6 research outputs found
Structuring a Wayfinder\u27s Dynamic and Uncertain Environment
Wayfinders typically travel in dynamic environments where barriers and requirements change over time. In many cases, uncertainty exists about the future state of this changing environment. Current geographic information systems lack tools to assist wayfinders in understanding the travel possibilities and path selection options in these dynamic and uncertain settings. The goal of this research is a better understanding of the impact of dynamic and uncertain environments on wayfinding travel possibilities. An integrated spatio-temporal framework, populated with barriers and requirements, models wayfinding scenarios by generating four travel possibility partitions based on the wayfinder\u27s maximum travel speed. Using these partitions, wayfinders select paths to meet scenario requirements. When uncertainty exists, wayfinders often cannot discern the future state of barriers and requirements. The model to address indiscemibility employs a threevalued logic to indicate accessible space, inaccessible space, and possibly inaccessible space. Uncertain scenarios generate up to fifteen distinct travel possibility categories. These fifteen categories generalize into three-valued travel possible partitions based on where travel can occur and where travel is successful. Path selection in these often-complex environments is explored through a specific uncertain scenario that includes a well-defined initial requirement and the possibility of an additional requirement somewhere beforehand. Observations from initial path selection tests with this scenario provide the motivation for the hypothesis that paths arriving as soon as possible to well-defined requirements also maximize the probability of success in meeting possible additional requirements. The hypothesis evaluation occurs within a prototype Travel Possibility Calculator application that employs a set of metrics to test path accessibility in various linear and planar scenarios. The results did not support the hypothesis, but showed instead that path accessibility to possible additional requirements is greatly influenced by the spatio-temporal characteristics of the scenario\u27s barriers
Near-Optimal Min-Sum Motion Planning for Two Square Robots in a Polygonal Environment
Let be a planar polygonal environment
(i.e., a polygon potentially with holes) with a total of vertices, and let
be two robots, each modeled as an axis-aligned unit square, that can
translate inside . Given source and target placements
of and , respectively, the goal is to
compute a \emph{collision-free motion plan} , i.e., a motion
plan that continuously moves from to and from to
so that and remain inside and do not collide with
each other during the motion. Furthermore, if such a plan exists, then we wish
to return a plan that minimizes the sum of the lengths of the paths traversed
by the robots, . Given and a parameter , we present an
-time -approximation algorithm
for this problem. We are not aware of any polynomial time algorithm for this
problem, nor do we know whether the problem is NP-Hard. Our result is the first
polynomial-time -approximation algorithm for an optimal motion
planning problem involving two robots moving in a polygonal environment.Comment: The conference version of the paper is accepted to SODA 202
Recent progress in exact geometric computation
AbstractComputational geometry has produced an impressive wealth of efficient algorithms. The robust implementation of these algorithms remains a major issue. Among the many proposed approaches for solving numerical non-robustness, Exact Geometric Computation (EGC) has emerged as one of the most successful. This survey describes recent progress in EGC research in three key areas: constructive zero bounds, approximate expression evaluation and numerical filters
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
A digital computer is generally believed to be an efficient universal
computing device; that is, it is believed able to simulate any physical
computing device with an increase in computation time of at most a polynomial
factor. This may not be true when quantum mechanics is taken into
consideration. This paper considers factoring integers and finding discrete
logarithms, two problems which are generally thought to be hard on a classical
computer and have been used as the basis of several proposed cryptosystems.
Efficient randomized algorithms are given for these two problems on a
hypothetical quantum computer. These algorithms take a number of steps
polynomial in the input size, e.g., the number of digits of the integer to be
factored.Comment: 28 pages, LaTeX. This is an expanded version of a paper that appeared
in the Proceedings of the 35th Annual Symposium on Foundations of Computer
Science, Santa Fe, NM, Nov. 20--22, 1994. Minor revisions made January, 199
Planification de pas pour robots humanoïdes : approches discrètes et continues
Dans cette thèse nous nous intéressons à deux types d'approches pour la planification de pas pour robots humanoïdes : d'une part les approches discrètes où le robot n'a qu'un nombre fini de pas possibles, et d'autre part les approches où le robot se base sur des zones de faisabilité continues. Nous étudions ces problèmes à la fois du point de vue théorique et pratique. En particulier nous décrivons deux méthodes originales, cohérentes et efficaces pour la planification de pas, l'une dans le cas discret (chapitre 5) et l'autre dans le cas continu (chapitre 6). Nous validons ces méthodes en simulation ainsi qu'avec plusieurs expériences sur le robot HRP-2. ABSTRACT : In this thesis we investigate two types of approaches for footstep planning for humanoid robots: on one hand the discrete approaches where the robot has only a finite set of possible steps, and on the other hand the approaches where the robot uses continuous feasibility regions. We study these problems both on a theoretical and practical level. In particular, we describe two original, coherent and efficient methods for footstep planning, one in the discrete case (chapter 5), and one in the continuous case (chapter 6). We validate these methods in simulation and with several experiments on the robot HRP-2