scholarly journals Robotic Assembly for Irregular Shaped Peg-in-Hole with Partial Constraints

2021 ◽  
Vol 11 (16) ◽  
pp. 7394
Author(s):  
Wei Li ◽  
Hongtai Cheng ◽  
Chengpeng Li ◽  
Xiaohua Zhang
Keyword(s):  
Force Control ◽  
Stable Equilibrium ◽  
Control Policy ◽  
Robotic Assembly ◽  
Force Model ◽  
Stable Equilibrium Point ◽  
Position Errors ◽  
Hybrid Controller ◽  
Compliant Behavior ◽  
Searching Method

The tight tolerance peg-in-hole process brings great challenges for robotic assembly. Force control-based methods have been proposed to generate complex compliant behavior to deal with the shape and clearance variances. However, existing solutions are based on the assumption that the peg and hole parts are fixed during the assembly process and can absorb the contact force completely. For this purpose, customized fixtures have to be designed and utilized, which greatly affect the system’s deployment cost, time, and flexibility. Considering the fact that in an assembly, the parts are naturally related to each other, this paper studies the irregular-shaped peg-in-hole assembly problem with partial constraints. Firstly, geometric and force model are developed for the natural constraints between the parts; by analyzing the behavior of the partial constraint, a control policy is proposed to compensate the position errors and drive the parts to a stable equilibrium point; For the irregular-shaped parts, a multiple-stage searching method is developed to efficiently search for the real hole location; Finally, a switching force/position hybrid controller is designed to coordinate the alignment, searching and insertion processes. The method is implemented in a real platform. The experiment results verify the effectiveness of the proposed methods.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

scholarly journals Dynamics of transposable elements under the selection model

1999 ◽  
Vol 74 (2) ◽  
pp. 159-164 ◽  
Author(s):  
A. TSITRONE ◽  
S. CHARLES ◽  
C. BIÉMONT
Keyword(s):  
Equilibrium Point ◽  
Dynamic Characteristics ◽  
Time Scale ◽  
Copy Number ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Weak Selection ◽  
Strong Selection ◽  
Long Time

We examine an analytical model of selection against the deleterious effects of transposable element (TE) insertions in Drosophila, focusing attention on the asymptotic and dynamic characteristics. With strong selection the only asymptotically stable equilibrium point corresponds to extinction of the TEs. With very weak selection a stable and realistic equilibrium point can be obtained. The dynamics of the system is fast for strong selection and slow, on the human time scale, for weak selection. Hence weak selection acts as a force that contributes to the stabilization of mean TE copy number. The consequence is that under weak selection, and ‘out-of-equilibrium’ situation can be maintained for a long time in populations, with mean TE copy number appearing stabilized.

scholarly journals An Evolutionary Game Analysis of Internet Public Opinion Events at Universities: A Case from China

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hongying Wen ◽  
Kairong Liang ◽  
Yiquan Li
Keyword(s):  
Public Opinion ◽  
University Students ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Evolutionary Game ◽  
Stable Equilibrium Point ◽  
University Administration ◽  
Negative Effects ◽  
Internet Medium ◽  
The University

Internet public opinion events at universities in China occurred frequently, creating painful repercussions for reputation and stability of colleges and universities. To better cope with the problem, this paper explores an evolutionary mechanism of the university Internet public opinion events. Firstly, we discuss the interactions and behavior of three key participants: an Internet medium, university students as a whole, and administration. Secondly, we construct a tripartite evolutionary game model consisting of an Internet medium, student group, and university administration and then analyze and obtain the differential dynamic equations and equilibrium points. Subsequently, the evolutionary stable equilibrium is further analyzed. Finally, we employ numerical studies to examine how the tripartite behavior choices affect evolutionary paths and evolutionary equilibrium strategies. Results are derived as follows: under certain conditions, there exists an asymptotically stable equilibrium point for the tripartite evolutionary game. On the one hand, appropriate penalties and rewards should be provided to foster objectives and fair behaviors of the network medium. On the other hand, university students should be educated and guided to deal rationally with negative effects of Internet public opinion events. Moreover, online real-name authentication is an important and necessary measure. Finally, the university administration should release truthful, timely, and comprehensive information of Internet public opinion events to mitigate potential negative impacts.

