Output-Sensitive Computation of All Form-Closure Grasps of a Semi-Algebraic Set

2006 ◽  
Author(s):  
Jae-Sook Cheong ◽  
A.F. van der Stappen
Keyword(s):  
Algebraic Set ◽  
Form Closure

scholarly journals On the Cardinality of A Semi-Algebraic Set

1994 ◽  
Vol 1 (3) ◽  
pp. 277-286
Author(s):  
G. Khimshiashvili
Keyword(s):  
Quadratic Forms ◽  
Real Closed Field ◽  
Closed Field ◽  
Algebraic Subset ◽  
Algebraic Set

Abstract It is shown that the cardinality of a finite semi-algebraic subset over a real closed field can be computed in terms of signatures of effectively constructed quadratic forms.

scholarly journals Exploiting Sparsity for Semi-Algebraic Set Volume Computation

2021 ◽  
Author(s):  
Matteo Tacchi ◽  
Tillmann Weisser ◽  
Jean Bernard Lasserre ◽  
Didier Henrion
Keyword(s):  
Algebraic Set ◽  
Volume Computation

scholarly journals Joining of plastic‐metal hybrid components by overmoulding of specially designed form‐closure elements

2021 ◽  
Vol 52 (4) ◽  
pp. 367-378
Author(s):  
S. Wurzbacher ◽  
S. Gach ◽  
U. Reisgen ◽  
C. Hopmann
Keyword(s):  
Plastic Metal ◽  
Form Closure

scholarly journals Numerical computation of the genus of an irreducible curve within an algebraic set

2011 ◽  
Vol 215 (8) ◽  
pp. 1844-1851 ◽  
Author(s):  
Daniel J. Bates ◽  
Chris Peterson ◽  
Andrew J. Sommese ◽  
Charles W. Wampler
Keyword(s):  
Numerical Computation ◽  
Irreducible Curve ◽  
Algebraic Set

Equations and Complexity for the Dubois–Efroymson Dimension Theorem

2009 ◽  
Vol 52 (2) ◽  
pp. 224-236
Author(s):  
Riccardo Ghiloni
Keyword(s):  
Real Closed Field ◽  
Closed Field ◽  
Algebraic Subset ◽  
Algebraically Closed Field ◽  
Algebraic Set ◽  
Real Algebraic Set ◽  
Nonsingular Point ◽  
Minimum Integer ◽  
The Ideal

AbstractLetRbe a real closed field, letX⊂Rnbe an irreducible real algebraic set and letZbe an algebraic subset ofXof codimension ≥ 2. Dubois and Efroymson proved the existence of an irreducible algebraic subset ofXof codimension 1 containingZ. We improve this dimension theorem as follows. Indicate by μ the minimum integer such that the ideal of polynomials inR[x1, … ,xn] vanishing onZcan be generated by polynomials of degree ≤ μ. We prove the following two results: (1) There exists a polynomialP∈R[x1, … ,xn] of degree≤ μ+1 such thatX∩P–1(0) is an irreducible algebraic subset ofXof codimension 1 containingZ. (2) LetFbe a polynomial inR[x1, … ,xn] of degreedvanishing onZ. Suppose there exists a nonsingular pointxofXsuch thatF(x) = 0 and the differential atxof the restriction ofFtoXis nonzero. Then there exists a polynomialG∈R[x1, … ,xn] of degree ≤ max﹛d, μ + 1﹜ such that, for eacht∈ (–1, 1) \ ﹛0﹜, the set ﹛x∈X|F(x) +tG(x) = 0﹜ is an irreducible algebraic subset ofXof codimension 1 containingZ. Result (1) and a slightly different version of result (2) are valid over any algebraically closed field also.

Multi-Agent Form Closure Capture of a Generic 2D Polygonal Object Based on Projective Path Planning

2006 ◽  
Author(s):  
Pankaj Sharma ◽  
Anupam Saxena ◽  
Ashish Dutta
Keyword(s):  
Path Planning ◽  
Contact Point ◽  
Point Contact ◽  
Object Boundary ◽  
Actual Object ◽  
Contact Points ◽  
Correct Orientation ◽  
Novel Approach ◽  
Form Closure ◽  
Multi Agent

The study of multi-agent capture and manipulation of an object has been an area of active interest for many researchers. This paper presents a novel approach using Genetic Algorithm to determine the optimal contact points and the total number of agents (mobile robots) required to capture a stationary generic 2D polygonal object. After the goal points are determined the agents then reach their respective goals using a decentralized projective path planning algorithm. Form closure of the object is obtained using the concept of accessibility angle. The object boundary is first expanded and the robots reach the expanded object goal points and then converge on the actual object. This ensures that the agents reach the actual goal points at the same time and have the correct orientation. Frictionless point contact between the object and robots is assumed. The shape of the robot is considered a circle such that it can only apply force in outward radial direction from its center and along the normal to the object boundary at the contact point. Simulations results are presented that prove the effectiveness of the proposed method.

Algebraic test of relative form closure grasps with its implementation

2014 ◽  
Vol 57 (7) ◽  
pp. 1401-1410 ◽  
Author(s):  
YouLun Xiong ◽  
Tao Xiong ◽  
YuHui Wang
Keyword(s):  
Form Closure ◽  
Relative Form ◽  
Algebraic Test

The Pierce-Birkhoff Conjecture for Curves

1992 ◽  
Vol 44 (6) ◽  
pp. 1262-1271 ◽  
Author(s):  
Murray Marshall
Keyword(s):  
Real Closed Field ◽  
Noetherian Rings ◽  
Closed Field ◽  
Polynomial Functions ◽  
Piecewise Polynomial ◽  
Algebraic Set ◽  
Dedekind Domains ◽  
Piecewise Polynomial Functions ◽  
Relative Case

AbstractThe results obtained extend Madden’s result for Dedekind domains to more general types of 1-dimensional Noetherian rings. In particular, these results apply to piecewise polynomial functions t:C → R where R is a real closed field and C ⊆ Rn is a closed 1-dimensional semi-algebraic set, and also to the associated “relative” case where t, C are defined over some subfield K ⊆ R.

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