Stabilization and tracking in the nonholonomic integrator via sliding modes

Bloch, Anthony M.; Drakunov, S.

doi:10.1016/s0167-6911(96)00049-7

Cited by 143 publications

(86 citation statements)

References 6 publications

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“…in a way such that x 3 converges faster than x 1 , x 2 to zero. This is consistent with other relevant control designs for Brockett's integrator [19], [20].…”

Section: B Brockett's Nonholonomic Double Integratorsupporting

confidence: 89%

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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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“…in a way such that x 3 converges faster than x 1 , x 2 to zero. This is consistent with other relevant control designs for Brockett's integrator [19], [20].…”

Section: B Brockett's Nonholonomic Double Integratorsupporting

confidence: 89%

“…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%

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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“…Many approaches have been proposed to address this issue of nonholonomic stabilization. As pointed out by Kim and Tsiotras [15], the majority of nonholonomic control laws are based on kinematic models [16]- [18]. Stabilization of dynamic models for nonholonomic systems has also been addressed in [19]- [21].…”

Section: Introductionmentioning

confidence: 99%

Decentralized Coverage Control for Multi-Agent Systems with Nonlinear Dynamics

Dirafzoon

Menhaj

Afshar

2011

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper, we study the decentralized coverage control problem for an environment using a group of autonomous mobile robots with nonholonomic kinematic and dynamic constraints. In comparison with standard coverage control procedures, we develop a combined controller for Voronoi-based coverage approach in which kinematic and dynamic constraints of the actual mobile sensing robots are incorporated into the controller design. Furthermore, a collision avoidance component is added in the kinematic controller in order to guarantee a collision free coverage of the area. The convergence of the network to the optimal sensing configuration is proven with a Lyapunov-type analysis. Numerical simulations are provided approving the effectiveness of the proposed method through several experimental scenarios.

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“…Works on the stabilization problem for such systems have mainly focused on the design of time-varying or discontinuous feedback controllers. Thus, many control strategies such as smooth time-varying feedbacks [3], sinusoidal and polynomial controls [4], controls based on backstepping approaches [5], and nonsmooth feedbacks [6,7,8,9] have been investigated.…”

Section: Introductionmentioning

confidence: 99%

“…In many works about the stabilization of the Heisenberg system [7,8,10] (or, in general, about the stabilization of nonholonomic systems [11,12,13]), the derived control laws are of discontinuous type and can lead to discontinuous velocities in practice. This difficulty can be overcome by adding cascade integrators in the path of the usual control inputs so that the discontinuous part of the control is embedded in higher time derivatives of the variables associated to the mechanical parts.…”

Section: Introductionmentioning

confidence: 99%