The Duffing-Holmes Oscillator With Hybrid Position Feedback Controller: Stability and Response Analysis

2018 ◽  
Author(s):  
Mehmet R. Simsek ◽  
Onur Bilgen
Keyword(s):  
Stable Equilibrium ◽  
Turbine Blades ◽  
Response Analysis ◽  
Response Type ◽  
Wind Turbine Blades ◽  
Hybrid Controller ◽  
Position Feedback ◽  
Multiple Cross ◽  
Single Cross ◽  
Control Concept

The dynamic behavior of a Duffing-Holmes oscillator subjected to a Hybrid Position Feedback (HPF) controller is investigated. The so-called hybrid controller is a combination of two controllers, namely, the Negative Position Feedback (NPF), and Positive Position Feedback (PPF) controllers. The controller uses the inertial properties of the structure around its stable positions to achieve large displacements by effectively destabilizing the system using an NPF controller. Once the unstable equilibrium is reached, the system is stabilized to the target stable equilibrium using the PPF controller. This dynamic switch of controllers creates the HPF control concept, which specifically enables the monotonic and controlled transition between the states of bistable systems such as the Duffing-Holmes oscillator. This concept can be implemented to morphing structures such as bistable wings, wind turbine blades, and deployable structures. In this paper, a detailed response type and stability analyses of a Duffing-Holmes oscillator controlled by the HPF controller are presented. First, the response types for the components of the HPF, NPF and PPF controllers are analyzed individually. For the NPF controller, three response types are defined. These are intra-well, single cross-well, and multiple cross-well response types describing the possible responses. For the PPF controller, only two response types are defined. These are stabilized and not-stabilized, since the role of the PPF controller is to generate an attractor to the desired stable equilibrium. Finally, the complete HPF controller is analyzed in terms of response type. In this case, three response types are defined: intra-well, single cross-well and multiple cross-well. The paper summarizes all the response types with detailed analyses, and recommends controller parameters for best control performance.

The Qualitative Analysis of Two Populations Commensalisms Model

2012 ◽  
Vol 524-527 ◽  
pp. 3705-3708
Author(s):  
Guang Cai Sun
Keyword(s):  
Qualitative Analysis ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Mathematics Model ◽  
Stable Equilibrium Point ◽  
The Stability ◽  
Two Populations

This paper deals with the mathematics model of two populations Commensalisms symbiosis and the stability of all equilibrium points the system. It has given the conclusion that there is only one stable equilibrium point the system. This paper also elucidates the biology meaning of the model and its equilibrium points.

Position and Force Control of Two CRS A460 Robots Manipulating a Flexible Sheet: Theory and Experiment

1998 ◽  
Vol 120 (4) ◽  
pp. 529-533 ◽  
Author(s):  
Dong Sun ◽  
James K. Mills
Keyword(s):  
Force Control ◽  
Industrial Robots ◽  
Pd Control ◽  
Hybrid Controller ◽  
Position Feedback ◽  
Proper Design ◽  
First Time ◽  
Theory And Experiment

It is verified in theory and experiment that through proper design of the control gains, the simple PD position feedback can control a flexible sheet manipulated by two industrial robots to a desired position while regulating its deformations at the contacts to zero. The offsets of all static deformations of the sheet with reference to the original positions decay to zero. A hybrid controller is further developed to control the motion of the sheet as well as its interactions with the manipulators by adding a force feedforward term to the PD scheme. This is the first time that conventional PD control has been shown to be applicable for use in the manipulation of flexible payload.

scholarly journals Computational Stability Analysis of Lotka-Volterra Systems

2016 ◽  
Vol 44 (2) ◽  
pp. 113-120
Author(s):  
Péter Polcz ◽  
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Stability Region ◽  
Stable Equilibrium ◽  
Linear Matrix ◽  
Stable Equilibrium Point ◽  
Computational Stability ◽  
Volterra Systems ◽  
Selection For ◽  
The Stability

Abstract This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

A New Aspheric Surfaces Polishing by Parallel Orthogonality Movement/Force Servomechanism

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Jianming Zhan ◽  
Sihai Yu
Keyword(s):  
Control System ◽  
Force Control ◽  
Movement Control ◽  
Computer Numerical Control ◽  
Numerical Control ◽  
Aspheric Surfaces ◽  
Coupling Relationship ◽  
Position Errors ◽  
Compliant Control ◽  
Compliant Polishing

According to the all-pervading theory, the best strategy for multiaxis compliant control system is the famous hybrid movement/force control. Until now, the typical way to get it inclines to integrate force control with movement control into one numerical control (NC) interpolator. The more axes being taken for the interpolator, the lower calculating and computerizing speed and the greater errors are. Furthermore, the errors of movement control, including the position errors and pose errors, would inevitably disturb the processing of force control for their coupling relationship. In this paper, the orthogonal movement/force servo strategy is brought forward based on the orthogonality relation of force control and movement control. Combining with the processing of aspheric surfaces polishing, the paper develops a new three-axis computer numerical control (CNC) compliant polishing method and system by the hybrid orthogonal movement/force servomechanism, in which the force controlling and movement controlling are taken in its orthogonal complement space, respectively. Experiments show that this new polishing system is of great robustness for the change of slope and curvature of the aspheric surfaces and it can polish aspheric surfaces to get ultrasmooth surfaces at nanoscale.

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