An Observer for Rigid Body Motion With Almost Global Finite-Time Convergence

An observer that obtains estimates of the translational and rotational motion states for a rigid body under the influence of known forces and moments is presented. This nonlinear observer exhibits almost global convergence of state estimates in finite time, based on state measurements of the rigid body’s pose and velocities. It assumes a known dynamics model with known resultant force and resultant torque acting on the body, which may include feedback control force and control torque. The observer design based on this model uses the exponential coordinates to describe rigid body pose estimation errors on SE(3), which provides an almost global description of the pose estimate error. Finite-time convergence of state estimates and the observer are shown using a Lyapunov analysis on the nonlinear state space of motion. Numerical simulation results confirm these analytically obtained convergence properties for the case that there is no measurement noise and no uncertainty (noise) in the dynamics. The robustness of this observer to measurement noise in body velocities and additive noise in the force and torque components is also shown through numerical simulation results.

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Tail shapes lead to different propulsive mechanisms in the body/caudal fin undulation of fish

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220967687 ◽

2020 ◽

pp. 095440622096768

Author(s):

Jialei Song ◽

Yong Zhong ◽

Ruxu Du ◽

Ling Yin ◽

Yang Ding

Keyword(s):

Numerical Simulation ◽

Aspect Ratio ◽

High Efficiency ◽

The Body ◽

Caudal Fin ◽

Fish Model ◽

Swimming Efficiency ◽

Simulation Results ◽

Propulsive Mechanism ◽

High Depth

In this paper, we investigate the hydrodynamics of swimmers with three caudal fins: a round one corresponding to snakehead fish ( Channidae), an indented one corresponding to saithe ( Pollachius virens), and a lunate one corresponding to tuna ( Thunnus thynnus). A direct numerical simulation (DNS) approach with a self-propelled fish model was adopted. The simulation results show that the caudal fin transitions from a pushing/suction combined propulsive mechanism to a suction-dominated propulsive mechanism with increasing aspect ratio ( AR). Interestingly, different from a previous finding that suction-based propulsion leads to high efficiency in animal swimming, this study shows that the utilization of suction-based propulsion by a high- AR caudal fin reduces swimming efficiency. Therefore, the suction-based propulsive mechanism does not necessarily lead to high efficiency, while other factors might play a role. Further analysis shows that the large lateral momentum transferred to the flow due to the high depth of the high- AR caudal fin leads to the lowest efficiency despite the most significant suction.

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The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0286 ◽

1995 ◽

Author(s):

X. Tong ◽

B. Tabarrok

Keyword(s):

Rigid Body ◽

Equations Of Motion ◽

Melnikov Method ◽

The Body ◽

Body Motion ◽

Heteroclinic Orbits ◽

Coordinate Frame ◽

Global Motion ◽

Stable And Unstable Manifolds ◽

Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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A New Method to Concentrate Electromagnetic Field Within ROI Using a High Dielectric Material in 3T Body MRI

ASME 2013 Conference on Frontiers in Medical Devices: Applications of Computer Modeling and Simulation ◽

10.1115/fmd2013-16135 ◽

2013 ◽

Cited By ~ 1

Author(s):

Bu S. Park ◽

Sunder S. Rajan ◽

Leonardo M. Angelone

Keyword(s):

Numerical Simulation ◽

Electromagnetic Field ◽

Human Body ◽

Region Of Interest ◽

Dielectric Materials ◽

The Body ◽

Human Body Model ◽

Body Model ◽

Simulation Results ◽

High Dielectric

We present numerical simulation results showing that high dielectric materials (HDMs) when placed between the human body model and the body coil significantly alter the electromagnetic field inside the body. The numerical simulation results show that the electromagnetic field (E, B, and SAR) within a region of interest (ROI) is concentrated (increased). In addition, the average electromagnetic fields decreased significantly outside the region of interest. The calculation results using a human body model and HDM of Barium Strontium Titanate (BST) show that the mean local SAR was decreased by about 56% (i.e., 18.7 vs. 8.2 W/kg) within the body model.

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4WID: A New Concept in Electrical Vehicles

10.1115/imece2001/de-23241 ◽

2001 ◽

Author(s):

E. Esmailzadeh ◽

A. Goodarzi ◽

G. R. Vossoughi

Keyword(s):

Motor Control ◽

The Body ◽

Body Motion ◽

Full Description ◽

Vehicle Dynamic ◽

Control Laws ◽

Vehicle Performance ◽

Electrical Vehicles ◽

Different Types ◽

Simulation Results

Abstract A comprehensive new dynamic model of a four-wheel independent drive electric vehicle has been developed and different types of the motor control laws were addressed. The first part of this study deals with the full description of the model scope in which the structure of the model including the sub-models has been fully developed. Subsequently, the sub-models including the tire sub-model, the body motion, and the motor dynamics were investigated, and the computer model of the vehicle has been simulated. Finally, the proposed motor control laws and the vehicle dynamic behavior of the vehicle were presented. Detailed analyses of the vehicle performance and comparison of the simulation results were also carried out.

