scholarly journals Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ayman A. El-Badawy ◽  
Mohamed A. Bakr
Keyword(s):  
Control Problem ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Singular Configurations

Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust) are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.

Effects of Tip Mass and Interaction Force on Nonlinear Behavior of Force Modulation FM-AFM Cantilever

2016 ◽  
Vol 33 (2) ◽  
pp. 257-268 ◽  
Author(s):  
K. E. Torkanpouri ◽  
H. Zohoor ◽  
M. H. Korayem
Keyword(s):  
Frequency Shift ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Interaction Force ◽  
Beam Model ◽  
Frequency Shifts ◽  
Excitation Mode ◽  
Force Modulation ◽  
Tip Mass

AbstractInfluences of the tip mass, excitation mode of Frequency Modulated Atomic Force Microscope (FM-AFM) on the resonance frequency shift in force modulation (FM) mode are studied. Governing equations of motion are determined based on Timoshenko beam model with concentrated end mass. Approach point and base amplitude are set such that the FM-AFM remains just in FM mode. Either the linearized and nonlinear Derjaguin-Muller-Toporov (DMT) model are investigated. Then frequency shifts are determined for various interaction force regimes. It is showed the effect of tip mass on frequency shift is significant even for small tips. Nonlinear model shows lower frequency shifts in comparison with linearized model. It is showed that the amplitude of response is increased by increasing the tip mass and order of base excitation. Deviation of frequency shift between linearized and nonlinear solution are studied. It is declared that the error between linearized and nonlinear model is complicated. A deviation index is used for explaining behavior of error while tip mass and excitation mode are changed. It is showed, this index predicts the trend of error in all excitation modes and force cases. Behavior of system is linearizing by increasing the order of excitation, generally.

Dynamic models for the contact analysis of a tensioned beam with a moving oscillator

2013 ◽  
Vol 228 (4) ◽  
pp. 676-689
Author(s):  
Kyuho Lee ◽  
Jintai Chung
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Frequency Ratio ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Contact Analysis ◽  
Contact Forces ◽  
Accurate Analysis ◽  
Moving Oscillator ◽  
Velocity Decrease

Several dynamic models are proposed for the contact analysis of a tensioned beam with a moving oscillator. Depending on whether the strain and stress used to derive the equations of motion are nonlinear, four models are established to analyze the beam deflections and the contact force between the beam and moving oscillator. We find that the differences in the contact forces and deflections computed with the models become large as the beam tension and moving velocity decrease and the natural frequency ratio of the oscillator to the beam increases. The nonlinear model derived with nonlinear strain and stress is desirable for an accurate analysis.

Two Wheeled Robot Self Balancing Control Research

2016 ◽  
Vol 2 (3) ◽  
pp. 617 ◽  
Author(s):  
Ni Dan ◽  
Jingfang Wang
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Nonlinear Model ◽  
Position Control ◽  
Fixed Position ◽  
Wheeled Robot ◽  
Control Research ◽  
Simulation Results ◽  
Balancing Control

According to movement balancing and position control problem of Self Balancing Two Wheeled Robot, a method based on H∞ Robust Control was proposed. We apply it onto the MIMO nonlinear model of robot, and simulated it in the MATLAB environment The simulation results shows that the robot can be balanced in fixed position well by this method, and also it have the ability to anti interference.

Singularity-Free Joint Actuation in Omnidirectional Mobile Platforms With Powered Offset Caster Wheels

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Denny Oetomo ◽  
Marcelo H. Ang
Keyword(s):  
Equations Of Motion ◽  
Mobile Platform ◽  
Mobile Platforms ◽  
Free Condition ◽  
Singular Configurations ◽  
Workspace Analysis ◽  
Equations Of Motions

This paper presents the analysis of singularity and motion capability of a mobile platform articulated by offset powered caster wheels. Specifically, it presents the analysis of the equations of motion resulting in the sufficient and necessary actuation condition to yield a workspace that is entirely free of singular configurations. This paper shows that powering both the steer and drive joints on two sets of offset caster wheels in a mobile platform guarantees a singularity-free condition throughout the entire workspace. Analysis and discussion on equations of motions that lead to this result are presented.

Nonlinear Polarisationoscillations in a Biophysical Model-System I: Internal Dynamics

1981 ◽  
Vol 36 (9-10) ◽  
pp. 888-892 ◽  
Author(s):  
F. Kaiser ◽  
Z. Szabo
Keyword(s):  
Nonlinear Model ◽  
Biological System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dipole Interaction ◽  
Model Potential ◽  
Model System ◽  
Biophysical Model ◽  
Internal Dynamics ◽  
Dipole State

Abstract To describe a metastable electrical dipole state in a biological system. Fröhlich suggested a nonlinear model potential. In this paper we investigate a system of two such dipoles coupled by a dipole-dipole interaction. M athem atically this model is described by two coupled nonlinear differential equations. In the investigation of the dynamics of the system we distinguish three solution types of the equations of motion.

