Output Tracking for a Nonlinear Flexible Arm

1993 ◽  
Vol 115 (1) ◽  
pp. 78-85 ◽  
Author(s):  
P. Lucibello ◽  
M. D. Di Benedetto
Keyword(s):  
Rigid Motion ◽  
Inverse System ◽  
Inertial Forces ◽  
Robot Arm ◽  
Bounded Solutions ◽  
Flexible Robot ◽  
Controlled System ◽  
End Effector ◽  
Output Tracking ◽  
Flexible Arm

In this paper, an inversion-based control of the end effector of a two-link flexible robot arm is investigated. The challenge in solving this problem consists in the instability of the inverse system. Arbitrary initialization of the inverse system leads to unbounded elastic vibrations, even if along the desired trajectory the inertial forces associated with the rigid motion are bounded. We show that bounded solutions of the inverse system exist and we provide procedures for computing such solutions in the case of periodic velocities of the end effector. In particular, we consider the case of tracking an unbounded trajectory, e.g., an end point ramp. A technique for the stabilization of the trajectories to be tracked is also proposed and some numerical simulations illustrate the performance of the controlled system.

Free Vibrations of a Flexible Arm Attached to a Compliant Finite Hub

1988 ◽  
Vol 110 (1) ◽  
pp. 118-120 ◽  
Author(s):  
T. P. Mitchell ◽  
J. C. Bruch
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
The Other ◽  
Physical Parameters ◽  
Robot Arm ◽  
Flexible Robot ◽  
Concentrated Mass ◽  
End Effector ◽  
Flexible Arm ◽  
Free Beam

A single-joint flexible robot arm consisting of one link and carrying an end effector is modeled by a continuous, uniform, clamped-free beam having a concentrated mass at the free end and being clamped at the other end to a compliant finite hub. The first six natural frequencies are given for various ratios of physical parameters. The modal shapes are also presented along with their orthogonality relationship. The limiting cases of some of the physical parameters are discussed.

Compensating Control of a Flexible Robot Arm

1990 ◽  
Vol 2 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Masaru Uchiyama ◽  
◽  
Zhao Hui Jiang ◽  
Kyojiro Hakomori
Keyword(s):  
Control System ◽  
Vibration Suppression ◽  
Hierarchical Control ◽  
Elastic Vibration ◽  
Convergence Condition ◽  
Robot Arm ◽  
Flexible Robot ◽  
End Effector ◽  
Flexible Arm ◽  
Arm Motion

Since the characteristics of flexible robot arm motion is far more complex than that of rigid arm motion due to its link elastic deflections, the flexible arm end-effector positioning problem also becomes more complex. The problem is finally resolved into the following three subproblems: (1) how to suppress the link elastic vibration, (2) how to achieve accurate joint positioning, and (3) how to compensate the end-effector positioning errors due to the link deflections. The problem (1) is being solved by many pieces of work. The problem (2) arises also in the case of rigid arms but, since the joint positioning and link vibration suppressing are coupled, it becomes more complex for the case of flexible arms. The problem (3) is important in order for the arms to perform tasks but no effective method has been presented so far to solve it. This paper presents a hierarchical control system which incorporates organically three control functions: joint positioning, link vibration suppression, and end-effector positioning error compensation. The convergence condition for the compensating control is derived theoretically for the condition of static gravitational loads. The effectiveness of the proposed control system is proved by experiments using a two-link flexible arm. The link deflections are measured by a newly devised and developed sensor consisting of a semiconductor laser and a position sensitive detector (PSD).

Control of a Flexible Robot Arm: Experimental and Theoretical Results

1987 ◽  
Vol 109 (4) ◽  
pp. 299-309 ◽  
Author(s):  
N. G. Chalhoub ◽  
A. G. Ulsoy
Keyword(s):  
Partial Evaluation ◽  
Digital Simulation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Motion Controller ◽  
Positional Accuracy ◽  
Spherical Coordinate ◽  
End Effector ◽  
Theoretical Results ◽  
Observation Spillover

The operation of high precision robots is severely limited by. their manipulator dynamic deflection, which persists for a period of time after a move is completed. These unwanted vibrations deteriorate the end effector positional accuracy and reduce significantly the robot arm production rate. A “rigid and flexible motion controller” is derived to introduce additional damping into the flexible motion. This is done by using additional sensors to measure the compliant link vibrations and feed them back to the controller. The existing actuators at the robot joints are used (i.e., no additional actuators are introduced). The performance of the controller is tested on a dynamic model, developed in previous work, for a spherical coordinate robot arm whose last link only is considered to be flexible. The simulation results show a significant reduction in the vibratory motion. The important issue of control and observation spillover is examined and found to present no significant practical problems. Partial evaluation of this approach is performed experimentally by testing two controllers, a “rigid body controller” and a “rigid and flexible motion controller,” on a single joint of a spherical coordinate, laboratory robot arm. The experimental results show a significant reduction in the end effector dynamic deflection; thus partially validating the results of the digital simulation studies.

Neural-Network Based Learning Control of Flexible Mechanism With Application to a Single-Link Flexible Arm

1994 ◽  
Vol 116 (4) ◽  
pp. 792-795 ◽  
Author(s):  
Kazuhiko Takahashi ◽  
Ichiro Yamada
Keyword(s):  
Neural Network ◽  
Angular Position ◽  
Target System ◽  
Space Representation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Neural Network Controller ◽  
Flexible Arm ◽  
Single Link ◽  
Flexible Mechanism

This paper shows the effectiveness of a neural-network controller for controlling a flexible mechanism such as a flexible robot arm. An adaptive-type direct neural controller is formulated using state-space representation of the dynamics of the target system. The characteristics of the controller are experimentally investigated by using it to control the tip angular position of a single-link flexible arm.

