…This approach, however, is not directly applicable to underactuated systems which undergo non-integrable (nonholonomic) constraints (Bloch, Reyhanoglu andMcClamroch 1992 andReyhanoglu et al 1999). As a consequence of Brockett's Theorem (Brockett 1983), a nonholonomic system is not triangulable via any smooth static state feedback.…”

Section: Remark 3 the Approach Of Nssft Is Mainly Applicable To A Clamentioning

confidence: 99%

Stabilization of underactuated mechanical systems: A non-regular back-stepping approach

Sun¹,

Ge²,

Lee³

2001

International Journal of Control

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This paper presents a design framework for the stabilization of a class of underactuated mechanical systems. By utilizing nonregular static state feedbacks, these systems are transformed into a class of nonlinear systems with chain structures. Then, controller design is presented by applying the backstepping design technique. The design procedure is applied to an underactuated robotic system and simulation tests are carried out for illustrating the effectiveness of the proposed approach.

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Section: Remark 3 the Approach Of Nssft Is Mainly Applicable To A Clamentioning

confidence: 99%

Stabilization of underactuated mechanical systems: A non-regular back-stepping approach

Sun¹,

Ge²,

Lee³

2001

International Journal of Control

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“…A robust control architecture for mechanical systems that are subject to p nonholonomic Pfaffian constraints is given in [15], which guarantees the convergence of the system to a pdimensional desired manifold. The stabilization of dynamic nonholonomic systems is also addressed in [2], [8], [16]- [18]. Finally, various stabilization control schemes have been proposed for specific systems, like the unicycle and Brockett's nonholonomic double integrator [19]- [22].…”

Section: Introductionmentioning

confidence: 99%

“…Brockett's theorem [1] states that nonholonomic systems can not be stabilized by continuously differentiable, timeinvariant state feedback control laws. In fact, nonholonomic mechanical systems can not be asymptotically stabilized to a single equilibrium using any control method that employs smooth, or even continuous, time-invariant feedback [2]. Various solutions have been proposed, usually classified as piecewise continuous feedback [2], [3], time-varying feedback [4]- [8], discontinuous feedback [9]- [11] and hybrid/switching control strategies [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Dipole-like fields for stabilization of systems with Pfaffian constraints

Panagou

Tanner

Kyriakopoulos

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-This paper introduces a framework that guides the design of stabilizing feedback control laws for systems with Pfaffian constraints. A new class of N -dimensional vector fields, the dipole-like vector fields is proposed, inspired by the form of the flow lines of the electric point dipole. A general connection between the dipole-like field and the Pfaffian constraints of catastatic nonholonomic systems is exploited, to establish systematic guidelines on the design of stabilizing control laws. The methodology is applied to the stabilization of the unicycle and of the nonholonomic double integrator. Based on these guidelines, switching control laws are constructed. The efficacy of the methodology is demonstrated through simulation results.

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“…[2] and [3] and references therein give a good overview of these methods. These methods are within three categories: Smooth time-invariant methods [4], [5], discontinuous time invariant methods [6],7] to cite few which are based on the so-called σ-process transformation [6] , and hybrid stabilization techniques, [8] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Predictor-based stabilization for chained form systems with input time delay

Mnif

2016

Archives of Control Sciences

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This note addresses the stabilization problem of nonlinear chained-form systems with input time delay. We first employ the so-called σ-process transformation that renders the feedback system under a linear form. We introduce a particular transformation to convert the original system into a delay-free system. Finally, we apply a state feedback control, which guarantees a quasi-exponential stabilization to all the system states, which in turn converge exponentially to zero. Then we employ the so-called -type control to achieve a quasi-exponential stabilization of the subsequent system. A simulation example illustrated on the model of a wheeled mobile robot is provided to demonstrate the effectiveness of the proposed approach.

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Control and stabilization of nonholonomic dynamic systems

Cited by 735 publications

References 22 publications

Stabilization of underactuated mechanical systems: A non-regular back-stepping approach

Stabilization of underactuated mechanical systems: A non-regular back-stepping approach

Dipole-like fields for stabilization of systems with Pfaffian constraints

Predictor-based stabilization for chained form systems with input time delay

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