Robust Geometric Navigation of a Quadrotor UAV on SE(3)

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 1019-1040 ◽  
Author(s):  
O. Garcia ◽  
E. G. Rojo-Rodriguez ◽  
A. Sanchez ◽  
D. Saucedo ◽  
A. J. Munoz-Vazquez
Keyword(s):  
Equations Of Motion ◽  
Normal Velocity ◽  
Sliding Modes ◽  
Tracking Errors ◽  
Navigation Algorithm ◽  
Algorithm Validation ◽  
Smooth Tracking ◽  
Sliding Manifold ◽  
Cascade Structure ◽  
Twisting Algorithm

SUMMARYIn this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton–Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the contour of the task with small normal velocity. For this purpose, a super twisting algorithm controls the nonlinear rotational and translational dynamics as a cascade structure in order to establish the fast and yet smooth tracking with the typical robustness of sliding modes. In this sense, the controller provides robustness against parameter uncertainty, disturbances, convergence to the sliding manifold in finite time, and asymptotic convergence of the trajectory tracking. The algorithm validation is presented through experimental results showing the feasibility of the proposed approach and illustrating that the tracking errors converge asymptotically to the origin.

On Wave Propagation in Thermoplastic Media

1966 ◽  
Vol 33 (3) ◽  
pp. 514-520 ◽  
Author(s):  
A. D. Fine ◽  
H. Kraus
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
Wave Front ◽  
Dynamic Behavior ◽  
Static Analysis ◽  
Equations Of Motion ◽  
Normal Velocity ◽  
Wave Fronts ◽  
Closed Form Solutions ◽  
Infinite Region

The dynamic behavior of a medium, according to the uncoupled thermoplastic theory, is presented and is compared to the behavior that would be obtained from an uncoupled quasi-static analysis. Since the inertia terms are retained in the equations of motion, wave fronts (or surfaces of discontinuity) are produced in the medium. The normal velocity of the wave front separating the elastic and plastic regions is determined. General closed-form solutions of the displacement (according to both the dynamic and the quasi-static approaches) are obtained; their unique forms are found for the semi-infinite region, and an illustrative numerical example is then presented.

Heterogeneous Nonlinear Systems Synchronization Based on Adaptive Super Twisting

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Oscar Salas-Peña ◽  
Jesús De León-Morales
Keyword(s):  
Nonlinear Systems ◽  
Control Strategy ◽  
Heterogeneous System ◽  
Degrees Of Freedom ◽  
Heterogeneous Systems ◽  
Experimental Results ◽  
Uncertain Nonlinear Systems ◽  
Sliding Modes ◽  
Control Scheme ◽  
Twisting Algorithm

In this work, the synchronization of a group of heterogeneous uncertain nonlinear systems is addressed. A strategy based on adaptive super twisting algorithm is proposed, in order to synchronize the outputs of the heterogeneous systems. With the aim of implementing the proposed control strategy, unmeasurable states are estimated by means of high-order sliding modes differentiators. This control scheme increases robustness against unknown dynamics and disturbances, whose bounds are not required to be known. Finally, experimental results for synchronizing a heterogeneous system platform, constituted by an inertial stabilization platform (ISP) and a helicopter of two degrees-of-freedom (DOF), are used to illustrate the performance of the proposed control scheme.

scholarly journals Spatially Quasi-Periodic Water Waves of Infinite Depth

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Jon Wilkening ◽  
Xinyu Zhao
Keyword(s):  
Initial Value Problem ◽  
Water Waves ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Small Scale ◽  
Normal Velocity ◽  
Natural Setting ◽  
Two Dimensional ◽  
Periodic Functions ◽  
Initial Value

AbstractWe formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

2-SMC of Electro-Hydraulic Drives Using the Twisting Algorithm

2012 ◽  
Vol 233 ◽  
pp. 131-134 ◽  
Author(s):  
Lasse Schmidt ◽  
Torben O. Andersen ◽  
Henrik C. Pedersen ◽  
Michael M. Bech
Keyword(s):  
Tracking Control ◽  
Sliding Modes ◽  
Parameter Perturbations ◽  
Control Concept ◽  
Position Tracking Control ◽  
Twisting Algorithm ◽  
Linear Controllers ◽  
Hydraulic Valve ◽  
Nonlinear Nature ◽  
Piston Position

In this paper a controller utilizing second order sliding modes, generally applicable for position tracking control of electro-hydraulic valve-cylinder drives (VCD), is proposed. The proposed controller requires pressure measurements, and only the signs of the valve spool position and piston position- and velocity. The main objective is to introduce a control concept that provide for increased performance compared to linear controllers, in the presence of the inherent nonlinear nature characterizing such systems. To accomplish this task, a controller based on the twisting algorithm and knowledge of system gain variations is proposed. Results demonstrate strong robustness when subjected to parameter perturbations and that control chattering is eliminated.

