Causal end-effector inversion of a flexible link manipulator

Vakil, M.; Fotouhi, Reza; Nikiforuk, P.N.

doi:10.1016/j.mechatronics.2009.03.010

Cited by 8 publications

(6 citation statements)

References 24 publications

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“…Remark 2: To make the torque discontinuity at the end of the manoeuvre approach zero, the desired trajectory in the last segment can be redefined so that, at the end of the manoeuvre, t f , not only the redefined displacement and its velocity have the same values as their desired ones but also the link's deflection due to the link flexibility and its velocity are set to be zero, which is under study and preliminary results are available in [16,18]. Therefore, after applying the torque obtained by the inversion process to the dynamic model, the manipulator comes to rest at the end of the manoeuvre, for a rest-to-rest motion, while the end-effector moves along a desired path.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…This method is easy to implement and makes it possible to continue and explore the concept of piece-wise trajectory redefinition by SSEF which is the main focus of this paper. Other way of selecting m jk can be found in [16].…”

Section: Selection Of the Variables (M Jk R) Of The Redefined Outputmentioning

confidence: 99%

“…(35) (after the selection of (C f dec ) k and (C s dec ) k ), the other m are chosen between m f k and m s k . To have the maximum difference between the m for the numerical stability of the solution of the linear equations [16], the other m are equally spaced between m f k and m s k . Therefore, the m for the kth segment are:…”

Section: Selection Of the Variables (M Jk R) Of The Redefined Outputmentioning

confidence: 99%

See 2 more Smart Citations

Piece-Wise Causal Inversion by Output Redefinition for a Flexible Link Manipulator

Vakil

Fotouhi

Nikiforuk

2009

Transactions of the Canadian Society for Mechanical Engineering

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A new causal dynamic end-effector inversion method for a single flexible link manipulator is introduced. Contrary to the available non-causal inversion technique, this method does not lead to pre-actuation and works even in the presence of the purely imaginary zeros for the transfer function. Based on this approach, the desired end-effector trajectory is divided into a finite number of segments. In each segment, the desired trajectory is redefined so that a bounded continuous torque through causal dynamic inversion is obtained. The redefinition of the desired trajectory at each segment employs summation of stable exponential functions. This leads to a family of answers for the redefined trajectory, which is an advantage for control engineers. The results of the simulation and experimental studies show the feasibility and effectiveness of this new technique.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Selection Of the Variables (M Jk R) Of The Redefined Outputmentioning

confidence: 99%

Section: Selection Of the Variables (M Jk R) Of The Redefined Outputmentioning

confidence: 99%

See 1 more Smart Citation

Piece-Wise Causal Inversion by Output Redefinition for a Flexible Link Manipulator

Vakil

Fotouhi

Nikiforuk

2009

Transactions of the Canadian Society for Mechanical Engineering

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“…Due to the presence of link flexibility, the system will exhibit nonminimum phase characteristics when selecting the end-effector of the manipulator as the output. The literature [3][4][5] redefines the output of the manipulator's end position by taking the link elasticity into account, and uses the control algorithm for the rigid-body manipulator to control the new output; however, this method can only realize the point-to-point position control and cannot guarantee tracking control of the end trajectory [6]. The singular perturbation method is another effective method to deal with the nonminimum phase characteristics of manipulators with elastic links.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Tracking Control of Parallel Manipulator with Integral Manifold and Observer

Chen¹

2019

Manifolds II - Theory and Applications

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In view of the problem that notable flexible displacement will occur for parallel manipulators when operating at high speed, the composite controller based on the integral manifold and high-gain observer is proposed for trajectory tracking and the 3RRR parallel manipulator is taken as the object. Based on the stiffness matrix, the small variable is introduced to decompose the rigid-flexible coupling dynamic model into slow and fast subsystem. For the slow subsystem, the backstepping control is applied for rigid motion tracking. In order to account for the links' flexible displacement the corrective torque is deduced, and the compensation for the flexible displacement is realized. For the fast subsystem, the sliding mode control is utilized to suppress the vibration. The high-gain observer is designed to avoid the measurement of the curvature rate of flexible links. Also, the stability of the overall system is proven with the Lyapunov stability theorem and the upper bound of the small variable is obtained. At last, the proposed composite controller together with the singular perturbation control and the rigid body model-based backstepping control are simulated, and vibration suppression and tracking performances are compared to validate the proposed control scheme.

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“…Flexible link manipulators (FLM) are underactuated systems (De Luca et al, 2001). Moreover, considering the end-effector displacement as the output, the FLM are non-minimum phase systems (Green and Sasiadek, 2004;Vakil et al, 2009). These limitations of the FLM have made their end-effector trajectory tracking (EETT) a challenging subject.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Tracking for the End-effector of a Class of Flexible Link Manipulators

Vakil

Fotouhi

Nikiforuk

2010

Journal of Vibration and Control

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A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their time derivative. For the slow subsystem, the new controller requires only ‘‘one’’ corrective torque in addition to the computed torque command of the rigid link counterpart of the CRFE for the reduction of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of the new controller is an advantage for it. To facilitate the derivation and implementation of this controller, several properties of the matrices in the dynamic model of the CRFE are introduced and used which are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies.

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Causal end-effector inversion of a flexible link manipulator

Cited by 8 publications

References 24 publications

Piece-Wise Causal Inversion by Output Redefinition for a Flexible Link Manipulator

Piece-Wise Causal Inversion by Output Redefinition for a Flexible Link Manipulator

Trajectory Tracking Control of Parallel Manipulator with Integral Manifold and Observer

Trajectory Tracking for the End-effector of a Class of Flexible Link Manipulators

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