Learning Control of Robot Manipulators

1993 ◽  
Vol 115 (2B) ◽  
pp. 402-411 ◽  
Author(s):  
Roberto Horowitz
Keyword(s):  
Adaptive Learning ◽  
Robot Manipulators ◽  
Learning Control ◽  
Integral Transforms ◽  
Stability And Convergence ◽  
Control Algorithms ◽  
Convergence Properties ◽  
Motor Dexterity ◽  
The Stability ◽  
Learning Schemes

Learning control encompasses a class of control algorithms for programmable machines such as robots which attain, through an iterative process, the motor dexterity that enables the machine to execute complex tasks. In this paper we discuss the use of function identification and adaptive control algorithms in learning controllers for robot manipulators. In particular, we discuss the similarities and differences between betterment learning schemes, repetitive controllers and adaptive learning schemes based on integral transforms. The stability and convergence properties of adaptive learning algorithms based on integral transforms are highlighted and experimental results illustrating some of these properties are presented.

scholarly journals A New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations

2021 ◽  
pp. 58-69
Author(s):  
Lawrence Osa Adoghe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Stiff Systems ◽  
Convergence Properties ◽  
Main Method ◽  
The Stability ◽  
Third Derivative

In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.

scholarly journals Formation Control of Robotic Swarm Using Bounded Artificial Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Long Qin ◽  
Yabing Zha ◽  
Quanjun Yin ◽  
Yong Peng
Keyword(s):  
Formation Control ◽  
Control Algorithm ◽  
Stability And Convergence ◽  
Multirobot Systems ◽  
Convergence Properties ◽  
Swarm Behavior ◽  
Detailed Simulation ◽  
Robotic Swarm ◽  
The Stability ◽  
Significant Attention

Formation control of multirobot systems has drawn significant attention in the recent years. This paper presents a potential field control algorithm, navigating a swarm of robots into a predefined 2D shape while avoiding intermember collisions. The algorithm applies in both stationary and moving targets formation. We define the bounded artificial forces in the form of exponential functions, so that the behavior of the swarm drove by the forces can be adjusted via selecting proper control parameters. The theoretical analysis of the swarm behavior proves the stability and convergence properties of the algorithm. We further make certain modifications upon the forces to improve the robustness of the swarm behavior in the presence of realistic implementation considerations. The considerations include obstacle avoidance, local minima, and deformation of the shape. Finally, detailed simulation results validate the efficiency of the proposed algorithm, and the direction of possible futrue work is discussed in the conclusions.

scholarly journals Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Eleonora Messina ◽  
Antonia Vecchio
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Volterra Integral Equations ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Convergence Properties ◽  
Convergence Of Solutions ◽  
Long Time ◽  
The Stability

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

Application of Learning Control to Active Damping of Forced Vibration for Periodically Time Variant Systems

1990 ◽  
Vol 112 (4) ◽  
pp. 489-496 ◽  
Author(s):  
A. Hac´ ◽  
M. Tomizuka
Keyword(s):  
Learning Control ◽  
Forced Vibrations ◽  
Control Algorithms ◽  
Convergence Properties ◽  
Periodic Disturbances ◽  
Control Rules ◽  
Stiffness Properties ◽  
Feedforward Controller ◽  
Simulation Results ◽  
Inertia Forces

This paper deals with discrete time learning controllers for systems with periodically varying parameters. Several control rules are proposed which use a basic principle of learning control that is to utilize the information from the most recent cycle to improve the system performance in the next cycle. Convergence properties of proposed learning control algorithms are examined. These algorithms can easily be implemented without additional measurements and without modification of existing feedback/feedforward controller. In a numerical example learning controllers are applied to eliminate the forced vibrations of a magnetically suspended rotor with nonsymmetric stiffness properties. The vibrations result from unbalanced inertia forces. Simulation results show that the learning controller is effective in absorbing periodic disturbances.

scholarly journals Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
E. H. van Brummelen
Keyword(s):  
Incompressible Flows ◽  
Fluid Structure Interaction ◽  
Added Mass ◽  
Stability And Convergence ◽  
Time Interval ◽  
Convergence Properties ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Mass Effects ◽  
The Stability

The subiteration method, which forms the basic iterative procedure for solving fluid-structure-interaction problems, is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the subiteration process, and for the stability and accuracy of loosely coupled staggered time-integration methods.

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