Dynamic Finite Element Analysis of the Position Control System of a Two-Link Horizontal Flexible Robot

1990 ◽  
Vol 2 (2) ◽  
pp. 83-90
Author(s):  
Hiroyuki Kojima ◽  
Keyword(s):  
Finite Element ◽  
Control System ◽  
Position Control ◽  
Velocity Curve ◽  
Element Formulation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Element Analysis ◽  
Flexible Arm ◽  
Position Control System

In this paper, a finite element formulation method for a horizontal flexible robot arm with two links is first presented. In the analysis, the kinetic energy of the flexible arm is represented in brief compared with previous methods, and the matrix equation of motion in consideration of the nonlinear forces, such as the Coriolis force, is derived by the finite element method and the variational theorem. Then, the state equation of the mechatronics system consisting of the flexible arm and the position control system is obtained. Secondly, numerical simulations in the case of applying path control based on the trapezoidal velocity curve are carried out by use of the Wilson-<I>θ</I> method, and the effects of the bending rigidity and the shape of the trapezoidal velocity curve on the dynamic characteristics of the mechatronics system are demonstrated.

Nonlinear Regulation of End-Effector Motion for a Flexible Robot Arm

1991 ◽  
pp. 229-236 ◽  
Author(s):  
Alessandro De Luca ◽  
Leonardo Lanari ◽  
Giovanni Ulivi
Keyword(s):  
Robot Arm ◽  
Flexible Robot ◽  
End Effector ◽  
Nonlinear Regulation

Experimental Investigation of Vibration Suppression Control for Flexible Robot Arm

1999 ◽  
Author(s):  
Kengo Inoue ◽  
Nobuyuki Kobayashi
Keyword(s):  
Output Feedback ◽  
Vibration Suppression ◽  
Sliding Mode ◽  
Output Feedback Control ◽  
Sliding Mode Controller ◽  
Robot Arm ◽  
Flexible Robot ◽  
Modeling Methodology ◽  
Flexible Arm ◽  
Good Agreement

Abstract Experimental evaluation of the vibration suppression control performance about the output feedback sliding mode controller for the two-link flexible robot arm is presented. The reduce-order controller is designed based on a kind of the component mode synthesis modeling methodology, and is also designed by the combination of the suboptimal output feedback control and the sliding mode control algorithm. From the experiments of the two-link flexible robot arm model, the good agreement between the numerical simulation results and the experimental ones are obtained not only the motion of the joints but also the arm vibration. And it is verified that the presented output feedback sliding mode controller suppresses the vibration of the flexible arm quit well for various attitude.

Mechatronic robot arm with active vibration absorbers

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1145-1156 ◽  
Author(s):  
Karel Kraus ◽  
Zbyněk Šika ◽  
Petr Beneš ◽  
Jan Krivošej ◽  
Tomáš Vyhlídal
Keyword(s):  
Vibration Suppression ◽  
High Accuracy ◽  
Robot Arm ◽  
Frequency Range ◽  
Flexible Robot ◽  
Linear Quadratic ◽  
Mass System ◽  
End Effector ◽  
End Point ◽  
Serial Robots

Serial robots are typically able to cover large workspace, but their mass/stiffness ratio does not allow combining high accuracy and high dynamic of the end effector operations. Widely spread usage of serial robots, even for tasks such as drilling, leads to high accuracy demands through its workspace. Absolute measurement of the end point for position feedback can be challenging due to objects or even a workpiece in the workspace. Moreover, inbuilt motors of the serial robot cannot response in the frequency range high enough as vibration of the end point. Instead, an additional spring–mass system is attached to the robot to suppress vibrations. The narrow frequency range of a passive dynamic absorber can be extended with active elements between the robot and absorber. An active approach is also necessary because of robots eigenfrequencies and eigenmodes variability. The study deals with a planar flexible robot equipped with a three-degree-of-freedom planar active absorber. The absorber is tuned passively to one value of multiple eigenfrequency. The linear-quadratic regulator control with a state observer has been designed as an active absorber control algorithm. Feedback inputs are absorber body acceleration, end effector acceleration, and relative motions in three absorber actuators realized by voice coils. The end effector vibration suppression along the robot trajectory is achieved using gain scheduling of local controller’s outputs.

Adaptive Output Regulation of a Flexible Arm

1996 ◽  
Vol 118 (1) ◽  
pp. 167-172 ◽  
Author(s):  
P. Lucibello ◽  
F. Bellezza
Keyword(s):  
Adaptive Controller ◽  
Least Square ◽  
Linear Feedback ◽  
Robot Arm ◽  
Flexible Robot ◽  
End Point ◽  
Flexible Arm ◽  
Controller Performance ◽  
Payload Mass ◽  
Total Stability

A self-tuned version of a controller for asymptotic trajectory tracking of the end point of a two-link flexible robot arm is presented. The bounded solution to the inverse system, which is used in the control law, is tuned by the estimates of the unknown robot parameters, generated by a least square identification scheme. Soundness of the state of the adaptive controller is achieved by a stabilizing linear feedback from the output error, with fixed gains and robust with respect to variations of the parameters. This guarantees the total stability of the system, which is the main ingredient used in the proof of the controller properties, through a Lyapunov-like approach. The controller performance is finally illustrated by numerically simulating the tracking of an end point ramp under payload mass variations.

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