Designing Efficient Trajectories for Underwater Vehicles Using Geometric Control Theory

2005 ◽  
Author(s):  
M. Chyba ◽  
T. Haberkorn
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Underwater Vehicles ◽  
Lagrangian Mechanics ◽  
The Maximum Principle ◽  
Marine Vehicles ◽  
Time Problem ◽  
Time Optimal ◽  
6 Degrees Of Freedom ◽  
Minimum Time Problem

In this paper, we consider the minimum time problem for underwater vehicles. Using Lagrangian mechanics, we write the equations of motion for marine vehicles with 6 degrees of freedom as a controlled mechanical system. We then apply the necessary conditions from the maximum principle for a trajectory to be time optimal. Using techniques from differential geometry we analyze the resuls. Finally we supplement the theoretical study with numerical simulations.

Autonomous Underwater Vehicle Control in Presence of Waves

2008 ◽  
Author(s):  
L. Moreira ◽  
C. Guedes Soares
Keyword(s):  
Degrees Of Freedom ◽  
Autonomous Underwater Vehicle ◽  
Equations Of Motion ◽  
Wave Force ◽  
Underwater Vehicle ◽  
Principle Of Superposition ◽  
Wave Disturbances ◽  
Underwater Vehicle Control ◽  
Different Depths ◽  
6 Degrees Of Freedom

In this paper, the 6 degrees of freedom equations of motion of an autonomous underwater vehicle (AUV) are described as a linear model and divided into three non-interacting (or lightly interacting) subsystems for speed control, steering and diving. In addition to the model of the AUV dynamics, the first and the second order wave force disturbances, i.e. the Froude-Kriloff and diffraction forces are introduced. Based on the principle of superposition it is possible to represent the AUV dynamics as the sum of low and high frequency motions. An algorithm of non-linear regression for the rationalization of the sub-surface sea spectrum is provided. Two different control designs, based on H2 and H∞ methodologies, were applied to the diving and course control of the vehicle considering the presence of the wave disturbances. The work is based on the slender form of the Naval Postgraduate School AUV, considering that the subsystems can be controlled by means of two single-screw propellers, a rudder, port and starboard bow planes and a stern plane. The wave effect on the corresponding motions of the underwater vehicle is analyzed and evaluated considering the AUV operating at different depths and different sea states using both controllers. The model presented here can be a useful simulation tool to predict the underwater vehicles behavior in different mission scenarios.

SYMBOLIC EQUATIONS FOR A FULL-CAR MODEL

2000 ◽  
Vol 24 (3-4) ◽  
pp. 493-514
Author(s):  
Natalie Baddour ◽  
K. A. Morris
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
Active Suspension ◽  
Lagrangian Mechanics ◽  
Full Generality ◽  
Active Suspensions ◽  
Car Model ◽  
Simplifying Assumptions ◽  
Improved Performance

Active suspensions provide improved performance over conventional, passive suspensions. In this paper, modelling issues for an active suspension are considered. Symbolic equations for a full car model are derived using Lagrangian mechanics. The model has ten degrees of freedom instead of the usual seven. Furthermore, many of the usual simplifying assumptions are not made a priori so that the model retains its full generality. The model is developed so that modifications to any of the assumptions might easily be made and so that the equations of motion can be easily altered to satisfy more restrictive assumptions.

scholarly journals Minimum time optimal control simulation of a GP2 race car

2017 ◽  
Vol 232 (9) ◽  
pp. 1180-1195 ◽  
Author(s):  
Nicola Dal Bianco ◽  
Roberto Lot ◽  
Marco Gadola
Keyword(s):  
Optimal Control ◽  
Degrees Of Freedom ◽  
Load Transfer ◽  
Control Method ◽  
Multibody Model ◽  
Race Car ◽  
Optimal Control Method ◽  
Time Problem ◽  
Time Optimal ◽  
The Impact

In this work, optimal control theory is applied to minimum lap time simulation of a GP2 car, using a multibody car model with enhanced load transfer dynamics. The mathematical multibody model is formulated with use of the symbolic algebra software MBSymba and it comprises 14 degrees of freedom, including full chassis motion, suspension travels and wheel spins. The kinematics of the suspension is exhaustively analysed and the impact of tyre longitudinal and lateral forces in determining vehicle trim is demonstrated. An indirect optimal control method is then used to solve the minimum lap time problem. Simulation outcomes are compared with experimental data acquired during a qualifying lap at Montmeló circuit (Barcelona) in the 2012 GP2 season. Results demonstrate the reliability of the model, suggesting it can be used to optimise car settings (such as gearing and aerodynamic setup) before executing track tests.

