scholarly journals Leader–follower formation with reduction of the off-tracking and velocity estimation under visibility constraints

2021 ◽  
Vol 18 (6) ◽  
pp. 172988142110576
Author(s):  
C. Mauricio Arteaga-Escamilla ◽  
Rafael Castro-Linares ◽  
Jaime Álvarez-Gallegos
Keyword(s):  
Formation Control ◽  
Kinematic Model ◽  
Velocity Estimation ◽  
Lyapunov Theory ◽  
Time Varying ◽  
Absolute Position ◽  
Nonholonomic Mobile Robots ◽  
The Stability ◽  
Time Invariant ◽  
Explicit Communication

This article addresses the time-varying leader–follower formation control problem for nonholonomic mobile robots, under communication and visibility constraints. Although the leader–follower formation control under visibility constraints has been studied, the elimination of the off-tracking effect has not been widely addressed yet. In this work, a new method to eliminate the off-tracking effect, considering the time-invariant formation as a tractor–trailer system, for unknown and circular tractor paths, taking into account the visibility constraints, is proposed. For a time-varying formation with not circular tractor’s path, the proposed method significantly reduces the off-tracking. Only the relative position and the relative orientation, provided by the on board monocular camera, are required. Thus, both the leader robot’s absolute position and the leader robot’s velocities are not needed. Furthermore, to avoid explicit communication among the robots, an extended state observer is implemented to estimate both the translational and the rotational leader’s velocity. In this way, the desired tasks are executed and achieved in a decentralized manner. For a time-varying formation, with constant leader robot’s velocities, the proposed control strategy, based on the kinematic model, guarantees that the formation errors asymptotically converge to the origin. Based on the Lyapunov theory, the stability proof of the formation errors dynamics is shown. Simulation results, considering time-varying leader robot’s velocities, show the efficiency of the proposed scheme.

scholarly journals Robust Time-Varying Output Formation Control for Swarm Systems with Nonlinear Uncertainties

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiaofeng Chai ◽  
Qing Wang ◽  
Yao Yu ◽  
Changyin Sun
Keyword(s):  
Stability Problem ◽  
Formation Control ◽  
Directed Network ◽  
Control Problems ◽  
Time Varying ◽  
Robust Controller ◽  
Nonlinear Uncertainties ◽  
The Stability ◽  
High Order Time ◽  
Time Invariant

Time-varying output formation control problems for high-order time-invariant swarm systems are studied with nonlinear uncertainties and directed network topology in this paper. A robust controller which consists of a nominal controller and a robust compensator is applied to achieve formation control. The nominal controller based on the output feedback is designed to achieve desired time-varying formation properties for the nominal system. And the robust compensator based on the robust signal compensator technology is constructed to restrain nonlinear uncertainties. The time-varying formation problem is transformed into the stability problem. And the formation errors can be arbitrarily small with expected convergence rate. Numerical examples are provided to illustrate the effectiveness of the proposed strategy.

scholarly journals Optimal New Sliding Mode Controller Combined with Modified Supertwisting Algorithm for a Perturbed Quadrotor UAV

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yassine El Houm ◽  
Ahmed Abbou ◽  
Moussa Labbadi ◽  
Mohamed Cherkaoui
Keyword(s):  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Variables ◽  
Quadrotor Uav ◽  
The Stability ◽  
Quadrotor System

This paper deals with the design of a novel modified supertwisting fast nonlinear sliding mode controller (MSTFNSMC) to stabilize a quadrotor system under time-varying disturbances. The suggested control strategy is based on a modified supertwisting controller with a fast nonlinear sliding surface to improve the tracking performance. The paper suggests a simple optimization tool built-in MATLAB/Simulink to tune the proposed controller parameters. Fast convergence of state variables is established by using a nonlinear sliding surface for rotational and translational subsystems. The modified supertwisting controller is developed to suppress the effect of chattering, reject disturbances, and ensure robustness against external disturbance effect. The stability of the proposed controller (MSTFNSMC) is proved using the Lyapunov theory. The performance of the proposed MSTFNSMC approach is compared with the supertwisting sliding mode controller (STSMC) by numerical simulations to verify its effectiveness.

