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High-speed robots are being applied more and more widely in the scenarios of aviation manufacturing, electronic packaging, and three-dimensional printing, etc. To achieve high speed, the robots are typically designed to be lightweight, hence suffer from undesired vibration, so that the dynamic performance would deteriorate. In light of this, this paper considers the dynamic modeling and active control of an emerging redundant parallel robot. First, the recursively dynamic model is modularly established by means of Lagrangian multipliers method. For completeness, the model of permanent magnet synchronous motor is further integrated with the model of mechanical system to formulate the electromechanically coupled dynamic model (ECDM). To facilitate dynamic control, the ECDM is cleverly projected into the null space of constraint Jacobian matrix eliminating the need to compute Lagrangian multipliers explicitly. Based on singular perturbation approach and Tikhonov theorem, the ECDM is decomposed into two subsystems in different timescales. On this basis, a nonlinear hybrid control scheme is proposed for both trajectory tracking and vibration suppression. Numerical simulations suggest that the nonlinear hybrid control exhibits overwhelming performance than the conventional joint-based proportional and differential feedback control. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of rigid-flexible coupling dynamic modeling and active control of a novel flexible parallel manipulator (PM) with multiple actuation modes. Firstly, based on the flexible multi-body dynamics theory, the rigid-flexible coupling dynamic model (RFDM) of system is developed by virtue of the augmented Lagrangian multipliers approach. For completeness, the mathematical models of permanent magnet synchronous motor (PMSM) and piezoelectric transducer (PZT) are further established and integrated with the RFDM of mechanical system to formulate the electromechanical coupling dynamic model (ECDM). To achieve the trajectory tracking and vibration suppression, a hierarchical compound control strategy is presented. Within this control strategy, the proportional-differential (PD) feedback controller is employed to realize the trajectory tracking of end-effector, while the strain and strain rate feedback (SSRF) controller is developed to restrain the vibration of the flexible links using PZT. Furthermore, the stability of the control algorithm is demonstrated based on the Lyapunov stability theory. Finally, two simulation case studies are performed to illustrate the effectiveness of the proposed approach. The results indicate that, under the redundant actuation mode, the hierarchical compound control strategy can guarantee the flexible PM achieves singularity-free motion and vibration attenuation within task workspace simultaneously. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and efficient controller design of other flexible PMs, especially the emerging ones with multiple actuation modes. [ABSTRACT FROM AUTHOR]

A systematic dynamic modeling methodology is presented to develop the rigid-flexible coupling dynamic model (RFDM) of an emerging flexible parallel manipulator with multiple actuation modes. By virtue of assumed mode method, the general dynamic model of an arbitrary flexible body with any number of lumped parameters is derived in an explicit closed form, which possesses the modular characteristic. Then the completely dynamic model of system is formulated based on the flexible multi-body dynamics (FMD) theory and the augmented Lagrangian multipliers method. An approach of combining the Udwadia-Kalaba formulation with the hybrid TR-BDF2 numerical algorithm is proposed to address the nonlinear RFDM. Two simulation cases are performed to investigate the dynamic performance of the manipulator with different actuation modes. The results indicate that the redundant actuation modes can effectively attenuate vibration and guarantee higher dynamic performance compared to the traditional non-redundant actuation modes. Finally, a virtual prototype model is developed to demonstrate the validity of the presented RFDM. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and controller design of other planar flexible parallel manipulators, especially the emerging ones with multiple actuation modes. [ABSTRACT FROM AUTHOR]