Integral backstepping control for trajectory and yaw motion tracking of quadrotors

Robotica ◽  
2018 ◽  
Vol 37 (2) ◽  
pp. 300-320 ◽  
Author(s):  
Alexander Poultney ◽  
Peiyan Gong ◽  
Hashem Ashrafiuon
Keyword(s):  
Motion Tracking ◽  
Equations Of Motion ◽  
Backstepping Control ◽  
Tracking Errors ◽  
Modeling Uncertainties ◽  
Controller Performance ◽  
Simplifying Assumptions ◽  
Bounded Disturbances ◽  
System States ◽  
Nonlinear Equations Of Motion

SUMMARYThis work presents a novel trajectory tracking, hovering, and yaw motion control for quadrotors subject to unknown modeling uncertainties and disturbances. Nonlinear equations of motion are used to model the quadrotor's motion without any simplifying assumptions. An integral backstepping control is developed by defining the tracking errors, their integral, and their first through third time derivatives as the system states. The resulting surge force and roll and pitch moments are shown to asymptotically stabilize the error states subject to bounded disturbances and modeling uncertainties. Similarly, a yaw moment is derived through integral backstepping that simultaneously stabilizes yaw motion errors. The controller performance in simultaneous trajectory and yaw motion tracking is verified through both simulations and experiments.

Experimental tests of a sliding mode controller for trajectory tracking of a car-like mobile robot

Robotica ◽  
2013 ◽  
Vol 32 (1) ◽  
pp. 63-76 ◽  
Author(s):  
F. Hamerlain ◽  
T. Floquet ◽  
W. Perruquetti
Keyword(s):  
Tracking Control ◽  
Sliding Mode ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Sliding Mode Controller ◽  
Tracking Errors ◽  
Output Tracking ◽  
Comparative Results ◽  
Twisting Algorithm ◽  
Second Order Sliding Mode

SUMMARYThis paper deals with the problem of the practical tracking control of an experimental car-like system called the Robucar. The car-like Robucar is a four-wheeled car in a single steering mode. Based on a kinematic model of the car-like Robucar, a practical tracking controller is designed using the second-order sliding mode control of the super twisting algorithm. Hence, the output tracking of the desired trajectory is achieved, and the tracking errors vanish asymptotically. Experimental tests on the car-like Robucar are presented for simple and real-time nonholonomic trajectories, and comparative results with the conventional sliding controller demonstrate the applicability and efficiency of the proposed controller.

scholarly journals A formation maneuvering controller for multiple non-holonomic robotic vehicles

Robotica ◽  
2018 ◽  
Vol 37 (1) ◽  
pp. 189-211 ◽  
Author(s):  
Milad Khaledyan ◽  
Marcio de Queiroz
Keyword(s):  
Spanning Tree ◽  
Equations Of Motion ◽  
Parametric Uncertainty ◽  
Control Law ◽  
Wheeled Mobile Robots ◽  
Tracking Errors ◽  
Position Errors ◽  
Dynamic Level ◽  
Control Scheme ◽  
Individual Tracking

SUMMARYIn this paper, we present a new leader–follower type solution to the translational maneuvering problem for formations of multiple, non-holonomic wheeled mobile robots. The solution is based on the graph that models the coordination among the robots being a spanning tree. Our control law incorporates two types of position errors: individual tracking errors and coordination errors for leader–follower pairs in the spanning tree. The control ensures that the robots globally acquire a given planar formation while the formation as a whole globally tracks a desired trajectory, both with uniformly ultimately bounded errors. The control law is first designed at the kinematic level and then extended to the dynamic level. In the latter, we consider that parametric uncertainty exists in the equations of motion. These uncertainties are accounted for by employing an adaptive control scheme. The main contributions of this work are that the proposed control scheme minimizes the number of control links and global position measurements, and accounts for the uncertain vehicle dynamics. The proposed formation maneuvering controls are demonstrated experimentally and numerically.

Adaptive Second Order Sliding Mode Control: Application to Position and Force Control of Electro-Pneumatic Actuators

2012 ◽  
Author(s):  
Mohammed Taleb ◽  
Franck Plestan
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Limited Information ◽  
Pneumatic Actuators ◽  
Mode Control ◽  
Sliding Manifold ◽  
Set Up ◽  
Twisting Algorithm ◽  
Control Application ◽  
Pneumatic Cylinders

This paper presents an application of adaptive 2nd order sliding mode control. This control is based on twisting algorithm and ensures a finite time convergence to the sliding manifold σ = σ̇ = 0, σ being the sliding variable and defined from the control objectives. The control solution required a limited information about the uncertainties and the disturbances acting on the system. This control strategy is applied to an electropneumatic set-up. This bench consists of two rod coupled pneumatic cylinders: one cylinder is controlled on position and perturbed by the second cylinder which is force-controlled. The efficacy of this strategy is evaluated through some simulations.

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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