A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints

Astolfi, Alessandro; Ortega, Roméo; Venkatraman, Aneesh

doi:10.1016/j.automatica.2009.10.027

Cited by 127 publications

(115 citation statements)

References 14 publications

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“…The first one is that now the mapping F(q, τ , w) also contains the (time-varying) interaction forces with the human and the environment. Thus, the stability proof requires different arguments than those reported in [22,23]. The second difference is that k 1 is not a positive constant but rather a positive function of r. This modification does not alter the properties of the observer neither the r-dynamics and, in fact, as it is shown in this section, it is used to dominate the cross-terms appearing from the observer-plant-controller interconnection.…”

Section: Remarkmentioning

confidence: 94%

“…The mapping S has the following properties, related to the properties of the Coriolis matrix C [22,23], that are useful for the derivations:…”

Section: Nonlinear Dynamical Modelmentioning

confidence: 99%

“…For further details the interested reader should consult [22,24]. For system (5), it is proposed the manifold…”

Section: Immersion and Invariance Observermentioning

confidence: 99%

“…One can note two differences with respect to the original I&I observer proposed in [22], [23]. The first one is that now the mapping F(q, τ , w) also contains the (time-varying) interaction forces with the human and the environment.…”

Section: Remarkmentioning

confidence: 99%

“…The main contributions of this paper are: 1) the extension of the authors' previous P+d controllers for variable time-delays [11] to the more challenging case when velocity measurements are not available; 2) it is proved, under the commonly adopted assumption that the human operator and the environment define passive maps, from velocity to force, that when the bilateral teleoperator is in closed-loop with the P+d controller and the full-order I&I observer [22] is used to find a velocity estimation, position error and velocities are globally bounded. Moreover, it is also shown that, if the human operator and the environment do not exert any forces on the local and remote manipulators then position error and velocities asymptotically converge to zero; 3) the design, different from previous works, in particular to [27], of a velocity observer for general nonlinear manipulators interconnected with a communication channel that can induce variable time-delays.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Position tracking in delayed bilateral teleoperators without velocity measurements

Sarras

Nuño

Basañez

et al. 2015

Int. J. Robust. Nonlinear Control

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SUMMARYThis work considers the control of nonlinear bilateral teleoperators with variable time-delays without the need of velocity measurements. The recently proposed Immersion and Invariance (I&I) observer is used to obtain an exponentially convergent estimate of the unmeasured velocities. Under the classical assumption that the human operator and the environment define passive, velocity to force, maps it is proved that with this observer together with a Proportional plus damping (P+d) controller, velocities and position error are globally bounded. Finally, in the case that the human operator and the environment do not exert forces on the local and remote manipulators, respectively, global asymptotic convergence of velocities and of position error to zero is achieved. The theoretical results are sustained with simulations using a couple of two degreesof-freedom nonlinear manipulators.

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Section: Remarkmentioning

confidence: 94%

“…The mapping S has the following properties, related to the properties of the Coriolis matrix C [22,23], that are useful for the derivations:…”

Section: Nonlinear Dynamical Modelmentioning

confidence: 99%

“…For further details the interested reader should consult [22,24]. For system (5), it is proposed the manifold…”

Section: Immersion and Invariance Observermentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Position tracking in delayed bilateral teleoperators without velocity measurements

Sarras

Nuño

Basañez

et al. 2015

Int. J. Robust. Nonlinear Control

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show abstract

Output feedback tracking control for rigid body attitude via immersion and invariance angular velocity observers

Xia

Yue

Wen

2020

Adaptive Control & Signal

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A novel immersion and invariance (I&I) angular velocity observer is presented for the attitude tracking control of a rigid body with the lack of angular rate. Global exponential convergence of angular velocity estimate errors are guaranteed by an innovative filter design for the estimates' Euclidean norm. The proposed method requires fewer filter states compared with existing I&I angular velocity observer designs, which achieves a simpler closed-loop structure (dynamic reduction). The observer synthesis and convergence are independent of the control torque, which leads to much convenience in establishing "separation property" when combining a proportional-derivative attitude tracking controller driven by angular velocity estimates. A rigorous stability analysis is provided to ensure the (almost) global asymptotic convergence of the overall closed-loop tracking errors, and several numerical simulations are carried out to demonstrate the effectiveness of the combined implementation of proposed angular velocity observer and full-state feedback attitude tracking controller.

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An I&I‐Based Observer to Solve the Output‐Feedback Synchronization Problem for a Class of Chaotic Systems

Aguilar-Ibáñez

García–Canseco²,

Martínez‐García

et al. 2017

Asian Journal of Control

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A novel robust observer, intended to solve the output-feedback chaos synchronization problem for the Master/Slave Configuration, is proposed here. Assuming that the given Master system belongs to a specific class of feedback-linearized systems, our solution is based on the well-known Immersion and Invariance (I&I) method. The proposed observer is devoted to the asymptotic estimation of the Master system's underlying dynamics, and its effectiveness is illustrated via computer-based simulations that involve both the so-called Duffing's oscillator and the Genesio & Tesi system.

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A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints

Cited by 127 publications

References 14 publications

Position tracking in delayed bilateral teleoperators without velocity measurements

Position tracking in delayed bilateral teleoperators without velocity measurements

Output feedback tracking control for rigid body attitude via immersion and invariance angular velocity observers

An I&I‐Based Observer to Solve the Output‐Feedback Synchronization Problem for a Class of Chaotic Systems

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