Flow Computations on Imprecise Terrains

We study the computation of the flow of water on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x,y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time

Flow computations on imprecise terrains

Abstract. We study water flow computation on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x, y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, or a set of vertices, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time. Rose knew almost everything that water can do, there are an awful lot when you think what. Gertrude Stein, The World is Round

Flow computations on imprecise terrains

We study water flow computation on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x, y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time.Peer ReviewedPostprint (published version

Computing Realistic Terrains from Imprecise Elevations

It is ideal for triangulated terrains to have characteristics or properties that are realistic. In the imprecise terrain model, each vertex of a triangulated terrain has an imprecise eleva- tion value only known to lie within some interval. Under some objective function, the goal is to compute a precise terrain by assigning a single elevation value to each point, so that the objective function is optimized. This thesis examines various objectives, such as minimizing the number of local extrema and minimizing the terrain’s surface area. We give algorithms in some cases, hardness results in other cases. Specifically, we consider four objectives: (1) minimizing the number of local extrema; (2) optimizing coplanar features; (3) minimizing the surface area; (4) minimizing the maximum steepness. Problem (1) is known to be NP-hard, but we give an algorithm for a special case. For problem (2) we give an NP-hardness proof for the general case and a positive result for a special case. Meanwhile, problems (3) and (4) can be approximated using Second Order Cone Programming. We also consider versions of these problems for terrains one dimension down, where the output is a polyline. Here we give very efficient algorithms for all objective functions considered. Finally, we go beyond terrains and briefly consider the distant representatives problem, where the goal is to choose precise points from segments to be as far from each other as possible. For this problem, we give a parameterized algorithm for vertical segments, prove NP-hardness for unit horizontal segments, and show hardness of approximation for vertical and horizontal segments

Uncertain Curve Simplification

We study the problem of polygonal curve simplification under uncertainty, where instead of a sequence of exact points, each uncertain point is represented by a region, which contains the (unknown) true location of the vertex. The regions we consider are disks, line segments, convex polygons, and discrete sets of points. We are interested in finding the shortest subsequence of uncertain points such that no matter what the true location of each uncertain point is, the resulting polygonal curve is a valid simplification of the original polygonal curve under the Hausdorff or the Fr\'echet distance. For both these distance measures, we present polynomial-time algorithms for this problem.Comment: 25 pages, 5 figure

MOTION PLANNING ALGORITHM FOR VEHICLE PARKING SIMULATION

This project implements an intelligent autonomous vehicle parking control system. Intelligence of the system means that the car is capable of analyzing its own environment and act accordingly to it as a human being would do. This project focuses on creation of the motion planning algorithm of the system and developing a simulation to simulate the vehicle movements. The system controls the vehicle based on the vehicle and the target parking space coordinates. It will automatically generate the steering commands in order to park itself inside the parking space. Prototyping method is used in this project, where the prototype of the system is developed as soon as possible and it is then enhanced by adding more functions. The development of the system is using C# .net programming language. The system is successfully working as it has been tested multiple times in the simulation environment

Autonomous navigation of a wheeled mobile robot in farm settings

This research is mainly about autonomously navigation of an agricultural wheeled mobile robot in an unstructured outdoor setting. This project has four distinct phases defined as: (i) Navigation and control of a wheeled mobile robot for a point-to-point motion. (ii) Navigation and control of a wheeled mobile robot in following a given path (path following problem). (iii) Navigation and control of a mobile robot, keeping a constant proximity distance with the given paths or plant rows (proximity-following). (iv) Navigation of the mobile robot in rut following in farm fields. A rut is a long deep track formed by the repeated passage of wheeled vehicles in soft terrains such as mud, sand, and snow. To develop reliable navigation approaches to fulfill each part of this project, three main steps are accomplished: literature review, modeling and computer simulation of wheeled mobile robots, and actual experimental tests in outdoor settings. First, point-to-point motion planning of a mobile robot is studied; a fuzzy-logic based (FLB) approach is proposed for real-time autonomous path planning of the robot in unstructured environment. Simulation and experimental evaluations shows that FLB approach is able to cope with different dynamic and unforeseen situations by tuning a safety margin. Comparison of FLB results with vector field histogram (VFH) and preference-based fuzzy (PBF) approaches, reveals that FLB approach produces shorter and smoother paths toward the goal in almost all of the test cases examined. Then, a novel human-inspired method (HIM) is introduced. HIM is inspired by human behavior in navigation from one point to a specified goal point. A human-like reasoning ability about the situations to reach a predefined goal point while avoiding any static, moving and unforeseen obstacles are given to the robot by HIM. Comparison of HIM results with FLB suggests that HIM is more efficient and effective than FLB. Afterward, navigation strategies are built up for path following, rut following, and proximity-following control of a wheeled mobile robot in outdoor (farm) settings and off-road terrains. The proposed system is composed of different modules which are: sensor data analysis, obstacle detection, obstacle avoidance, goal seeking, and path tracking. The capabilities of the proposed navigation strategies are evaluated in variety of field experiments; the results show that the proposed approach is able to detect and follow rows of bushes robustly. This action is used for spraying plant rows in farm field. Finally, obstacle detection and obstacle avoidance modules are developed in navigation system. These modules enables the robot to detect holes or ground depressions (negative obstacles), that are inherent parts of farm settings, and also over ground level obstacles (positive obstacles) in real-time at a safe distance from the robot. Experimental tests are carried out on two mobile robots (PowerBot and Grizzly) in outdoor and real farm fields. Grizzly utilizes a 3D-laser range-finder to detect objects and perceive the environment, and a RTK-DGPS unit for localization. PowerBot uses sonar sensors and a laser range-finder for obstacle detection. The experiments demonstrate the capability of the proposed technique in successfully detecting and avoiding different types of obstacles both positive and negative in variety of scenarios