Occlusion-Aware Path Planning to Promote Infrared Positioning Accuracy for Autonomous Driving in a Warehouse

Infrared positioning is a critical module in an indoor autonomous vehicle platform. In an infrared positioning system, the ego vehicle is equipped with an infrared emitter while the infrared receivers are fixed onto the ceiling. The infrared positioning result is accurate only when the number of valid infrared receivers is more than three. An infrared receiver easily becomes invalid if it does not receive light from the infrared emitter due to indoor occlusions. This study proposes an occlusion-aware path planner that enables an autonomous vehicle to navigate toward the occlusion-free part of the drivable area. The planner consists of four layers. In layer one, a homotopic A* path is searched for in the 2D grid map to roughly connect the initial and goal points. In layer two, a curvature-continuous reference line is planned close to the A* path using numerical optimal control. In layer three, a Frenet frame is constructed along the reference line, followed by a search for an occlusion-aware path within that frame via dynamic programming. In layer four, a curvature-continuous path is optimized via quadratic programming within the Frenet frame. A path planned within the Frenet frame may violate the curvature bounds in a real-world Cartesian frame; thus, layer four is implemented through trial and error. Simulation results in CarSim software show that the derived paths reduce the poor positioning risk and are easily tracked by a controller.

Intersection curve of two parametric surfaces in Euclidean n-space

The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.

The pseudo-null geometric phase along optical fiber

In this study, a pseudo-null space curve in Minkowski 3-space is used to describe an optical fiber that is injected into monochromatic linear polarized light. The direction of the electric field vector with respect to the Frenet frame of a pseudo-null curve determines the state polarization of a monochromatic linearly polarized light wave traveling along an optical fiber. For the Frenet frame of a pseudo-null curve in Minkowski 3-space, the polarization vector [Formula: see text] is assumed to be perpendicular to the tangent vector [Formula: see text] with respect to anholonomic coordinates. Anholonomic coordinates for the Frenet frame of a pseudo-null curve are used to describe pseudo-null electromagnetic curves in the normal and binormal directions along an optical fiber. For the Frenet frame of the pseudo-null curve, Lorentz force equations in the normal and binormal directions along the optical fiber are presented. Pseudo-normal and binormal Rytov parallel transport laws for electric fields in the normal and binormal directions along with the optical fiber for the Frenet frame of the pseudo-null curve via anholonomic coordinates are presented. For anholonomic coordinates in Minkowski 3-space, rotations of the polarization planes of a light wave traveling in the normal and binormal directions along with the optical fiber with respect to the Frenet frame of the pseudo-null curve are obtained. Finally, a pseudo-null curve’s Maxwellian evolution is determined.

1-TYPE AND HARMONIC 1-TYPE TIMELIKE CURVES IN SEMI-EUCLIDEAN SPACE 42

In the present study we consider 1-type, biharmonic, weak biharmonic and harmonic 1-type curves in semi-Euclidean space 42R according to the timelike Frenet frame. We give some characterizations and classifications of these type curves.

Smarandache curves of Bertrand curves pair according to Frenet frame

In this paper, the curvature and the torsion of Smarandache curves obtained by the vectors of the Bertrand partner curve are calculated. These values are expressed depending upon the curve. Besides, we illustrate example with our main results.

Parallel Transport Frame of Smarandache Curves in Euclidean Space

In the present work, we introduce Parallel transport frames of Smarandache curves in Euclidean space. In the first section, we give the basic tools of a parallel transport frame of a curve in 4-dimensional Euclidean space. In the second section, we study Smarandache curve of Euclidean space in parallel transport frame, we solve a few theorems, corollaries and examples. Again third section, we define parallel transport frame to the Smarandache curve and obtain some definitions and their apparatus. Further fourth section, we have also explained to Frenet frame of principal normal, binomial and their derivatives in the curvatures of the curve. In the end section, we discussed about the Smarandache curve in the Euclidean space of all apparatus Frenet-Serret in the differential geometry.