Modeling and Adaptive Control for Tracking Wing Trajectories

2013 ◽  
Author(s):  
Ian P. Murphy ◽  
Shirin Dadashi ◽  
Jessica Gregory ◽  
Yu Lei ◽  
Javid Bayandor ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Micro Air Vehicles ◽  
Adaptive Controller ◽  
Flapping Wing ◽  
Lyapunov Analysis ◽  
Unknown Parameters ◽  
Open Problems ◽  
Nonlinear Equations Of Motion

Studies of Micro Air Vehicles (MAVs) have gained increased attention over the past decade, while a significant range of open problems in this emerging field remain unaddressed. This paper highlights the investigations entailing flapping wing vehicles, designed based on inspiration from observations of avian flight. The nonlinear equations of motion of a ground fixed flapping wing robot are derived that incorporates a quasi-steady model of aerodynamics. The equations of motion are developed using Lagrange’s equations and the aerodynamic contributions are formulated using virtual work principles. The aerodynamics are constructed with a quasi-steady state formulation where the functions representing lift and drag coefficients as a function of angle of attack are treated as unknowns. An adaptive controller is introduced that seeks to learn the aerodynamic effects. A Lyapunov analysis of the controller guarantees boundedness of all error terms and asymptotic stability in both the joint position and derivative error. The controllers are simulated using two dynamic models based on flapping wing prototypes designed at Virginia Tech. The numerical experiments validate the Lyapunov analysis and verify that unknown parameters are learned if persistently excited.

Combined Trajectory Planning and Parameter Identification of a Two-Link Rigid Manipulator

1998 ◽  
Author(s):  
Reza Fotouhi-C. ◽  
Peter N. Nikiforuk ◽  
Walerian Szyszkowski
Keyword(s):  
Path Planning ◽  
Trajectory Planning ◽  
Equations Of Motion ◽  
Adaptive Controller ◽  
Time Variable ◽  
Physical Parameters ◽  
Planning Problem ◽  
Unknown Parameters ◽  
On Line ◽  
Line Path

Abstract A combined trajectory planning problem and adaptive control problem for a two-link rigid manipulator is presented in this paper. The problem is divided into two parts: path planning for off-line processing, followed by on-line path tracking using an adaptive controller. The path planning is done at the joint level. The motion of the robot is specified by a sequence of knots (positions of the robot’s tip) in space Cartesian coordinates. These knots are then transformed into two sets of joint displacements, and piecewise cubic polynomials are used to fit these two sequences of joint displacements. The cubic spline function is used to construct a trajectory with the velocity and the acceleration as constraints. Linear scaling of the time variable is used to accommodate the velocity and acceleration constraints. A nonlinear scaling of the time variable is performed to fit the velocity to a pre-specified velocity profile. The adaptive scheme used takes full advantage of the known parameters of the manipulator while estimating the unknown parameters. In deriving the dynamic equations of motion, all of the physical parameters of the manipulator, including the distributed masses of the links, are taken into account. Some simulation results for the manipulator with unknown payload masses following a planned trajectory are presented.

Inverse Dynamics of a 3-P[2(US)] Translational Parallel Robot

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 708-728 ◽  
Author(s):  
Mahmood Mazare ◽  
Mostafa Taghizadeh ◽  
M. Rasool Najafi
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Parallel Robot ◽  
Qualitative Behavior ◽  
Work Model ◽  
Forward Kinematic ◽  
Good Agreement

SummaryIn this paper, a type of parallel robot with three translational degrees of freedom is studied. Inverse and forward kinematic equations are extracted for position and velocity analyses. The dynamic model is derived by Lagrange’s approach and the principle of virtual work and related computational algorithms implementing inverse and forward dynamics are presented. Furthermore, some numerical simulations are performed using the kinematic and dynamic models in which the results show good agreement with expected qualitative behavior of the mechanism. Comparisons with the results of work-energy and impulse-momentum methods quantitatively verify the validity of the derived equations of motion. Also, a relative computational effectiveness is observed in implementation of virtual work model via the simulations.

Dynamics of Beams Using a Geometrically Exact Elastic Rod Approach

2006 ◽  
Author(s):  
Fredy Coral Alamo ◽  
Hans Ingo Weber
Keyword(s):  
Virtual Work ◽  
Fundamental Problem ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Dynamic Responses ◽  
Elastic Rod ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Slender Beams ◽  
Nonlinear Equations Of Motion

The dynamics of a long slender beam, intrinsically straight, is addressed systematically for 3-D problems using the Cosserat rod theory. The model developed allows for bending, extension/compression and torsion, thus enabling the study of the dynamics of various types of elastic deformations. In this work a linear constitutive relation is used, also, the Bernoulli hypothesis is considered and the shear deformations are neglected. The fundamental problem when using any finite element (FE) formulation is the choice of the displacement functions. When using Cosserat rod theory this problem is handled using approximate solutions of the nonlinear equations of motion (in quasi-static sense). These nonlinear displacement functions are functions of generic nodal displacements and rotations. Based on the Lagrangian approach formed by the kinetic and strain energy expressions, the principle of virtual work is used to derive the nonlinear ordinary differential equations of motion that are solved numerically. As an application, a curved rod, formed by many straight elements is investigated numerically. When using the Cosserat rod approach, that take into account all the geometric nonlinearities in the rod, the higher accuracy of the dynamic responses is achieved by dividing the system into a few elements which is much less than the traditional FE methods, this is the main advantage when using this approach. Overall, the Cosserat model provides an accurate way of modelling long slender beams and simulation times are greatly reduced through this approach.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

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