A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs

Zavala‐Río, Arturo; Santibáñez, Víctor

doi:10.1109/tro.2007.892224

Cited by 95 publications

(90 citation statements)

References 19 publications

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“…The variables often considered are those of the amplitude of the actuators. This is to avoid the possibility of an irreversible damage to the actuator [22,23]. An in-depth description of this control method is given in [24].…”

Section: Introductionmentioning

confidence: 99%

Bounded Control of an Actuated Lower-Limb Exoskeleton

Ajayi

Djouani

Hamam

2017

Journal of Robotics

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A bounded control strategy is employed for the rehabilitation and assistance of a patient with lower-limb disorder. Complete and partial lower-limb motor function disorders are considered. This application is centered on the knee and the ankle joint level, thereby considering a user in a sitting position. A high gain observer is used in the estimation of the angular position and angular velocities which is then applied to the estimation of the joint torques. The level of human contribution is feedback of a fraction of the estimated joint torque. This is utilised in order to meet the demands for a bounded human torque; that is, ℎ ≤ 2, ≤ 1, . The asymptotic stability of the bounded control law without human contribution and the convergence analysis of the high gain observer is verified using Lyapunov-based analysis. Simulations are performed to verify the proposed control law. Results obtained guarantee a fair trajectory tracking of the physiotherapist trajectory.

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Section: Introductionmentioning

confidence: 99%

Bounded Control of an Actuated Lower-Limb Exoskeleton

Ajayi

Djouani

Hamam

2017

Journal of Robotics

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“…Motivated by these issues, some efforts have focused on developing saturated controllers for the regulation problem (cf. [1]- [3]) and the more general tracking problem (cf. [4]- [10]).…”

Section: Introductionmentioning

confidence: 99%

“…In [11], the authors developed an adaptive, full-state feedback controller to yield asymptotic tracking while compensating for unknown parametric uncertainties using multiple embedded hyperbolic saturation functions. The authors of [4] were able to extend the PID-based work of [1] to the tracking control problem by utilizing a general class of saturation functions to achieve a global uniform asymptotic tracking result for a linearly parameterizable system. The work was based on prior results in [12] and [5] which incorporated hyperbolic saturation functions into the saturated PD+ control strategy developed in [6].…”

Section: Introductionmentioning

confidence: 99%

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

Fischer

Kan

Kamalapurkar

et al. 2014

IEEE Trans. Automat. Contr.

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Abstract-A saturated controller is developed for a class of uncertain, second-order, nonlinear systems which includes time-varying and nonlinearly parameterized functions with bounded disturbances using a continuous control law with smooth saturation functions. Based on the robust integral of the sign of the error (RISE) control methodology, the developed controller is able to utilize the benefits of high gain control strategies while guaranteeing saturation limits are not surpassed. The bounds on the control are known a priori and can be adjusted by changing the feedback gains. The saturated controller yields asymptotic tracking despite model uncertainty and added disturbances in the dynamics. Experimental results using a two-link robot manipulator demonstrate the performance of the developed controller.

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“…The first approach includes both the P and D actions (at every joint) within a single saturation function, while in the second one all the terms of the controller (P, D and gravity compensation) are covered by one such function, with the P terms internally embedded within an additional saturation. The exclusive use of a single saturation (at every joint) including all the terms of the controller was further achieved through desired gravity compensation in [13]. Moreover, velocityfree versions of the SP-SD controllers in [7] and [6] (still depending on the exact values of the system parameters) are obtained through the design methodologies developed in [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Output-Feedback Adaptive SP-SD-Type Control with an Extended Continuous Adaptation Algorithm for the Global Regulation of Robot Manipulators with Bounded Inputs

López-Araujo

Zavala‐Río

Santibáñez

et al. 2013

International Journal of Advanced Robotic Systems

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In this work, an output-feedback adaptive SP-SD-type control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared with the output-feedback adaptive approaches previously developed in a boundedinput context, the proposed velocity-free feedback controller guarantees the adaptive regulation objective globally (i.e. for any initial condition), avoiding discontinuities throughout the scheme, preventing the inputs from reaching their natural saturation bounds and imposing no saturation-avoidance restrictions on the choice of the P and D control gains. Moreover, through its extended structure, the adaptation algorithm may be configured to evolve either in parallel (independently) or interconnected to the velocity estimation (motion dissipation) auxiliary dynamics, giving an additional degree of design flexibility. Furthermore, the proposed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results on a 3-degree-of-freedom manipulator corroborate the efficiency of the proposed scheme.

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A Natural Saturating Extension of the PD-With-Desired-Gravity-Compensation Control Law for Robot Manipulators With Bounded Inputs

Cited by 95 publications

References 19 publications

Bounded Control of an Actuated Lower-Limb Exoskeleton

Bounded Control of an Actuated Lower-Limb Exoskeleton

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

Output-Feedback Adaptive SP-SD-Type Control with an Extended Continuous Adaptation Algorithm for the Global Regulation of Robot Manipulators with Bounded Inputs

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