Global trajectory tracking through static feedback for robot manipulators with input saturations

Aguinaga-Ruiz, E.; Zavala‐Río, Arturo; Santibáñez, Víctor; Reyes, Fernando

doi:10.1109/cdc.2008.4738679

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…A strictly increasing continuously differentiable GSF, σ ( x ), has the following three properties (as proven in Lemma 1 of ).…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 97%

“…Generalized saturation functions (GSFs) are used in control design, which are defined as follows. Definition A function σ : R → R is said to be a GSF with bound

\overset{σ}{true}

,if it is locally Lipschitz, non‐decreasing, and satisfies the following: P1: x σ ( x ) > 0, ∀ x ≠ 0. | σ ( x )|≤

\overset{σ}{true}

, ∀ x ∈ R .A strictly increasing continuously differentiable GSF, σ ( x ), has the following three properties (as proven in Lemma 1 of ). P3:The derivative of σ with respect to its argument (i.e.,

σ^{'} ((), x) = \frac{dσ}{dx} ((), x)

) is positive and bounded, that is, there exist a constant

σ_{M}^{'} \in ((), 0, \infty)

such that

0 < σ^{'} ((), x) \leq σ_{M}^{'}

, ∀ x ∈ R . P4: σ ( x ) is globally Lipschitz, that is,

(||, σ ((), x_{1}) - σ ((), x_{2})) \leq σ_{M}^{'} (||, x_{1} - x_{2}), \forall x_{1}, x_{2} \in R .

P5:

\int_{0}^{x} σ (τ) dτ \to + \infty as (||, x) \to + \infty .

It is easy to check that t a n h ( x ) and

\frac{x}{\sqrt{1 + x^{2}}}

are two GSFs satisfying P1–P5 with

\overset{σ}{true} = 1

.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Robust consensus tracking of double-integrator dynamics by bounded distributed control

Zhu

Meng

2015

Int. J. Robust. Nonlinear Control

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SUMMARYThis paper studies the robust consensus tracking problem of multiple second-order systems with additive disturbances and a direct communication topology. We design a continuous, bounded and distributed controller that is composed of a tracker and an uncertainty and disturbance estimator. The tracker makes the nominal closed-loop system globally asymptotically stable, while the output of uncertainty and disturbance estimator attenuates the effect of disturbances. We show that if the disturbances converge to constants, the tracking error converges asymptotically to zero, whereas for other types of disturbances, the obtained error system is small-signal L 1 stable. Some inequalities are developed to show the relationship between the ultimate bounds of tracking errors and the design parameters. Finally, simulation results for four cases are presented to demonstrate the performance of the controller.

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“…A strictly increasing continuously differentiable GSF, σ ( x ), has the following three properties (as proven in Lemma 1 of ).…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 97%

“…Generalized saturation functions (GSFs) are used in control design, which are defined as follows. Definition A function σ : R → R is said to be a GSF with bound

\overset{σ}{true}

,if it is locally Lipschitz, non‐decreasing, and satisfies the following: P1: x σ ( x ) > 0, ∀ x ≠ 0. | σ ( x )|≤

\overset{σ}{true}

σ^{'} ((), x) = \frac{dσ}{dx} ((), x)

) is positive and bounded, that is, there exist a constant

σ_{M}^{'} \in ((), 0, \infty)

such that

0 < σ^{'} ((), x) \leq σ_{M}^{'}

, ∀ x ∈ R . P4: σ ( x ) is globally Lipschitz, that is,

(||, σ ((), x_{1}) - σ ((), x_{2})) \leq σ_{M}^{'} (||, x_{1} - x_{2}), \forall x_{1}, x_{2} \in R .

P5:

\int_{0}^{x} σ (τ) dτ \to + \infty as (||, x) \to + \infty .

It is easy to check that t a n h ( x ) and

\frac{x}{\sqrt{1 + x^{2}}}

are two GSFs satisfying P1–P5 with

\overset{σ}{true} = 1

.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Robust consensus tracking of double-integrator dynamics by bounded distributed control

Zhu

Meng

2015

Int. J. Robust. Nonlinear Control

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show abstract

Position and force tracking in nonlinear teleoperation systems with sandwich linearity in actuators and time-varying delay

Ganjefar

Rezaei

Hashemzadeh

2017

Mechanical Systems and Signal Processing

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Adaptive neural network control of robotic manipulators with input constraints and without velocity measurements

Zhang,

Zhao,

Wang

et al. 2024

IET Control Theory & Appl

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This paper addresses the trajectory tracking problem for a class of uncertain manipulator systems under the effect of external disturbances. The main challenges lie in the input constraints and the lack of measurements of joint velocities. An extend‐state‐observer is utilized to estimate the velocity signals; then, a neural‐network‐based adaptive controller is proposed to solve the problem, where a term based on the nominal model is included to enhance the tracking ability, and the effect of uncertainties and disturbances are compensated by a neural‐network term. Compared with the existing methods, the main distinctive features of the presented approach are: (i) The control law is guaranteed to be bounded by design, instead of directly bounded by a saturation function. (ii) The trade‐off between the performance and robustness of the presented controller can be easily tuned by a parameter that depends on the size of model uncertainties and external disturbances. By virtue of the Lyapunov theorem, the convergence properties of the proposed controller are rigorously proved. The performance of the controller is validated via both simulations and experiments conducted on a two‐degree‐of‐freedom robot manipulator.

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Global trajectory tracking through static feedback for robot manipulators with input saturations

Cited by 7 publications

References 9 publications

Robust consensus tracking of double-integrator dynamics by bounded distributed control

Robust consensus tracking of double-integrator dynamics by bounded distributed control

Position and force tracking in nonlinear teleoperation systems with sandwich linearity in actuators and time-varying delay

Adaptive neural network control of robotic manipulators with input constraints and without velocity measurements

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