Elastic Robot Control: Nonlinear Inversion and Linear Stabilization

Singh, Sahjendra N.; Schy, A. A.

doi:10.1109/taes.1986.310769

Cited by 35 publications

(14 citation statements)

References 12 publications

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“…We choose the stabilization signal of the form: u f = -\E^q (19) where A > 0. For proving stability of the system (14) and (19) with E 2 \ -0, we use the Lyapunov stability theory. We choose a positive definite function:…”

Section: Decoupled Stabilization Using a Velocity Feedbackmentioning

confidence: 99%

“…W(x f ) = q T M 22 (z*)q (20) Then the derivative of W along the solution of the system (14) and (19) is given by:…”

Section: Decoupled Stabilization Using a Velocity Feedbackmentioning

confidence: 99%

“…Based on perturbation approach [9,10] and Lyapunov stability theory, controllers have been designed in [7,8,11,12] for space robots. Nonlinear inversion technique has been applied in [13,14] for the space robots, however, control of the spacecraft has not been considered in these. Singular perturbation method has been used to develop continuous path tracking control system for free-flying space robots [15].…”

Section: Introductionmentioning

confidence: 99%

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Dual mode inverse control and stabilization of flexible space robots

Rivals-Mazères

Yimf²,

Mora-Caminot³

et al. 1997

Guidance, Navigation, and Control Conference

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The question of control and stabilization of flexible space robots is considered. Although, this approach is applicable to space robots of other configurations, for definiteness, a flexible planar two-link robot, mounted on a rigid floating platform in space, is considered. The robotic arm has two revolute joints and its links undergo elastic deformation in the plane of rotation. Based on nonlinear inversion technique, a control law is derived for controlling output variables describing the position and orientation of the platform and the joint angles of the robot. Although, the inverse controller accomplishes reference trajectory tracking, it excites the elastic modes of the arm. Using linear quadratic optimal control theory, a composite stabilizer for stabilization of the rigid and flexible modes and a decoupled flexible mode stabilizer are designed for regulating the end point of the robot to the target point and vibration suppression. Stabilization using only elastic mode velocity feedback is also considered. For large maneuvers, first the inverse controller is active, and the stabilizer is switched for regulation when the motion of the robot lies in the neighborhood of the terminal equilibrium state. Simulation results are presented to show that in the closed-loop system including the inverse controller and the stabilizer, trajectory tracking and stabilization of elastic modes are accomplished.

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Section: Decoupled Stabilization Using a Velocity Feedbackmentioning

confidence: 99%

“…W(x f ) = q T M 22 (z*)q (20) Then the derivative of W along the solution of the system (14) and (19) is given by:…”

Section: Decoupled Stabilization Using a Velocity Feedbackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dual mode inverse control and stabilization of flexible space robots

Rivals-Mazères

Yimf²,

Mora-Caminot³

et al. 1997

Guidance, Navigation, and Control Conference

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“…16 " 18 When high accuracy in task execution is a strict requisite, exact trajectory tracking can be accomplished only by resorting to the inversion of the input/output map of the given system, 19 where nonlinear state feedback is used to compensate for coupled nonlinear terms. Controllers of this kind were developed for the cases of a one-link flexible arm, 20 of a multilink rigid robot with a single flexible boom, 21 ' 22 and of a planar manipulator with two flexible links. 23 The same strategy was also applied to spacecraft or satellites with 24 or without 25 flexible appendages.…”

Section: The Design Of Inversion-based Nonlinear Control Laws Solvingmentioning

confidence: 99%

“…From Eq. (22) it is clear that the desired trajectory must be at least twice differentiable for having exact reproduction.…”

Section: So-mentioning

confidence: 99%

Inversion-based nonlinear control of robot arms with flexible links

Luca

Siciliano

1993

Journal of Guidance, Control, and Dynamics

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Control of flexible joint robots via external linearization approach

Lin

Yuan

1990

J. Robotic Syst.

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Based on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multilink flexible joint robots is considered in this article. The resulting externally linearized and input‐output decoupled closed‐loop system contains a linear subsystem and a nonlinear subsystem. The linear part describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, the nonlinear joint deformation subsystem will cause perturbations in the nominal trajectory. To actively damp out the elastic vibrations and to render the complete closed‐loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the internal stabilization and error correcting control. The tracking errors of the end effector caused by the quasi‐static joint deflections due to gravity can be compensated for by taking into account the nominal deflections in the trajectory planning and LQ regulation. A three‐link PUMA type arm is tested via simulation.

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Elastic Robot Control: Nonlinear Inversion and Linear Stabilization

Cited by 35 publications

References 12 publications

Dual mode inverse control and stabilization of flexible space robots

Dual mode inverse control and stabilization of flexible space robots

Inversion-based nonlinear control of robot arms with flexible links

Control of flexible joint robots via external linearization approach

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