scholarly journals Topological representation of cloth state for robot manipulation

2021 ◽  
Author(s):  
Fabio Strazzeri ◽  
Carme Torras
Keyword(s):  
State Space ◽  
Configuration Space ◽  
Common Ground ◽  
Low Complexity ◽  
Flag Manifold ◽  
Infinite Dimensional ◽  
Articulated Objects ◽  
Research Goal ◽  
State Graphs ◽  
Deformable Materials

AbstractForty years ago the notion of configuration space (C-space) revolutionised robot motion planning for rigid and articulated objects. Despite great progress, handling deformable materials has remained elusive because of their infinite-dimensional shape-state space. Finding low-complexity representations has become a pressing research goal. This work tries to make a tiny step in this direction by proposing a state representation for textiles relying on the C-space of some distinctive points. A stratification of the configuration space for n points in the cloth is derived from that of the flag manifold, and topological techniques to determine adjacencies in manipulation-centred state graphs are developed. Their algorithmic implementation permits obtaining cloth state–space representations of different granularities and tailored to particular purposes. An example of their usage to distinguish between cloth states having different manipulation affordances is provided. Suggestions on how the proposed state graphs can serve as a common ground to link the perception, planning and manipulation of textiles are also made.

scholarly journals Eliciting probabilistic expectations: Collaborations between psychologists and economists

2017 ◽  
Vol 114 (13) ◽  
pp. 3297-3304 ◽  
Author(s):  
Wändi Bruine de Bruin ◽  
Baruch Fischhoff
Keyword(s):  
Common Ground ◽  
Research Process ◽  
Economic Modeling ◽  
Common Language ◽  
Mutual Benefit ◽  
Purchasing Decisions ◽  
Major Research ◽  
Sense Of Ownership ◽  
Research Goal ◽  
Essential Support

We describe two collaborations in which psychologists and economists provided essential support on foundational projects in major research programs. One project involved eliciting adolescents’ expectations regarding significant future life events affecting their psychological and economic development. The second project involved eliciting consumers’ expectations regarding inflation, a potentially vital input to their investment, saving, and purchasing decisions. In each project, we sought questions with the precision needed for economic modeling and the simplicity needed for lay respondents. We identify four conditions that, we believe, promoted our ability to sustain these transdisciplinary collaborations and coproduce the research: (i) having a shared research goal, which neither discipline could achieve on its own; (ii) finding common ground in shared methodology, which met each discipline’s essential evidentiary conditions, but without insisting on its culturally acquired tastes; (iii) sharing the effort throughout, with common language and sense of ownership; and (iv) gaining mutual benefit from both the research process and its products.

scholarly journals State space decomposition for non-autonomous dynamical systems

2011 ◽  
Vol 141 (5) ◽  
pp. 957-974 ◽  
Author(s):  
Xiaopeng Chen ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
State Space ◽  
Decomposition Theorem ◽  
Navier Stokes ◽  
Locally Compact ◽  
Infinite Dimensional ◽  
The Lorenz System ◽  
A Chain ◽  
Autonomous Dynamical Systems

The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.

FEYNMAN FORMULAS FOR AN INFINITE-DIMENSIONAL 𝔭-ADIC HEAT TYPE EQUATION

2011 ◽  
Vol 14 (01) ◽  
pp. 137-148 ◽  
Author(s):  
OLGA BELOSHAPKA
Keyword(s):  
Cauchy Problem ◽  
Configuration Space ◽  
Short Note ◽  
Type Equation ◽  
Spatial Variable ◽  
Feynman Formula ◽  
Cartesian Products ◽  
Infinite Dimensional

Smolyanov has introduced1 the term "Feynman formula" (in the configuration space) for the representation of a solution of a Cauchy problem by limit of integrals over finite Cartesian products of the domain of the solution when the number of multipliers tends to infinity. In this paper, such formulas (first written by Smolyanov, Shamarov and Kpekpassi in a short note2) are proved for a family of heat type equations where the spatial variable runs over 𝔭-adic space of countable sequences. Equations with 𝔭-adic variables describe, for example, the dynamics of proteins.

NONLINEAR PROBLEMS IN INFINITE INTERACTING PARTICLE SYSTEMS

2008 ◽  
Vol 11 (02) ◽  
pp. 179-211 ◽  
Author(s):  
ROBERT OLKIEWICZ ◽  
LIHU XU ◽  
BOGUSŁAW ZEGARLIŃSKI
Keyword(s):  
Configuration Space ◽  
Interacting Particle Systems ◽  
Nonlinear Problems ◽  
Particle Systems ◽  
Markov Semigroups ◽  
Infinite Dimensional ◽  
Interacting Particle

We introduce and study a class of nonlinear jump type Markov semigroups for systems with infinite dimensional configuration space.

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