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Institute for Robotics and Intelligent Machines (IRIM)

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Author: Siciliano, Bruno × End date: 1989 × Start date: 1980 × Has files: Yes ×

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A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators

1988-08 , Siciliano, Bruno , Book, Wayne J.

The control of lightweight flexible manipulators moving along predefined paths is the focus of this work. The flexible manipulator dynamics is derived on the basis of a Lagrangian-assumed modes method. The full order flexible dynamic system does not allow the determination of a tracking control as for rigid manipulators, since there are not as many control inputs as output variables. This drawback is overcome by accomplishing a model order reduction, based on a singular perturbation strategy, where the perturbation parameter can be identified as the ratio of speeds of the slow versus the fast dynamics. A composite control is adopted. First a slow control is designed with the purpose to track the trajectory in the joint space as accurately as possible. A quasi steady-state trajectory is then determined for the fast variables, and a fast control is in charge of stabilizing them along that trajectory. The one link flexible arm prototype in the Flexible Automation Laboratory at Georgia Tech is chosen for developing a case study. Extensive simulation results are illustrated.

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Symbolic modelling and dynamic analysis of flexible manipulators

1986-10 , Cetinkunt, Sabri , Siciliano, Bruno , Book, Wayne J.

This paper presents a systematic method to symbolically derive the full nonlinear dynamic equations of motion of Multi-link flexible manipulators. Lagrange's-Assumed Modes method is used for the dynamic modelling and implemented via a commercially available symbolic manipulation program. Adaptation of the method suitable for symbolic manipulation and advantages are discussed. Simulation results for a two-link planar flexible arm presented.

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Model Reference Adaptive Control of a One Link Flexible Arm

1986-12 , Siciliano, Bruno , Yuan, Bau-San , Book, Wayne J.

Based on a model reference adaptive control approach, a robust controller for a one link flexible arm moving along a pre-defined trajectory is proposed. In order to satisfy the perfect model following conditions, the model is chosen from the linearized model of the system as optimally controlled. The nominal trajectory is commanded to the system by means of a dynamic filter. Simulation results for the prototype in the laboratory show the improvements obtained with the outer adaptive feedback loop with respect to a pure optimal control regulator. Robustness is finally tested by varying the nominal payload mass

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Symbolic Modelling and Dynamic Analysis of Flexible Manipulators

1986 , Cetinkunt, Sabri , Siciliano, Bruno , Book, Wayne J.

This paper presents a systematic method to symbolically derive the full nonlinear dynamic equations of motion of Multi-link flexible manipulators. Lagrange's-Assumed Modes method is used for the dynamic modelling and implemented via a commercially available symbolic manipulation program. Adaptation of the method suitable for symbolic manipulation and advantages are discussed. Simulation results for a two-link planar flexible arm presented.

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An integral manifold approach to control of a one link flexible arm

1986-12 , Siciliano, Bruno , Book, Wayne J. , De Maria, Giuseppe

The problem of controlling a one link flexible arm is considered in this paper. An assumed mode method is adopted to derive the dynamic equations of motion; the system is then transformed to singularly perturbed form. An integral manifold approach is proposea leading to the derivation of a reduced order system which incorporates the effects of the flexibility distributed along the structure. An approximate technique is finally presented which allows the synthesis of a feedback linearizing control

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Application of Singular Perturbation Theory to the Control of Flexible Link Manipulators

1986 , Siciliano, Bruno , Book, Wayne J.

The control problem for robotic manipulators with flexible links is considered in this paper. The dynamic equations of motion can be derived by means of a recently developed Lagrangian-assumed modes method. In the case of flexibility at links it has been shown that there is no analogue of the well established computed torque method widely adopted for rigid arm control. Under the assumption that the flexible dynamics is faster than the rigid dynamics, singular perturbation theory provides an engineering tool for reduced order modeling. The resulting slow subsystem allows the determination of a tracking control as for rigid manipulators, since the number of control variables equals that of control led variables. For the fast subsystem an additive control is in charge of stabilizing the deflections along the joint angle trajectory. The result is a composite control strategy which combines the advantages of rigidity ("controllability") with those of flexibility ("lightweight compliant structures").

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