Qualitative Kinematics of Linkages

We have developed a qualitative calculus for three-dimensional directions and rotations. A direction is characterized in terms of the signs of its components relative to an absolute coordinate system. A rotation is characterized in terms of the signs of the components of the associated 3 × 3 rotation matrix.A system has been implemented that can solve the following problems:1. Given the signs of directionv and rotation matrix P , find the possible signs of the image of v under P . Moreover, for each possible sign vector ofv·P , generate numerical instantiations ofv and P that yields that result.2. Given the signs of rotation matrices P and Q, find the possible signs of the composition P · Q. Moreover, for each possible sign matrix for the composition, generate numerical instantiations of P and Q that yield that result.We have also proven some related complexity and expressivity results. The satisfiability problem for a qualitative rotation constraint network is NP-complete in two dimensions and NP-hard in three dimensions. In three dimensions, any two directions are distinguishable by a qualitative rotation constraint network.

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“…Kim's qualitative theory of linkages [11] used sign vectors to characterize orientations of segments in a two-dimensional linkage.…”

Section: Related Workmentioning

confidence: 99%

A Qualitative Calculus for Three-Dimensional Rotations

Asl

Davis

2013

Spatial Cognition & Computation

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“…A number of calculi have been developed for representation of orientation, including the Single‐Cross and Double‐Cross calculi,43 FlipFlop Calculus,44 Qualitative Trajectory Calculus,45 and the Oriented Point Relation Algebra46. Kim47 shows that representing angles via quadrants and relative inclination results in a qualitative vector algebra powerful enough to reason about the motion of four‐bar linkages. Intuitively, orientation relative to a reference often provides a way of defining location (e.g., in front of the house and under the table).…”

Section: Qualitative Spatial Reasoningmentioning

confidence: 99%

Qualitative modeling

Forbus

2010

WIRES Cognitive Science

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Qualitative modeling concerns the representations and reasoning that people use to understand continuous aspects of the world. Qualitative models formalize everyday notions of causality and provide accounts of how to ground symbolic, relational representations in perceptual processes. This article surveys the basic ideas of qualitative modeling and their applications from a cognitive science perspective. It describes the basic principles of qualitative modeling, and a variety of qualitative representations that have been developed for quantities and for relationships between them, providing a kind of qualitative mathematics. Three ontological frameworks for organizing modeling knowledge (processes, components, and field) are summarized, along with research on automatically assembling models for particular tasks from such knowledge. Qualitative simulation and how it carves up time into meaningful units is discussed. We discuss several accounts of causal reasoning about dynamical systems, based on different choices of qualitative mathematics and ontology. Qualitative spatial reasoning is explored, both in terms of relational systems and visual reasoning. Applications of qualitative models of particular interest to cognitive scientists are described, including how they have been used to capture the expertise of scientists and engineers and how they have been used in education. Open questions and frontiers are also discussed, focusing on relationships between ideas developed in the qualitative modeling community and other areas of cognitive science. WIREs Cogni Sci 2011 2 374-391 DOI: 10.1002/wcs.115 For further resources related to this article, please visit the WIREs website.

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“…Modeling many systems and components, such as internal combustion engines or flush toilets, requires smoothly integrating a sophisticated dynamics with geometric reasoning. Kim [11,12] is working on such an integration.…”

Section: MMMMMMMMMMMMMMMMMMMMMM Mmmmmmmmmmmmmmentioning

confidence: 99%

Building Qualitative Models of Thermodynamic Processes

Collins¹,

Forbus²

2007

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This paper describes a qualitative domain theory for core phenomena in engineering thermodynamics, expressed in Qualitative Process theory . It represents many of the best features of domain models developed by our group over the past five years . It focuses on supporting system-level qualitative analyses of typical fluid and thermal systems, such as refrigerators and power plants . We use explicit modeling assumptions [3] to control the level of detail used in building models of specific scenarios . We begin by outlining the primitives of the specific QP modeling language . The bulk of the paper describes the domain model itself, highlighting our design choices, simplifications, and use of modeling assumptions . Next we demonstrate how this domain model can be used to build models of a variety of specific scenarios, including simplified versions of a refrigerator, a steam plant, and a thermal control system . Finally, we describe some planned extensions to the model . Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Qualitative Kinematics of Linkages

Cited by 8 publications

References 4 publications

A Qualitative Calculus for Three-Dimensional Rotations

A Qualitative Calculus for Three-Dimensional Rotations

Qualitative modeling

Building Qualitative Models of Thermodynamic Processes

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