Single equation without inequalities to represent a composite curve

Chicurel-Uziel, Enrique

doi:10.1016/j.cagd.2003.07.011

Cited by 8 publications

(2 citation statements)

References 8 publications

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“…It consists of two stages: the first stage is the pre-optimization stage, in which an initial path is developed between the start and the target points guided with the edges of the obstacles. To develop this pre-optimization path, a straight line is developed based on the Heaviside unit step [58] between the start and target points. further, a mathematical equation is developed based on the Heaviside step function to describe the complete shape of obstacles in the environment.…”

Section: A Problem Statementmentioning

confidence: 99%

A Supervisory-Based Collaborative Obstacle-Guided Path Refinement Algorithm for Path Planning in Wide Terrains

2020

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Robotic exploration of wide terrains, such as agricultural fields, could be challenging while considering the limited robot's capabilities in terms of sensing and power. Thus, in this paper, we proposed OGPR*, an Obstacle Guided Path Refinement algorithm for quickly planning collision-free paths utilizing the obstacles existing in the environment. To tackle the issue of exploring wide terrains, a supervisorybased collaboration between quadcopter and mobile robots is proposed. The quadcopter is responsible for streaming subsequently live two-dimensional images for the environment under discussion while planning safe paths for the ground the mobile robot is planning safe paths to manoeuvre. Numerical simulations proved the significant performance of the proposed OGBR* algorithm when compared to the state of the art algorithms exist in the literature. INDEX TERMS collaborative, mobile robot, OGPR, path planning, tracking I. INTRODUCTION

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Section: A Problem Statementmentioning

confidence: 99%

A Supervisory-Based Collaborative Obstacle-Guided Path Refinement Algorithm for Path Planning in Wide Terrains

2020

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“…Some research (e.g., Milenkovic, 1993) has addressed the problem of polygon modelling but the models are mostly in two-dimensional (2D) and the models and their associated constraints often consist of inequalities. Chicurel-Uziel (2004) proposed a generalized 3D model for polygonal prisms without inequality but the x and y coordinates are modelled and estimated separately using two equations and they cannot be readily expressed in terms of the other. Also, no inclinations of the prism were considered in its model.…”

Section: Introductionmentioning

confidence: 99%

Geometric Modelling of Octagonal Lamp Poles

Chan

Lichti

2014

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the zaxis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.

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Symbolic Computations

The Mathematica GuideBook for Symbolics

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Single equation without inequalities to represent a composite curve

Cited by 8 publications

References 8 publications

A Supervisory-Based Collaborative Obstacle-Guided Path Refinement Algorithm for Path Planning in Wide Terrains

A Supervisory-Based Collaborative Obstacle-Guided Path Refinement Algorithm for Path Planning in Wide Terrains

Geometric Modelling of Octagonal Lamp Poles

Symbolic Computations

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