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 article presents the designs, simulations and real-time experimental results of two energy-based control strategies to stabilize an Unmanned Aerial Vehicles (UAV) using a quaternion representation of the attitude. The mathematical model is based on Euler-Lagrange formulation using a logarithmic mapping in the quaternion space. The proposed solutions introduce a new approach: a quaternion-energy-based control, which use an energy-based expression defined as a Lyapunov function. The control laws are described with unit quaternions and their axis-angle representation. The proposed algorithms allow the stabilization of the quadrotor in all its states. The strategies ensure the stability of the closed loop system. Simulation results and experimental validations are developed to verify the effectiveness of the proposed controllers.

/pdf/quadrotor-energy-based-control-laws-a-unit-quaternion-33fods5rbi.pdf

Quadrotor Energy-Based Control Laws: a Unit-Quaternion Approach

This paper presents a visual feedback control of a small UAV using image-based visual servoing with stereo vision. In order to control the orientation and the position of flying robot with respect to an object or target well defined, we propose to use a navigation system based on binocular vision system combined with inertial sensors. This combination of sensors, allows us to get a complete characterization of the state of aerial vehicle. It means, using the stereo vision system we are able to estimate the UAV 3D position, while from the inertial sensors we can obtain the orientation of rotorcraft. Real time experiences are developed to validate the performance of navigation system proposed.

/pdf/real-time-stereo-visual-servoing-control-of-an-uav-having-3mpdnzov71.pdf

Real-time stereo visual servoing control of an UAV having eight-rotors

A globally convergent adaptive control scheme for nonminimum phase systems is presented. The approach is based on a particular periodic pole-placement controller. An ad-hoc parameter estimate correction procedure is used to prevent any possible singularities in the control law computation. Furthermore, a lower bound on the estimated model controllability is ensured. The a priori knowledge on the system is reduced to the process order. >

Singularity-free adaptive pole placement using periodic controllers

Nonlinear control for a tandem rotor helicopter

There are many advantages in using UAVs for search and rescue operations. However, detecting people from a UAV remains a challenge: the embedded detector has to be fast enough and viewpoint robust to detect people in a flexible manner from aerial views. In this paper we propose a processing pipeline to 1) reduce the search space using infrared images and to 2) detect people whatever the roll and pitch angles of the UAV's acquisition system. We tested our approach on a multimodal aerial view dataset and showed that it outperforms the Integral Channel Features (ICF) detector in this context. Moreover, this approach allows real-time compatible detection.

/pdf/fast-and-viewpoint-robust-human-detection-for-sar-operations-n09wtbe4ft.pdf

Rogelio Lozano

Papers

Quadrotor Energy-Based Control Laws: a Unit-Quaternion Approach

Real-time stereo visual servoing control of an UAV having eight-rotors

Singularity-free adaptive pole placement using periodic controllers

Nonlinear control for a tandem rotor helicopter

Fast and viewpoint robust human detection for SAR operations