Time-varying output formation control for high-order linear time-invariant swarm systems

2015 ◽  
Vol 298 ◽  
pp. 36-52 ◽  
Author(s):  
Xiwang Dong ◽  
Zongying Shi ◽  
Geng Lu ◽  
Yisheng Zhong
Keyword(s):  
Formation Control ◽  
Linear Time ◽  
High Order ◽  
Time Varying ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Invariant

The determinants of parental childrearing behavior trajectories: The effects of parental and child time-varying and time-invariant predictors

2012 ◽  
Vol 36 (3) ◽  
pp. 186-196 ◽  
Author(s):  
Isabelle Roskam ◽  
Jean Christophe Meunier
Keyword(s):  
Self Efficacy ◽  
Externalizing Behavior ◽  
Efficacy Beliefs ◽  
Time Varying ◽  
Child Externalizing Behavior ◽  
Parental Educational Level ◽  
The Stability ◽  
Evidence Based Programs ◽  
Time Invariant ◽  
The Way

“Why do parents parent the way they do?” remains an important question since it concerns both scientific issues, such as the stability or change of childrearing behavior, and clinical issues, such as the way to promote positive parenting in evidence-based programs. Using an accelerated design, the aim of this study was to examine several parental and child predictors of childrearing behavior trajectories among 373 mothers and 356 fathers of 2- to 9-year-old children. Hypotheses were drawn from Belsky (1984) and subsequent studies of the determinants of parenting. The parental and child predictors were assessed and analyzed as time-varying (parental self-efficacy beliefs and child externalizing behavior) or time-invariant (parental educational level and personality traits) predictors, according to their conceptual properties. The results show a linear decrease in both supportive and controlling childrearing behavior in mothers and an improvement in supportive but a decrease in controlling childrearing behavior in fathers over time. Moreover, the results support the idea that childrearing behavior is determined by multiple factors, in particular the parents’ self-efficacy beliefs and the child’s behavior. Finally, the results confirm the hypothesis of a greater influence of child predictors than of parental ones in the case of mothers, while the reverse hypothesis of a greater predictive power of parental variables than of child ones is confirmed for fathers. The results are discussed both for research and clinical purposes.

Lyapunov-Based Formation Control of Underwater Robots

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 1105-1122 ◽  
Author(s):  
Ali Keymasi Khalaji ◽  
Rasoul Zahedifar
Keyword(s):  
Feedback Linearization ◽  
Formation Control ◽  
Control Algorithm ◽  
Kinematic Model ◽  
Lyapunov Theory ◽  
Control Law ◽  
Underwater Robots ◽  
Oceanographic Research ◽  
Inspection And Maintenance ◽  
Reliability And Robustness

SUMMARYToday, automatic diving robots are used for research, inspection, and maintenance, extensively. Control of autonomous underwater robots (AUVs) is challenging due to their nonlinear dynamics, uncertain models, and the system underactuation. Data collection using underwater robots is increasing within the oceanographic research community. Also, the ability to navigate and cooperate in a group of robots has many advantages compared with individual navigations. Among them, the effectiveness of using resources, the possibility of robots’ collaboration, increasing reliability, and robustness to defects can be pointed out. In this paper, the formation control of underwater robots has been studied. First, the kinematic model of the AUV is presented. Next, a novel Lyapunov-based tracking control algorithm is investigated for the leader robot. Subsequently, a control law is designed using Lyapunov theory and feedback linearization techniques to navigate a group of follower robots in a desired formation associated with the leader and follow it simultaneously. In the obtained results for different reference paths and various formations, the effectiveness of the proposed algorithm is represented.