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Estimation of the Order and Parameters of a Fractional Order Model From a Noisy Step Response Data1

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4026345 ◽

2014 ◽

Vol 136 (3) ◽

Cited By ~ 11

Author(s):

Mahsan Tavakoli-Kakhki ◽

Mohammad Saleh Tavazoei

Keyword(s):

Numerical Simulation ◽

Fractional Order ◽

Closed Loop ◽

Open Loop ◽

Measurement Noise ◽

Step Response ◽

Order Model ◽

Response Data ◽

Fractional Order Model ◽

Simulation Results

This paper deals with integral based methods to estimate the order and parameters of simple fractional order models from the extracted noisy step response data of a process. This data can be obtained from both open-loop and closed-loop tests. Numerical simulation results are presented to verify the robustness of these proposed methods in the presence of the measurement noise.

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Angular Velocity Stabilization of a Rigid Body Via VSS Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1316787 ◽

2000 ◽

Vol 122 (4) ◽

pp. 669-673 ◽

Cited By ~ 7

Author(s):

T. Floquet ◽

W. Perruquetti ◽

J.-P. Barbot

Keyword(s):

Angular Velocity ◽

Rigid Body ◽

Finite Time ◽

Sliding Mode ◽

Variable Structure ◽

External Disturbances ◽

First Order ◽

Finite Time Convergence ◽

Sliding Mode Controllers ◽

Second Order Sliding Mode

This paper is devoted to the stabilization of the angular velocity of a rigid body via variable structure based controllers. The system is supposed to have only two control torques and to be subject to external disturbances. A finite time convergence is obtained by switching between a first-order and a second-order sliding mode controllers. [S0022-0434(00)00304-X]

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A Velocity Metric for Rigid-Body Planar Motion

Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2010-28331 ◽

2010 ◽

Author(s):

Joseph M. Schimmels ◽

Luis E. Criales

Keyword(s):

Rigid Body ◽

Average Distance ◽

The Body ◽

Body Motion ◽

Length Scale ◽

Translational Velocity ◽

Body Velocity ◽

Assembly Problem ◽

Instantaneous Center ◽

Selection Of

A planar rigid-body velocity metric based on the instantaneous velocity of all particles that constitute a rigid body is developed. A measure based on the discrepancy in the translational velocity at each particle for two different planar twists is introduced. The calculation of the measure is simplified to the calculation of the product of: 1) the discrepancy in angular velocity, and 2) the average distance of the body from the instantaneous center associated with the twist discrepancy. It is shown that this measure satisfies the mathematical requirements of a metric and is physically consistent. It does not depend on either the selection of length scale or the frames used to describe the body motion. Although the metric does depend on body geometry, it can be calculated efficiently using body decomposition. An example demonstrating the application of the metric to an assembly problem is presented.

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An Efficient Modelling of Flexible Airships

Volume 3: Dynamic Systems and Controls, Symposium on Design and Analysis of Advanced Structures, and Tribology ◽

10.1115/esda2006-95741 ◽

2006 ◽

Cited By ~ 3

Author(s):

Selima Bennaceur ◽

Naoufel Azouz ◽

Djaber Boukraa

Keyword(s):

Rigid Body ◽

Equations Of Motion ◽

General System ◽

Rigid Body Motion ◽

The Body ◽

Body Motion ◽

Modal Synthesis ◽

Stiffness Matrices ◽

Updated Lagrangian ◽

Convenient Technique

This paper presents an efficient modelling of airships with small deformations moving in an ideal fluid. The formalism is based on the Updated Lagrangian Method (U.L.M.). This formalism proposes to take into account the coupling between the rigid body motion and the deformation as well as the interaction with the surrounding fluid. The resolution of the equations of motion is incremental. The behaviour of the airship is defined relatively to a virtual non-deformed reference configuration moving with the body. The flexibility is represented by a deformation modes issued from a Finite Elements Method analysis. The increment of rigid body motion is represented similarly by rigid modes. A modal synthesis is used to solve the general system equations of motion. Time constant matrices appears (i.e. mass and structural stiffness matrices), and we show a convenient technique to actualise the time dependant matrices.

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