Algorithmic Motion Planning and Related Geometric Problems on Parallel Machines (Dissertation Proposal)

The problem of algorithmic motion planning is one that has received considerable attention in recent years. The automatic planning of motion for a mobile object moving amongst obstacles is a fundamentally important problem with numerous applications in computer graphics and robotics. Numerous approximate techniques (AI-based, heuristics-based, potential field methods, for example) for motion planning have long been in existence, and have resulted in the design of experimental systems that work reasonably well under various special conditions [7, 29, 30]. Our interest in this problem, however, is in the use of algorithmic techniques for motion planning, with provable worst case performance guarantees. The study of algorithmic motion planning has been spurred by recent research that has established the mathematical depth of motion planning. Classical geometry, algebra, algebraic geometry and combinatorics are some of the fields of mathematics that have been used to prove various results that have provided better insight into the issues involved in motion planning [49]. In particular, the design and analysis of geometric algorithms has proved to be very useful for numerous important special cases. In the remainder of this proposal we will substitute the more precise term of algorithmic motion planning by just motion planning

09111 Abstracts Collection -- Computational Geometry

From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Optimal Mesh Algorithms for the Voronoi Diagram of Line Segments, Visibility Graphs and Motion Planning in the Plane

The motion planning problem for an object with two degrees of freedom moving in the plane can be stated as follows: Given a set of polygonal obstacles in the plane, and a two-dimensional mobile object B with two degrees of freedom, determine if it is possible to move B from a start position to a final position while avoiding the obstacles. If so, plan a path for such a motion. Techniques from computational geometry have been used to develop exact algorithms for this fundamental case of motion planning. In this paper we obtain optimal mesh implementations of two different methods for planning motion in the plane. We do this by first presenting optimal mesh algorithms for some geometric problems that, in addition to being important substeps in motion planning, have numerous independent applications in computational geometry. In particular, we first show that the Voronoi diagram of a set of n nonintersecting (except possibly at endpoints) line segments in the plane can be constructed in O(√n) time on a √n x √n mesh, which is optimal for the mesh. Consequently, we obtain an optimal mesh implementation of the sequential motion planning algorithm described in [14]; in other words, given a disc B and a polygonal obstacle set of size n, we can plan a path (if it exists) for the motion of B from a start position to a final position in O (√n) time on a mesh of size n. Next we show that given a set of n line segments and a point p, the set of segment endpoints that are visible from p can be computed in O (√n) mesh-optimal time on a √n x √n mesh. As a result, the visibility graph of a set of n line segments can be computed in O(n) time on an n x n mesh. This result leads to an O(n) algorithm on an n x n mesh for planning the shortest path motion between a start position and a final position for a convex object B (of constant size) moving among convex polygonal obstacles of total size n

Magnetic suspension turbine flow meter

Measurement of liquid flow in certain area such as industrial plant is in critical. Inaccurate measurement can cause serious result. Most of the liquid flow are using Bernoulli principle‘s but in turbine flow meter the flow rate is determine differently by using kinetic energy. Turbine flow meter is one of flow rate transducer that widely used in metallurgical, petroleum, chemical and other industrial and agricultural areas, as shown in Figure 1.1. It is present as high precision of flow meter and when fluid flow troughs it the impeller that faces the fluid will rotate due to flow force exist. The rotation speed is directly proportional to the speed of fluid. During the process, the working states of impeller and bearing are very complicated due the interactive effects from the fluid axial thrust, impeller rotating, and static and dynamic components. In current turbine flow meter design, the common material use for meter bulk body is 1Cr18Ni9Ti, while for the blade 2Gr13 are used. Axis and bearing are made from stainless steel or carbide alloy. The space between the axis and bearing determines it minimum flow rate and life span, and also determines its measurement range (1:10~1:15 - maximum flow rate to minimum flow rate). Since the turbine has movable parts it can produce friction between the axis and ring during the operation. This will cause accuracy of the measurement decrease and can damage the impeller blade. In this research, the friction can be reduced by adopting the principle of magnetic suspension. Rotating shaft will levitate in the magnetic field due to the forces. Friction coefficient reduced because of rotating shaft rotates without abrasion and mechanical contact in space