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

This paper presents the design of an embedded-control architecture for a four-rotor unmanned air vehicle (UAV) to perform autonomous hover flight. A non-linear control law based on nested saturations technique is presented that stabilizes the state of the aircraft around the origin. The control law was implemented in a microcontroller to stabilize the aircraft in real time. In order to obtain experimental results we have built a low-cost on-board system which drives the aircraft in position and orientation. The nonlinear controller has been successfully tested experimentally.

Embedded control of a four-rotor UAV

Combining Stereo Vision and Inertial Navigation System for a Quad-Rotor UAV

In this paper it is presented a control strategy to solve the trajectory tracking and flight formation problem, in horizontal plane, of multiple unmanned aerial vehicles (UAVs) kind quadrotor, by means of a leader-follower scheme. Time scale separation of the translational and rotational quadrotor dynamics is used to achieve trajectory tracking. A sliding mode controller is proposed for the translational dynamic and provides the desired orientation for the UAV, which is controlled by a linear PD control. Finally, from the formation error dynamics, a sliding mode control is used by the follower to preserve the formation with respect to a leader. Experimental results, using a virtual leader and a follower in formation, are shown to evaluate the proposed control law.

/pdf/quadrotors-flight-formation-control-using-a-leader-follower-5adw2hjktb.pdf

Quadrotors flight formation control using a leader-follower approach

An adaptive backstepping approach to obtain directional control of a fixed-wing UAV in presence of unknown crosswind is developed in this paper. The dynamics of the cross track error with respect to a desired trajectory is derived from the lateral airplane equations of motion. Adaptation laws are proposed to estimate the parameters of the unknown disturbances and are employed in closed-loop system. The stability analysis is proved using Lyapunov theory. In addition, several simulations taking into account unknown wind gusts are performed to analyze the behavior and the robustness of the control scheme. A test platform has been developed in order to validate the proposed control law.

https://hal.archives-ouvertes.fr/hal-00776093/document

Adaptive Trajectory Following for a Fixed-Wing UAV in Presence of Crosswind

This paper presents the problem of safe and fast transportation of packages by an Unmanned Aerial Vehicle (UAV) kind quadrotor. A mathematical model and a control strategy for a special class of underactuated mechanical systems, composed of a quadrotor transporting a cable-suspended payload, are proposed. The Euler-Lagrange formulation is used to obtain the dynamic model of the system, where the integrated dynamics of the quadrotor, cable and payload are considered. An Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) is chosen because of its inherent robustness against parametric uncertainty and unmodeled dynamics. Two cases are considered to obtain two different control laws, in the first case, the designed control law depends on the swing angle of the payload, in the second case the control law does not depend on it. The control objective is to transport the payload from point to point, with swing reduction along trajectory. Experimental results using monocular vision based navigation are shown to evaluate the proposed control law.

https://hal.archives-ouvertes.fr/hal-01682485/document

Rogelio Lozano

Papers

Embedded control of a four-rotor UAV

Combining Stereo Vision and Inertial Navigation System for a Quad-Rotor UAV

Quadrotors flight formation control using a leader-follower approach

Adaptive Trajectory Following for a Fixed-Wing UAV in Presence of Crosswind

Swing-attenuation for a quadrotor transporting a cable-suspended payload