Exact mirror equation via Berry's caustic touching theorem: plane and spherical mirrors.

In this work, we assume that in free space we have an observer, a smooth mirror, and an object placed at arbitrary positions. The aim is to obtain, within the geometrical optics approximation, an exact set of equations that gives the image position of the object registered by the observer. The general results are applied to plane and spherical mirrors, as an application of the caustic touching theorem introduced by Berry; the regions where the observer can receive zero, one, two, three, and one circle of reflected light rays are determined.

Refracting and reflecting interfaces transforming a given wavefront into another one.

The aim of this work is threefold. First, following Luneburg and using our own notation, we review the Cartesian ovals. Second, we obtain analytical expressions for the reflecting and refracting surfaces that transform a prescribed smooth two-dimensional wavefront into a spherical one.

Path-Tracking of a WMR Fed by Inverter-DC/DC Buck Power Electronic Converter Systems.

This paper is concerned with path-tracking control of a wheeled mobile robot. This robot is equipped with two permanent magnet brushed DC-motors which are fed by two inverter-DC/DC Buck power converter systems as power amplifiers. By taking into account the dynamics of all the subsystems we present, for the first time, a formal stability proof for this control problem.

A Novel Dynamic Three-Level Tracking Controller for Mobile Robots Considering Actuators and Power Stage Subsystems: Experimental Assessment.

In order to solve the trajectory tracking task in a wheeled mobile robot (WMR), a dynamic three-level controller is presented in this paper. The controller considers the mechanical structure, actuators, and power stage subsystems. Such a controller is designed as follows: At the high level is a dynamic control for the WMR (differential drive type).

Robust Switched Tracking Control for Wheeled Mobile Robots Considering the Actuators and Drivers.

By using the hierarchical controller approach, a new solution for the control problem related to trajectory tracking in a differential drive wheeled mobile robot (DDWMR) is presented in this paper. For this aim, the dynamics of the three subsystems composing a DDWMR, i.e.

Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens.

The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative positions to the caustic region, and third we describe in detail the structure of the null ronchigrating for this system; that is, we obtain the grating such that when it is placed at the flat surface of the axicon its associated pattern, at a given plane perpendicular to the optical axis, is a set of parallel fringes. We find that the caustic has only one branch, which is a segment of a line along the optical axis; the ronchigram exhibits self-intersecting fringes when the screen is placed at the caustic region, and the null ronchigrating exhibits closed loop rulings if we want to obtain its associated pattern at the caustic region.

Wavefronts, caustics, and ronchigrams of a spherical wave reflected by a spherical mirror.

The aim of the present work is twofold: first we obtain analytical expressions for both the wavefronts and the caustic associated with the light rays reflected by a spherical mirror after being emitted by a point light source located at an arbitrary position in free space, and second, we describe, in detail, the structure of the ronchigrams when the grating or Ronchi ruling is placed at different relative positions to the caustic region and the point light source is located on and off the optical axis. We find that, in general, the caustic has two branches: one is a segment of a line, and the other is a two-dimensional surface. The wavefronts, at the caustic region, have self intersections and singularities.

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface.

The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.