Transfer Orbit Design and Control Based on Forbes' Assumption

2010 ◽  
Vol 29-32 ◽  
pp. 1211-1216
Author(s):  
Li Li Zheng ◽  
Jian Ping Yuan ◽  
Zhan Xia Zhu
Keyword(s):  
Control Problem ◽  
Design Method ◽  
Equations Of Motion ◽  
Polar Coordinates ◽  
Keplerian Orbit ◽  
Orbit Design ◽  
Orbit Control ◽  
Transfer Orbit ◽  
And Control

In order to meet the requirements of space operation, the spacecrafts must maneuver agilely with the artifical propulsion. The orbit under artificial control is termed as Non-Keplerian orbit which does not follow Kepler’s Laws. The transfer orbit design under the continuous thrust is one of the most important topics in this new field. Shape-based method for Non-Keplerian orbit design is developed in this paper. Firstly, the equations of motion are established in polar coordinates system. And then the nondimensional variables are introduced for computation accuracy and speed, which give rise to nondimensional equations of motion. The general equation is derived with which common curves could be utilized in orbit design. In addition, the orbit design method is described based on Forbes’ velocity assumption and the formulation of the radius r with respect to time t, which is a sinusoidal function. The determination of the coefficients causes the orbit design problem to translate into an orbit control problem. The requisite thrust magnitude and direction are available via the simplified nondimensional equations of motion. In the end, an example of the transfer orbit is given. The result demonstrates that the shape-based method is feasible for the transfer orbit design or control problem under the continuous thrust, and the fuel expenditure is practicable.

Dynamic Modeling and Control of an Electromechanical Control Actuation System

2017 ◽  
Author(s):  
Ümit Yerlikaya ◽  
R. Tuna Balkan
Keyword(s):  
Nonlinear Model ◽  
Equations Of Motion ◽  
Ball Screw ◽  
Loop Control ◽  
Modeling And Control ◽  
Performance Requirements ◽  
Actuation System ◽  
Lever Mechanism ◽  
Actuation Systems ◽  
And Control

Electromechanical actuators are widely used in miscellaneous applications in engineering such as aircrafts, missiles, etc. due to their momentary overdrive capability, long-term storability, and low quiescent power/low maintenance characteristics. This work focuses on electromechanical control actuation systems (CAS) that are composed of a brushless direct current motor, ball screw, and lever mechanism. In this type of CAS, nonlinearity and asymmetry occur due to the lever mechanism itself, saturation limits, Coulomb friction, backlash, and initial mounting position of lever mechanism. In this study, both nonlinear and linear mathematical models are obtained using governing equations of motion. By using the linear model, it is shown that employing a PI-controller for position and a P-controller for velocity will be sufficient to satisfy performance requirements in the inner-loop control of an electromechanical CAS. The unknown controller parameters and anti-windup coefficient are obtained by the Optimization Tools of MATLAB using nonlinear model. Results obtained from the nonlinear model and real-time unloaded and loaded tests on a prototype developed are compared to verify the nonlinear model.

Nonlinear Model Predictive Control of a Stewart Platform Motion Stabilizer

2020 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Stewart Platform ◽  
Nonlinear Model Predictive Control ◽  
Operating Table ◽  
Prediction Errors ◽  
Time Step ◽  
Moving Vehicle

Abstract In an operating room of a hospital ship, to remotely perform surgery on a patient laid on an operating table utilizing the surgical manipulators attached to the table, the rotation and translation of the operating table must be properly isolated from the wave-induced motion of the floor. Similarly, on a moving vehicle, when a sensitive equipment is transported or a manipulator is utilized to perform precise positioning tasks, it becomes necessary to isolate them from undesirable motion of the vehicle. In response to the need for a motion stabilizer, which isolates a manipulator from undesirable ship or vehicle motion, we present a nonlinear model predictive control (NMPC) of a six degrees-of-freedom, base-moving Stewart platform. Analytical nonlinear equations of motion are utilized for nonlinear model predictive control, wherein an optimization problem in a finite time horizon at each time step is solved adopting C/GMRES algorithm. To predict the future motion caused by a ship or a moving vehicle, we employ an auto regressive moving average model which forecasts future behavior based on past behavior. Furthermore, to incorporate prediction errors as disturbance at each time step, we endow NMPC with the robustness. As a result, even if prediction errors exist, the set of all possible output states are predicted using the equations of motion in a finite time, while the system kinematic constraints are precisely satisfied. In order to assess the performance of the proposed controller, numerical simulations are presented for a base-moving Stewart platform.

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