There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Time-delay systems: an overview of some recent advances and open problems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

In this paper, a simple control algorithm for the PVTOL aircraft is proposed. The control strategy takes into the account input constraints and does not have any singularities. The control design is such that the acceleration satisfies arbitrary bounds. The stability analysis is proved by using very simple arguments. Satisfactory behavior is shown in simulations.

Control design for the PVTOL aircraft with arbitrary bounds on the acceleration

The paper presents the modeling and control of a class of multirotor miniature aerial vehicle (MAV) having an onboard robotic manipulator. These kind of configuration represents the logical evolution in the MAV development race. The main goal is to outstrip the current operational profile, specially in the civilian field, by endowing classical MAV config- urations with novel capabilities to interact with the surrounding environment. The equations that describes the dynamic model of this class of aerial robot, for translation and rotational motion, are obtained through the Euler-Lagrange formalism. This energy-based modeling approach allows to obtain the mechanical couplings between both aerial and manipulation systems, the aerial and manipulation. In terms of control, our main goal is to provide a simple-to-implement controller to perform aerial manipulation tasks using multirotor MAVs. A task-based control strategy is then proposed to cancel the couplings in the overall dynamic model (model simplification). The control law for the aerial system relies on a classical two- level scheme to fullfil tracking problem. On the other hand, the motion problem of the manipulation system is addressed via a switching-based controller. The controller corresponding stability proofs are presented and the performance of the control strategy is evaluated at simulation level. I. INTRODUCTION The pace of development of Unmanned Aerial Vehicles (UAVs) has increased over the last few years, due to the wide range of military or civilian applications were they could potentially be deployed. In the military field, applications such as delivering survival-kits to the troops, mobile commu- nication link with a ground station for information exchange, risk evaluation of hostile area, are just a few examples of drone-based applications. It is well know that growth rate of MAVs civilian application is not as high as that of its military counterpart. However, the operational profile offered by interactive MAVs unveils interesting novel applications, for instance, recovering mineral samplings in volcanic study, air- quality cartography/monitoring, placing/recovering sensors in constrained strategic areas, recovering potential explosive packages in sensitive facilities. The interactive MAV configu- ration represent a unique profile endowing manipulator robot with the 3D mobility of aerial vehicles. The latter allows to perform teleoperated/autonomous interactivity within hostile environments. Whereas this concept is very promising, it also comes with significant robotic and automation challenges. Foremost amongst these is the modeling the compound mechanical system and designing controllers that will work, in theory and practice, over partial or complete operational scope of the flying robot and an appropriate and optimized mechanical design to meet the desired flight performance requirements. Recent research activities related to interactive flying rotorcrafts can be found in the literature: (2)where the authors have presented the planar model and attitude control analysis of helicopter equipped with a gripper that is capable of grasping and transporting loads of different geometries and sizes. GRASP Research team uses different cooperative quadrotors fleet configurations to transport corresponding load geometries by means of gripper and cables (3). An alternative UAV configuration featuring a hook aiming at vision-based delivering and retrieving of cargo, is presented in (4). In (5) and (6), the problem of load transportation using autonomous small size helicopters is addressed. Likewise, the modeling and control of a variable number of helicopters transporting a load is presented. Indeed, the proposed con- troller prevent and compensate load oscillations during flight, which is demonstrated by real flight load transportation by three helicopters. The paper presents the study of a class of a multirotor MAV evolving in the longitudinal plane and capable of interacting with the surrounding environment by means of

Task-based control of a multirotor miniature aerial vehicle having an onboard manipulator

This paper explores the flight of small fixed-wing Unmanned Aerial Vehicle (UAV) in a non-steady environment. The vulnerability of light airplanes to wind is analyzed and the effect of such perturbations on airplane performance is incorporated in the equations of motion. A straightforward wind computation approach, which relies on the difference between the predicted motion of the aircraft and the real motion measured by sensors, is presented in order to be used for a path following application. The analysis takes into account the effect of the noise in sensors measurements and in estimates of orientation and airspeed components. One approach to reducing noise in wind estimates is proposed based on on-line adaptation techniques. Parameter estimation with minimum-order design is obtained using tuning functions. Simulations are carried out representing real flight scenarios in which the wind field is not constant and the sensor measurements are imperfect.

Wind Estimation for Accurate Airplane Path Following Applications

In this paper we propose a way to solve the problem of singularities in model reference adaptive control of linear multi-input-multi-output (MIMO) systems using a parameter modification procedure based on the least squares covariance matrix inverse. The scheme does not require any explicit prior knowledge about the leading coefficient matrix associated with the control input and secures a uniform lower bound for the determinant of the estimate of this matrix. A global convergence analysis is presented. >

Singularity-free multivariable model reference adaptive control

This paper presents the development of a micro coaxial helicopter (MCR UAV) whose main characteristic is that it should be carried by an air shuttle transporter and then released in a desired place far away from the launching site, to develop surveillance missions in hover flight. A real-time embedded system is built in order to validate the proposed aerodynamic prototype, and a classic control law based on a classical backstepping procedure for the dynamic system is implemented to test this vehicle in autonomous flight. Finally, simulation and practical results are presented for hover flight.

/pdf/micro-helicopter-for-long-distance-missions-description-and-2g5457nhg1.pdf

Rogelio Lozano

Papers

Control design for the PVTOL aircraft with arbitrary bounds on the acceleration

Task-based control of a multirotor miniature aerial vehicle having an onboard manipulator

Wind Estimation for Accurate Airplane Path Following Applications

Singularity-free multivariable model reference adaptive control

Micro-Helicopter for Long-Distance Missions: Description and Attitude Stabilization