scholarly journals Globally stable control of a dynamic bipedal walker using adaptive frequency oscillators

Robotica ◽  
2014 ◽  
Vol 32 (7) ◽  
pp. 1039-1063 ◽  
Author(s):  
Gabriel Aguirre-Ollinger
Keyword(s):  
Control Method ◽  
Initial Conditions ◽  
Recursive Algorithm ◽  
Basin Of Attraction ◽  
Initial Study ◽  
Knee Joints ◽  
Stride Frequency ◽  
Stable Limit ◽  
Inverted Pendulum Model ◽  
Simple Limit

SUMMARYWe present a control method for a simple limit-cycle bipedal walker that uses adaptive frequency oscillators (AFOs) to generate stable gaits. Existence of stable limit cycles is demonstrated with an inverted-pendulum model. This model predicts a proportional relationship between hip torque amplitude and stride frequency. The closed-loop walking control incorporates adaptive Fourier analysis to generate a uniform oscillator phase. Gait solutions (fixed points) are predicted via linearization of the walker model, and employed as initial conditions to generate exact solutions via simulation. Global stability is determined via a recursive algorithm that generates the approximate basin of attraction of a fixed point. We also present an initial study on the implementation of AFO-based control on a bipedal walker with realistic mass distribution and articulated knee joints.

Coexistence of Multiple Attractors, Metastable Chaos and Bursting Oscillations in a Multiscroll Memristive Chaotic Circuit

2017 ◽  
Vol 27 (05) ◽  
pp. 1750067 ◽  
Author(s):  
N. Henry Alombah ◽  
Hilaire Fotsin ◽  
Kengne Romanic
Keyword(s):  
Limit Cycle ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Stable Limit Cycle ◽  
Phase Portraits ◽  
Stable Limit ◽  
Nonlinear Phenomenon ◽  
Chaotic Circuit ◽  
Bursting Oscillations ◽  
Wide Range

In this paper, some complex nonlinear behaviors in a four-dimensional multiscroll autonomous memristor based chaotic system are investigated. This system is derived from the three-dimensional autonomous charge-controlled Muthuswamy–Chua simplest chaotic circuit. The system can generate four different coexisting attractors for a fixed set of parameters and different initial conditions. This phenomenon is relatively rare given that we have four different attractors namely: an equilibrium point, a stable limit cycle, a 16-peak limit cycle and a strange attractor that coexist in the system within a wide range of parameters. The nonlinear phenomenon of transient chaos is studied and revealed numerically in Matlab and Pspice environments. The complex transient dynamics of this memristive system under different initial states shows that the transient time depends strongly on the initial conditions. Moreover, this model displays spiking and bursting oscillations. The bursting behavior is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the fold-Hopf type. These complex dynamical behaviors of this system are investigated by means of numerical simulations and via Pspice circuit simulations. The use of bifurcation diagrams, Lyapunov exponents diagrams, power spectrums, phase portraits, time series, isospike diagram, basin of attraction, clearly shows these complex phenomena.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

scholarly journals Phase-Coupled Oscillations in the Brain: Nonlinear Phenomena in Cellular Signalling

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Vikas Rai ◽  
Sreenivasan Rajamoni Nadar ◽  
Riaz A. Khan
Keyword(s):  
Limit Cycles ◽  
Initial Conditions ◽  
Phase Relationship ◽  
Oscillatory System ◽  
Calcium Currents ◽  
Nonlinear Phenomena ◽  
Inhibitory Interneurons ◽  
Stable Limit ◽  
Principal Cells ◽  
Coupled Oscillations

We report the existence of phase-coupled oscillations in a model neural system. The model consists of a group of excitatory principal cells in interaction with local inhibitory interneurons. The voltages across the membranes of excitatory cells are governed primarily by calcium and potassium ion conductivities. The number of potassium channels open at any given instant changes in accordance with a deterministic law. The time scale of this change is set by a constant which depends on midpoint potentials at which potassium and calcium currents are half-activated. The growth of mean membrane potential of excitatory principal cells is controlled by that of the inhibitory interneurons. Nonlinear oscillatory system associated with these limit cycles starting from two different initial conditions maintain a definite phase relationship. The phase-coupled oscillations in electrical activity of the neuronal cells carry together amplitude, phase, and time information for cellular signaling. This mechanism supports an energy efficient way of information processing in the central nervous system. The information content is encoded as persistent periodic oscillations represented by stable limit cycles in the phase space.

