Second Order Sliding Mode Adaptive Neurocontrol for Robot Arms With Finite Time Convergence

Parra-Vega, V.; García-Rodríguez, R.; Ruiz-Sanchez, Francisco J.

doi:10.3182/20050703-6-cz-1902.01309

Cited by 10 publications

(18 citation statements)

References 16 publications

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“…∞ ∈ W L Then, the output of the neural network is also bounded. According previous arguments and the boundedness of the robot dynamics -Coriolis matrix, gravitational term; and due to inertia matrix is positivedefinite and upper bounded; the right hand side of (27) with v =0 is bounded, such that ˆ. (19) we have that …”

Section: Remarkmentioning

confidence: 96%

“…i.e., exponential stability of tracking errors is guaranteed since the solution of S x =0 goes to zero exponentially, . X X α ∆ = − ∆ Remark 5: It is important to notice that the mapping from T X W to ˆq S − defined in (26) is passive, that is 1 0…”

Section: Remarkmentioning

confidence: 99%

“…Finally, the open-loop error dynamics [26,27] is obtained adding and subtracting (16) into (1) such that available and assuming that the Jacobian is not exactly known, the nominal reference (9) cannot be used, that is…”

Section: Cartesian Adaptive Control Letmentioning

confidence: 99%

See 2 more Smart Citations

Task-space neuro-sliding mode control of robot manipulators under Jacobian uncertainties

García-Rodríguez

Parra-Vega

2011

Int. J. Control Autom. Syst.

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Cartesian robot control is an appealing scheme because it avoids the computation of inverse kinematics, in contrast to joint robot control approach. For tracking, high computational load is typically required to obtain Cartesian robot dynamics. In this paper, an alternative approach for Cartesian tracking is proposed under assumption that robot dynamics is unknown and the Jacobian are uncertain. A neuro-sliding second order mode controller delivers a low dimensional neural network, which roughly estimates inverse robot dynamics, and an inner smooth control loop guarantees exponential tracking. Experimental results are presented to confirm the performance in a real time environment.

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Section: Remarkmentioning

confidence: 96%

Section: Remarkmentioning

confidence: 99%

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Task-space neuro-sliding mode control of robot manipulators under Jacobian uncertainties

García-Rodríguez

Parra-Vega

2011

Int. J. Control Autom. Syst.

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“…Tuning k such that S d vanishes much faster than ω e = −αq e , let us analyse the slowest case (using the Gronwal-Bellman Inequality lemma), that is ω e = −αq e , which becomes instrumental to prove convergence. To see this, (15) becomeṡ…”

Section: ) Second Order Sliding Mode Controller For Attitude Dynamicsmentioning

confidence: 97%

“…No chattering is involved and dynamics are not required. To realizeû in arbitrary desired finite time, a wellposed, yet practical, terminal stability is proposed inspired by [15]. In this regard, this work establishes the nontrivial extension of [14] and [15] to this type of aerial robots.…”

Section: A the Dynamic Model Of A Quadrotormentioning

confidence: 98%

Toward force control of a quadrotor UAV in SE(3)

Parra-Vega

Sánchez

Izaguirre

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Two novel model-free second order sliding mode controllers are proposed for the constrained underactuated position and orientation dynamic model of the quadrotor, i.e., considering contact wrench, based on spring-like contact force model. The main theorem establishes conditions for the closedloop system to guarantee semi-global exponential and robust tracking of position and admissible contact forces, with zero yaw, by exploiting the solution in SE(3). It is proved an integral sliding mode for all time and for any initial condition at a quaternion-based sliding surface. This yields a causal and analytical computation of desired angular velocity in terms of position control, without involving derivatives of the state. A second theorem is derived for terminal stability with desired finite time convergence. This in turns produces three results, a) a singularity-free representation under proper and easy to meet initialization; b) stable transition from free flying to constrained motion, and c) realization of the virtual position controller due to finite time convergence of angular tracking errors. It is noted that there arises an evident physical limit for force interaction along underactuated directions: the more interaction force along the underactuated axes, the more roll and pitch angles are needed the less thrust that can be produced to sustain the UAV in the air. Comprehensive simulation study is discussed under various flying conditions, and finally, the explicit (active) force control, based on a differential algebraic model, is briefly addressed.

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A nonlinear robust PI controller for an uncertain system

Aguilar-Ibáñez

Mendoza-Mendoza

Suárez-Castañón

et al. 2014

International Journal of Control

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This paper presents a smooth control strategy for the regulation problem of an uncertain system, which assures uniform ultimate boundedness of the closed-loop system inside of the zero-state neighbourhood. This neighbourhood can be made arbitrarily small. To this end, a class of nonlinear proportional integral controllers or PI controllers was designed. The behaviour of this controller emulates very close a sliding mode controller. To accomplish this behaviour saturation functions were combined with traditional PI controller. The controller did not need a high-gain controller or a sliding mode controller to accomplish robustness against unmodelled persistent perturbations. The obtained closed-solution has a finite time of convergence in a small vicinity. The corresponding stability convergence analysis was done applying the traditional Lyapunov method. Numerical simulations were carried out to assess the effectiveness of the obtained controller.

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Second Order Sliding Mode Adaptive Neurocontrol for Robot Arms With Finite Time Convergence

Cited by 10 publications

References 16 publications

Task-space neuro-sliding mode control of robot manipulators under Jacobian uncertainties

Task-space neuro-sliding mode control of robot manipulators under Jacobian uncertainties

Toward force control of a quadrotor UAV in SE(3)

A nonlinear robust PI controller for an uncertain system

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