Limit Cycle Behavior and Model Reduction of an Oscillating Fish-Like Robot

The design and control of underwater robots has to contend with the coupled robot-hydrodynamic interactions. A key aspect of this coupled dynamics is the interaction of the robot with the fluid via the vorticity that is created by the robot’s motion. In this paper we develop a simplified and very low dimensional model of this interaction. This is done recognizing that the vortex shedding is a nonholonomic constraint. We apply the harmonic balance approach to analyze and compare the limit cycle in the dynamics of the fish-shaped body propelled by a periodic input with that of a Chaplygin sleigh, a well known nonholonomic system. The dynamics on the limit cycles lead to a very low dimensional model of the swimming of the fish-shaped body that could be very useful from the perspective of controlling a swimming robot.

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Limit Cycle Analysis and Control of the Dissipative Chaplygin Sleigh

Volume 2: Mechatronics; Estimation and Identification; Uncertain Systems and Robustness; Path Planning and Motion Control; Tracking Control Systems; Multi-Agent and Networked Systems; Manufacturing; Intelligent Transportation and Vehicles; Sensors and Actuators; Diagnostics and Detection; Unmanned, Ground and Surface Robotics; Motion and Vibration Control Applications ◽

10.1115/dscc2017-5193 ◽

2017 ◽

Cited By ~ 3

Author(s):

Vitaliy Fedonyuk ◽

Phanindra Tallapragada ◽

Yongqiang Wang

Keyword(s):

Limit Cycle ◽

Limit Cycles ◽

Horizontal Plane ◽

Translational Velocity ◽

Periodic Forcing ◽

Fluid System ◽

Chaplygin Sleigh ◽

Analysis Techniques ◽

And Control ◽

Gaining Insight

There are many types of systems in both nature and technology that exhibit limit cycles under periodic forcing. Sometimes, especially in swimming robots, such forcing is used to propel a body forward in a plane. Due to the complexity in studying a fluid system it is often useful to investigate the dynamics of an analogous land model. Such analysis can then be useful in gaining insight about and controlling the original fluid system. In this paper we investigate the behavior of the Chaplygin sleigh under the effect of viscous dissipation and sinusoidal forcing. This is shown to behave in a similar manner as certain robotic fish models. We then apply limit cycle analysis techniques to predict the behavior and control the net translational velocity of the sleigh in a horizontal plane.

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Asymptotic behavior of a low-dimensional model for magnetostriction for periodic input

Physica B Condensed Matter ◽

10.1016/j.physb.2007.08.023 ◽

2008 ◽

Vol 403 (2-3) ◽

pp. 257-260 ◽

Cited By ~ 1

Author(s):

D.B. Ekanayake ◽

R.V. Iyer

Keyword(s):

Asymptotic Behavior ◽

Dimensional Model ◽

Periodic Input ◽

Low Dimensional

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Reduced Order Modelling in Nonlinear Mechanical Oscillators With Energy Pumping

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-85214 ◽

2005 ◽

Author(s):

Xianghong Ma ◽

Alexander F. Vakakis ◽

Lawrence A. Bergman

Keyword(s):

Dimensional Model ◽

Reduced Order ◽

Energy Pumping ◽

Weakly Coupled ◽

Nonlinear Mechanical ◽

Dimensional Models ◽

Mechanical Oscillators ◽

Low Dimensional ◽

Nonlinear Components ◽

And Control

Energy pumping in nonlinear mechanical oscillators has been discovered and studied in mechanical systems consisting of weakly coupled, linear and nonlinear components [1–3]. In this paper this phenomenon is further studied and numerically verified on an 11 degree of freedom system. It also presents a technique to create low dimensional models for energy pumping systems using the Karhunen-Loeve (K-L) decomposition method. It is shown that energy pumping can be identified from the dominant K-L modes. The low dimensional models are used to reconstruct the system responses. From the comparisons between the reconstructed and simulated response, we can see that the K-L mode-based low-dimensional model can represent the system responses; it can be used for monitoring, diagnosis and control purposes.

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A low-dimensional model for simulating three-dimensional cylinder flow

Journal of Fluid Mechanics ◽

10.1017/s0022112002007991 ◽

2002 ◽

Vol 458 ◽

pp. 181-190 ◽

Cited By ~ 194

Author(s):

XIA MA ◽

GEORGE EM KARNIADAKIS

Keyword(s):

Limit Cycle ◽

Three Dimensional ◽

Orthogonal Decomposition ◽

Direct Numerical Simulations ◽

Two Dimensional ◽

Dimensional Model ◽

The Stability ◽

Low Dimensional ◽

Cylinder Flow ◽

Proper Orthogonal

We investigate the stability and dynamics of three-dimensional limit-cycle states in flow past a circular cylinder using low-dimensional modelling. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition. We show that the limit cycle is reproduced very accurately with only twenty three-dimensional modes. The addition of two-dimensional modes to the Karhunen–Loeve expansion basis improves the ability of the model to capture the three-dimensional bifurcation, including the discontinuity in the Strouhal number discovered experimentally.

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A low-dimensional model for the hexagon-to-roll transition in evaporating liquid with a shear flow

Proceedings of the Sixth International Symposium On Turbulence, Heat and Mass Transfer ◽

10.1615/ichmt.2009.turbulheatmasstransf.890 ◽

2009 ◽

Cited By ~ 1

Author(s):

V. Reutov ◽

G. Rybushkina ◽

A. Pavlychev

Keyword(s):

Shear Flow ◽

Dimensional Model ◽

Low Dimensional

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Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators

Nonlinear Dynamics ◽

10.1007/s11071-021-06703-w ◽

2021 ◽

Author(s):

Yuzuru Kato ◽

Anatoly Zlotnik ◽

Jr-Shin Li ◽

Hiroya Nakao

Keyword(s):

Limit Cycle ◽

Periodic Input

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Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.137.72 ◽

2011 ◽

Vol 137 ◽

pp. 72-76

Author(s):

Wei Zhang ◽

Xian Wen ◽

Yan Qun Jiang

Keyword(s):

Stability Analysis ◽

Circular Cylinder ◽

Global Stability ◽

Dimensional Model ◽

Global Stability Analysis ◽

The Stability ◽

Low Dimensional ◽

Proper Orthogonal ◽

Calculated Amount ◽

Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

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