Experimental Implementation of Trajectory Pattern Inverse Dynamics Model based Controller for a Flexible Structure

Author(s):  
J. Rastegar ◽  
Q. Tu ◽  
B. Fardanesh ◽  
N. Coleman ◽  
M. Mattice
Author(s):  
Q. Tu ◽  
J. Rastegar

Abstract A new approach to trajectory synthesis and formulation of the inverse dynamics model of flexible structures for point to point motions with minimal high frequency component of the actuating torques (forces) is presented. Trajectories are synthesized such that the flexible structure comes to rest undeformed at the completion of motion. The developed method is based on the Trajectory Pattern Method. In this approach, an appropriate trajectory pattern is selected and described in parametric form. The inverse dynamics model of the system is formulated in terms of the trajectory parameters. The trajectory patterns used are in terms of a number of basic sinusoidal time functions and their harmonics. The basic frequencies are selected such that the harmonics appearing in the actuating torques do not excite the natural modes of vibration of the system. For each motion, the trajectory parameters are determined for minimal amplitudes of the higher actuating torque harmonics, noting that from the vibration and control points of view, such trajectories are more desirable. The higher harmonics refers to the harmonics of the actuating torques with frequencies above the highest trajectory harmonic frequency. As an example, a flexible beam undergoing large displacements and rotations in a plane is considered. The effectiveness of the approach is illustrated by an example.


Author(s):  
Andreas Mu¨ller ◽  
Timo Hufnagel

Redundant actuation of parallel kinematics machines (PKM) is a way to eliminate input-singularities and so to enlarge the usable workspace. From a kinematic point of view the number m of actuator coordinates exceeds the DOF δ of a redundantly actuated PKM (RA-PKM). The dynamics model, being the basis for model-based control, is usually expressed in terms of δ independent actuator coordinates. This implies that the model exhibits the same singularities as the non-redundant PKM, even though the RA-PKM is not singular. Consequently the admissible range of motion of the RA-PKM model is limited to that of the non-redundant PKM. In this paper an alternative formulation of the dynamics model in terms of the full set of m actuator coordinates is presented. It leads to a redundant system of m motion equations that is valid in the entire range of motion. This formulation gives rise to an inverse dynamics formulation tailored for real-time implementation. In contrast to the standard formulation in independent coordinates, the proposed inverse dynamics formulation does not involve control forces in the null space of the control matrix, i.e. it does not allow for the generation of internal prestresses, however. This is not problematic as the latter is usually not exploited. The proposed method is compared to the recently proposed adaptive coordinate switching method. Experimental results are reported if the inverse dynamics solution is introduced in model-based computed torque control scheme of a planar 2DOF RA-PKM.


Author(s):  
Steeve Mbakop ◽  
Gilles Tagne ◽  
Marc-Henri Frouin ◽  
Melingui Achille ◽  
Rochdi Merzouki

Author(s):  
Q. Tu ◽  
J. Rastegar

Abstract The inherent characteristics of the (nonlinear) dynamics of robot manipulators are studied. The study is based on a new method, referred to as the trajectory pattern method. The inverse dynamics models of the manipulator are divided into classes of inverse dynamics models, each corresponding to a different trajectory pattern. For each trajectory pattern, the structure of the resulting inverse dynamics model is fixed and is used to study the characteristics of the dynamics of the manipulator by examining the harmonic content of the required actuation torques (forces) and the relative significance of each harmonic. The harmonic content of the actuating torques is shown to be a function of the path length in the joint coordinate space and the harmonic content of the selected trajectory pattern, but is independent of the number of degrees-of-freedom of the manipulator. The relative contribution of each harmonic is a function of the path length, direction of motion, the position of the path of motion within the workspace of the manipulator, and the magnitude of the fundamental frequency. The study provides a systematic approach to path and trajectory planning from the vibration control point of view. As an example, the characteristics of the dynamics of a spatial 3R manipulator is studied for motions with two different path lengths, starting from a specified point and extending in different directions.


2019 ◽  
Vol 392 ◽  
pp. 8-21 ◽  
Author(s):  
Christophe Laplanche ◽  
Pedro M. Leunda ◽  
Laurie Boithias ◽  
José Ardaíz ◽  
Francis Juanes

2015 ◽  
Vol 43 (1) ◽  
pp. 70-75 ◽  
Author(s):  
Jovana Jovanova ◽  
Viktor Gavriloski ◽  
Marjan Djidrov ◽  
Goce Tasevski

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