Multibody Dynamics of a Floating Wind Turbine Considering the Flexibility Between Nacelle and Tower

2018 ◽  
Vol 18 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Vahid Jahangiri ◽  
Mir Mohammad Ettefagh
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
System Response ◽  
Floating Wind Turbine ◽  
Conservation Of Momentum ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
6 Degrees Of Freedom

Stability and dynamic modeling of the floating wind turbine (FWT) is a crucial challenge in designing of the type of structures. In this paper, the tension leg platform (TLP) type FWT is modeled as a multibody system considering the flexibility between the nacelle and tower. The flexibility of the FWT is modeled as a torsional spring and damper. It has 6 degrees of freedom (DOFs) related to the large-amplitude translation and rotation of the tower and 4 DOFs related to the relative rotation between the rotor-nacelle assembly and the tower. First, the nonlinear equations of motion are derived by the theory of momentum cloud based on the conservation of momentum. Then, the equations of motion are solved and the system is simulated in MATLAB. Moreover, the effect of flexibility between the nacelle and tower is investigated via the dynamic response. The stability of the system in three different environmental conditions is studied. Finally, the spring and damping coefficients for the system response to get near to instability are determined, by which the critical region is defined. The simulation results demonstrate the importance of the flexibility between the nacelle and tower on the overall behavior of the system and its stability.

scholarly journals Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

2014 ◽  
Vol 1 (2) ◽  
pp. 77 ◽  
Author(s):  
Mohamed A Omar
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Dynamic Equations ◽  
Solution Stability ◽  
Simulation Code ◽  
Tracked Vehicles ◽  
Main System ◽  
6 Degrees Of Freedom

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system.  The proposed self-contained modular approach could be interfaced to any exiting multibody simulation code without need to alter the existing solver architecture.  Each track is modeled as a super-component that can be treated separate from the main system.  The super-component can be efficiently used in parallel processing environment to reduce the simulation time.  In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF).  To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection.  The spatial algebra operator is used to express the motion quantities and develop the link’s nonlinear kinematic and dynamic equations of motion.  The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules.  Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties.  The interaction forces are expressed in the Cartesian system, applied to the link’s equation of motion and the corresponding bodies in the main system.  For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach.

A New Method for Modeling of Fully Flexible Aircrafts

2011 ◽  
Vol 383-390 ◽  
pp. 2350-2355
Author(s):  
Dong Guo ◽  
Min Xu ◽  
Shi Lu Chen ◽  
Yu Qian
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Equations Of Motion ◽  
Flight Mechanics ◽  
Lagrangian Mechanics ◽  
Seamless Integration ◽  
Different Types ◽  
New Formulation ◽  
Nonlinear Rigid

The purpose of this study is to produce a modeling capability for integrated flight dynamics of flexible aircraft that can better predict some of the complex behaviors in flight due to multi-physics coupling. Based on the studying of the exiting modeling approaches, the author put forward a new modeling method, and developed a new formulation integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics for fully elastic aircrafts using Lagrangian mechanics. The new equations of motion overcome the disadvantages of the exiting methods, and include automatically all six rigid-body degrees of freedom and elastic information, the seamless integration is achieved by using the same reference frame and the same variables to describe the aircraft motions and the forces acting on it, including the aerodynamic forces. The formulation is modular in nature, in the sense that the structural model, the aerodynamic theory, and the controls method can be replaced by any other ones to better suit different types of aircraft.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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