Active Control of Linear Time-Varying Structures by Confinement of Vibrations

2005 ◽  
Vol 11 (1) ◽  
pp. 89-102 ◽  
Author(s):  
S. Choura ◽  
A. S. Yigit
Keyword(s):  
Control Strategy ◽  
Linear Time ◽  
Steady States ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Slowing Down ◽  
Rapid Removal ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

We propose a control strategy for the simultaneous suppression and confinement of vibrations in linear time-varying structures. The proposed controller has time-varying gains and can also be used for linear time-invariant systems. The key idea is to alter the original modes by appropriate feedback forces to allow parts of the structure reach their steady states at faster rates. It is demonstrated that the convergence of these parts to zero is improved at the expense of slowing down the settling of the remaining parts to their steady states. The proposed control strategy can be applied for the rapid removal of vibration energy in sensitive parts of a flexible structure for safety or performance reasons. The stability of the closed-loop system is proven through a Lyapunov approach. An illustrative example of a five-link manipulator with a periodic follower force is given to demonstrate the effectiveness of the method for time-varying as well as time-invariant systems.

scholarly journals A Dynamics Controller Design Method for Car-like Mobile Robot Formation Control

2018 ◽  
Vol 160 ◽  
pp. 06003
Author(s):  
Baofang Wang ◽  
Chen Qian ◽  
Qingwei Chen
Keyword(s):  
Mobile Robots ◽  
Formation Control ◽  
Controller Design ◽  
Sliding Mode ◽  
Design Method ◽  
Lyapunov Theory ◽  
State Equations ◽  
Characteristic Model ◽  
The Stability ◽  
Error State

A dynamics controller design method based on characteristic model is proposed for the formation control problem of car-like mobile robots. Only kinematics controller is not enough for some cases such as the environment is rugged, and the dynamics parameters of the robot are time-varying. Simulation results show that the proposed method can improve the responding speed of the mobile robots and maintain high formation accuracy. First, we obtain the kinematic error state equations according to the leader-follower method. A kinematics controller is designed and the stability is proved by Lyapunov theory. Then the characteristic model of the dynamics inner loop is established. A sliding mode controller is designed based on the second order discrete model, and the stability of the closed-loop system is analyzed. Finally, simulations are designed in MATLAB and Microsoft Robotics Developer Studio 4 (MRDS) to verify the effectiveness of the proposed method.

Analytical Stability Prediction and Design of Variable Pitch Cutters

1999 ◽  
Vol 121 (2) ◽  
pp. 173-178 ◽  
Author(s):  
Y. Altıntas¸ ◽  
S. Engin ◽  
E. Budak
Keyword(s):  
Time Delay ◽  
Depth Of Cut ◽  
Analytical Prediction ◽  
Time Varying ◽  
Chatter Stability ◽  
Variable Pitch ◽  
Analytical Stability ◽  
The Stability ◽  
Time Invariant ◽  
Regenerative Phase

An analytical prediction of stability lobes for milling cutters with variable pitch angles is presented. The method requires cutting constants, number of teeth, and transfer function of cutter mounted on the machine tool as inputs to a chatter stability expression. The stability is formulated by transforming time varying directional cutting constants into time invariant constants. Constant regenerative time delay in uniform cutters is transformed into nonuniform multiple regenerative time delay for variable pitch cutters. The chatter free axial depth of cut is solved from the eigenvalues of stability expression, whereas the spindle speed is identified from regenerative phase delays. The proposed technique has been verified with extensive cutting tests and time domain simulations. The practical use of the analytical solution is demonstrated by an optimal tooth spacing design application which increases the chatter free depth of cuts significantly.

scholarly journals Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Impulsive Controls ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

On Robust Stability and Performance With Time-Varying Control

1995 ◽  
Vol 117 (4) ◽  
pp. 635-637 ◽  
Author(s):  
Mohammed Dahleh
Keyword(s):  
Performance Improvement ◽  
Robust Stabilization ◽  
Point Of View ◽  
Time Varying ◽  
Discrete Time Systems ◽  
And Performance ◽  
The Stability ◽  
Bounded Perturbations ◽  
Time Invariant ◽  
Time Systems

The analysis of time-varying control for robust stabilization and performance improvement is considered. This problem has been investigated in recent years from the point of view of assessing the capabilities of time-varying control to stabilize plants with structured norm bounded perturbations. In this paper, it is shown that time-varying compensation provides no improvement over time-invariant compensation for the stability and performance robustness of discrete-time systems with structured, causal, time-varying, and norm-bounded perturbations, where the norm on the perturbations is the l2-induced norm. The results of this paper help in completing the picture for the case of time-varying perturbations.

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