Estimation-Based Control of a Magnetic Endoscope without Device Localization

2018 ◽  
Vol 03 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Janis Edelmann ◽  
Andrew J. Petruska ◽  
Bradley J. Nelson
Keyword(s):  
Field Experiments ◽  
Control Method ◽  
Initial Conditions ◽  
Medical Procedures ◽  
Proof Of Concept ◽  
Wide Range ◽  
Trajectory Length ◽  
Lung Phantom ◽  
Average Control ◽  
Inspection Task

Magnetically controlled catheters and endoscopes can improve minimally invasive procedures as a result of their increased maneuverability when combined with modern magnetic steering systems. However, such systems have two distinct shortcomings: they require continuous information about the location of the instrument inside the human body and they rely on models that accurately capture the device behavior, which are difficult to obtain in realistic settings. To address both of these issues, we propose a control algorithm that continuously estimates a magnetic endoscope’s response to changes in the actuating magnetic field. Experiments in a structured visual environment show that the control method is able to follow image-based trajectories under different initial conditions with an average control error that measures 1.8 % of the trajectory length. The usefulness for medical procedures is demonstrated with a bronchoscopic inspection task. In a proof-of-concept study, a custom 2[Formula: see text]mm diameter miniature camera endoscope is navigated through an anatomically correct lung phantom in a clinician-controlled manner. This represents the first demonstration of the controlled manipulation of a magnetic device without localization, which is critical for a wide range of medical procedures.

scholarly journals Height control for a two-mass hopping robot based on stable limit cycle

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141665774
Author(s):  
Taihui Zhang ◽  
Honglei An ◽  
Qing Wei ◽  
Wenqi Hou ◽  
Hongxu Ma
Keyword(s):  
Limit Cycle ◽  
Control Algorithm ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Inverted Pendulum Model ◽  
Hopping Robot ◽  
Control Objective ◽  
Upper Level ◽  
Mass Spring ◽  
And Control

Differing from the commonly used spring loaded inverted pendulum model, this paper makes use of a two-mass spring model considering impact between the foot and ground which is closer to the real hopping robot. The height of upper mass which includes the upper leg and body is the main control objective. Then we develop a new kind of control algorithm acting on two levels: The upper level aims to achieve the desired velocity of the upper mass based on a stable limit cycle, where three different controllers are used to regulate the limit cycle; the target of the lower level is to drive the system to converge to the desired state and control the contact force between the foot and ground within an appropriate range based on the inner force control at the same time. Simulation results presented in this paper confirm the efficiency of this control algorithm.

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

PARTIAL CONTROL OF TRANSIENT CHAOS IN ELECTRONIC CIRCUITS

2012 ◽  
Vol 22 (02) ◽  
pp. 1250032 ◽  
Author(s):  
ALEXANDRE WAGEMAKERS ◽  
SAMUEL ZAMBRANO ◽  
MIGUEL A. F. SANJUÁN
Keyword(s):  
Analog Circuit ◽  
Control Method ◽  
Initial Conditions ◽  
Simple Extension ◽  
The Novel ◽  
Partial Control ◽  
Time Dynamics ◽  
The One ◽  
Chaotic Transient ◽  
Chaotic Saddle

We present an analog circuit implementation of the novel partial control method, that is able to sustain chaotic transient dynamics. The electronic circuit simulates the dynamics of the one-dimensional slope-three tent map, for which the trajectories diverge to infinity for nearly all the initial conditions after behaving chaotically for a while. This is due to the existence of a nonattractive chaotic set: a chaotic saddle. The partial control allows one to keep the trajectories close to the chaotic saddle, even if the control applied is smaller than the effect of the applied noise, introduced into the system. Furthermore, we also show here that similar results can be implemented on a circuit that simulates a horseshoe-like map, which is a simple extension of the previous one. This encouraging result validates the theory and opens new perspectives for the application of this technique to systems with higher dimensions and continuous time dynamics.

Integrity Analysis of Electrically Actuated Resonators With Delayed Feedback Controller

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Fadi Alsaleem ◽  
Mohammad I. Younis
Keyword(s):  
Microelectromechanical Systems ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Capacitive Sensor ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Positive Gain ◽  
Delayed Feedback Controller ◽  
The Stability ◽  
Integrity Analysis

In this work, we investigate the stability and integrity of parallel-plate microelectromechanical systems resonators using a delayed feedback controller. Two case studies are investigated: a capacitive sensor made of cantilever beams with a proof mass at their tip and a clamped-clamped microbeam. Dover-cliff integrity curves and basin-of-attraction analysis are used for the stability assessment of the frequency response of the resonators for several scenarios of positive and negative gain in the controller. It is found that in the case of a positive gain, a velocity or a displacement feedback controller can be used to effectively enhance the stability of the resonators. This is confirmed by an increase in the area of the basin of attraction of the resonator and in shifting the Dover-cliff curve to higher values. On the other hand, it is shown that a negative gain can significantly weaken the stability and integrity of the resonators. This can be of useful use in MEMS for actuation applications, such as in the case of capacitive switches, to lower the activation voltage of these devices and to ensure their trigger under all initial conditions.

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