Signals and their functional representation

2018 ◽  
pp. 1-39
Author(s):  
Alexander D. Poularikas
Keyword(s):  
Functional Representation

scholarly journals A robotic grasping approach with elliptical cone-based potential fields under disturbed scenes

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142098573
Author(s):  
Wenjie Geng ◽  
Zhiqiang Cao ◽  
Zhonghui Li ◽  
Yingying Yu ◽  
Fengshui Jing ◽  
...  
Keyword(s):  
Principal Component ◽  
Major Axis ◽  
Target Object ◽  
Potential Fields ◽  
Single Shot ◽  
Robotic Grasping ◽  
Vertical Projection ◽  
Convex Curves ◽  
Functional Representation ◽  
Continuous Potential

Vision-based grasping plays an important role in the robot providing better services. It is still challenging under disturbed scenes, where the target object cannot be directly grasped constrained by the interferences from other objects. In this article, a robotic grasping approach with firstly moving the interference objects is proposed based on elliptical cone-based potential fields. Single-shot multibox detector (SSD) is adopted to detect objects, and considering the scene complexity, Euclidean cluster is also employed to obtain the objects without being trained by SSD. And then, we acquire the vertical projection of the point cloud for each object. Considering that different objects have different shapes with respective orientation, the vertical projection is executed along its major axis acquired by the principal component analysis. On this basis, the minimum projected envelope rectangle of each object is obtained. To construct continuous potential field functions, an elliptical-based functional representation is introduced due to the better matching degree of the ellipse with the envelope rectangle among continuous closed convex curves. Guided by the design principles, including continuity, same-eccentricity equivalence, and monotonicity, the potential fields based on elliptical cone are designed. The current interference object to be grasped generates an attractive field, whereas other objects correspond to repulsive ones, and their resultant field is used to solve the best placement of the current interference object. The effectiveness of the proposed approach is verified by experiments.

A Functionalization of Logical Kits

1991 ◽  
Vol 15 (2) ◽  
pp. 180-186
Author(s):  
Antoni Wiweger
Keyword(s):  
Functional Representation

Relations between general logical kits and kits of some particular type, called functional kits, are investigated. The functional representation R(K) of a logical kit K is constructed and it is shown that R(K) is a reflection of K in the category of kits and A-surjective kit homomorphisms with respect to the subcategory of functional kits.

scholarly journals A Functional Representation Model Facilitating Design Space Expansion

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Wei Xu ◽  
Ke Zhao ◽  
Yatao Li ◽  
Peitao Cheng
Keyword(s):  
Set Theory ◽  
Propositional Logic ◽  
Design Space ◽  
Functional Representation ◽  
Functional Reasoning ◽  
Variation Range ◽  
Relational Calculus ◽  
Event Model ◽  
Space Expansion ◽  
The Stability

This paper addresses the functional representation based on the event model. In the event model, the ontology is defined based on the theory of propositional logic to describe the connotation of the event, and the variant is defined based on the theories of domain relational calculus and set theory to express the variation range of the event, which is alterable part of the event under the constraints of the ontology. Function is an important concept in conceptual design and has its connotation and extension. The functional representation is proposed based on the event model. The ontology of event is used to describe the connotation of function and to reflect the stability of function. The variant of the event is used to represent the extension and to incarnate the variety of function. The extension of function is the change range of function under the constraints of the connotation. The proposed functional representation divides the function into the immutable part and the alterable part, facilitating the expansion of design space. A functional reasoning model is also put forward based on the event model to support the function reasoning on the computers. Finally, a simple case validates the feasibility of the model.

Product Data Management Systems: State-of-the-Art and the Future

1997 ◽  
Author(s):  
Taner Bilgiç ◽  
Dennis Rock
Keyword(s):  
Data Management ◽  
State Of The Art ◽  
Product Data Management ◽  
Management Systems ◽  
Systems Management ◽  
Engineering Project ◽  
Product Data ◽  
Current State ◽  
Functional Representation ◽  
Near Future

Abstract We survey the current state-of-the-art in (commercial) Product Data Management (PDM) systems. After identifying the major functions of PDM systems, we indicate various shortcomings of the current PDM technology. An important shortcoming is in the representation and use of functions. We review the functional representation literature in the context of PDM technology. Systems management aspects of an engineering project is also commented on. We believe these two areas are the next two challenges awaiting PDM technology in the near future.

A Statistical Approach to Ranking Similarities of Three Function Structure Groups Using Directed Graphs

2018 ◽  
Author(s):  
Briana M. Lucero ◽  
Matthew J. Adams
Keyword(s):  
Statistical Approach ◽  
Directed Graphs ◽  
Proof Of Concept ◽  
Function Structure ◽  
Fundamental Properties ◽  
Design Engineers ◽  
Functional Representation ◽  
Structure Databases ◽  
Further Development ◽  
Function Structures

Prior efforts in the study of engineering design employed various approaches to decompose product design. Design engineers use functional representation, and more precisely function structures, to define a product’s functionality. However, significant barriers remain to objectively quantifying the similarity between two function structures, even for the same product when developed by multiple designers. For function-structure databases this means that function-structures are implicitly categorized leaving the possibility of incorrect categorization and reducing efficacy of returned analogous correlations. Improvements to efficacy in database organization and queries are possible by objectively quantifying the similarity between function structures. The proposed method exploits fundamental properties of function-structures and design taxonomies. We convert function-structures into directed graphs (digraphs) and equivalent adjacency matrices. The conversion maintains the directed (function → flow → function) progression inherent to function-structures and enables the transformation of the function-structure into a standardized graph. For design taxonomies (e.g. D-APPS), graph nodes represent flows in a consistent (but arbitrary) ordering. By exploiting the directional properties of function-structures and defining the flows as the graphical nodes, the objective and standardized comparison of two function-structures becomes feasible. We statistically quantify the association between digraphs using the Pearson Product Moment Correlation (PPMC) for both within-group and between-group comparisons. The method was tested on three product types (ball thrower, food processor, and an ice cream maker) with function-structures defined by various designers. The method suggested herein is provided as a proof-of-concept with suggested verification and validation approaches for further development.

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