Optimal and Conforming Motion of a Point in a Constrained Plane

1994 ◽  
Vol 116 (2) ◽  
pp. 474-479 ◽  
Author(s):  
C. Ahrikencheikh ◽  
A. A. Seireg ◽  
B. Ravani
Keyword(s):  
Time Complexity ◽  
Automatic Generation ◽  
Geometric Constraints ◽  
Computational Time ◽  
Motion Generation ◽  
Optimal Point ◽  
Computational Tools ◽  
Kinematic Constraints ◽  
Generation Algorithm ◽  
Efficient Representation

This paper deals with automatic generation of the motion of a point under both geometric and kinematic constraints. Optimal point paths are generated which are not only free of collisions with polygonal obstacles representing geometric constraints but also conform to kinematic constraints such as limits on velocity and acceleration. A specified minimum clearance from the boundaries of the obstacles is also satisfied. The new computational tools employed are an efficient representation of the free space, and a new motion generation algorithm with a computational time complexity of only O(n3 log n), where n is the total number of obstacle vertices. The algorithm finds the shortest or fastest curved path that also conforms with preset constraints on the motion of the point.

Optimal and Conforming Motion of a Point in a Constrained Plane

1989 ◽  
Author(s):  
C. Ahrikencheikh ◽  
A. A. Seireg ◽  
B. Ravani
Keyword(s):  
Free Space ◽  
Time Complexity ◽  
Velocity Vector ◽  
Automatic Generation ◽  
Geometric Constraints ◽  
Computational Time ◽  
Motion Generation ◽  
Optimal Point ◽  
Generation Algorithm

Abstract This paper deals with automatic generation of motion of a point under both geometric and non-geometric constraints. Optimal point paths are generated which are not only free of collisions with polygonal obstacles representing geometric constraints but also conform to non-geometric constraints such as speed of the motion, a maximum allowable change in the velocity vector and a minimum clearance from the obstacle boundaries. The concept of passage networks and conforming paths on the network are introduced. These are used to provide a new representation of the free space as well as a motion generation algorithm with a computational time complexity of only O(n3.log(n)), where n designates the total number of obstacle vertices. The algorithm finds the shortest or fastest (curved) path that also conforms with preset constraints on the motion of the point. The point paths generated are proved to be optimal while conforming to the constraints.

scholarly journals A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen
Keyword(s):  
Stochastic Programming ◽  
Benders Decomposition ◽  
Equivalent Model ◽  
Computational Time ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Equivalent ◽  
Location Routing ◽  
Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

Modal Reduced Order Model for Vision Sensing of IPMC Actuator

2006 ◽  
Vol 326-328 ◽  
pp. 1523-1526
Author(s):  
Il Kweon Oh ◽  
Seong Won Yeom ◽  
Dong Weon Lee
Keyword(s):  
Reduced Order Model ◽  
Mode Shapes ◽  
Computational Time ◽  
Transverse Displacement ◽  
Metal Composite ◽  
Motion Generation ◽  
Order Model ◽  
Lower Mode ◽  
Reduced Order ◽  
Vision Sensing

In order to control the IPMC (Ionic Polymer Metal Composite) actuators, it is necessary to use a vision sensing system and a reduced order model from the vision sensing data. In this study, the MROVS (Modal Reduced Order Vision Sensing) model using the least square method has been developed for implementation of the biomimetic motion generation. The simulated transverse displacement is approximated with a sum of the lower mode shapes of the cantilever beam. The NIPXI 1409 image acquisition board and CCD camera (XC-HR50) are used in the experimental setup. Present results show that the MROVS model can efficiently process the vision sensing of the biomimetic IPMC actuator with cost-effective computational time.

Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

2018 ◽  
Author(s):  
Vincent Delos ◽  
Santiago Arroyave-Tobón ◽  
Denis Teissandier
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Geometric Constraints ◽  
Computational Time ◽  
Manufacturing Defects ◽  
Design Tolerance ◽  
Polyhedral Objects ◽  
The Difference ◽  
Bounded Sets ◽  
Accumulation Of Defects

In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

Accurate and efficient representation of intramolecular energy in ab initio generation of crystal structures. II. Smoothed intramolecular potentials

2019 ◽  
Vol 75 (3) ◽  
pp. 423-433 ◽  
Author(s):  
Isaac J. Sugden ◽  
Claire S. Adjiman ◽  
Constantinos C. Pantelides
Keyword(s):  
Structure Prediction ◽  
Weighted Average ◽  
Lattice Energy ◽  
Comparative Investigation ◽  
Computational Effort ◽  
Flufenamic Acid ◽  
Computational Time ◽  
Crystal Structure Prediction ◽  
Efficient Representation ◽  
First Time

The application of crystal structure prediction (CSP) to industrially relevant molecules requires the handling of increasingly large and flexible compounds. A revised model for the effect of molecular flexibility on the lattice energy that removes the discontinuities and non-differentiabilities present in earlier models (Sugden et al., 2016), with a view to improving the performance of CSP is presented. The approach is based on the concept of computing a weighted average of local models, and has been implemented within the CrystalPredictor code. Through the comparative investigation of several compounds studied in earlier literature, it is shown that this new model results in large reductions in computational effort (of up to 65%) and in significant increases in reliability. The approach is further applied to investigate, for the first time, the computational polymorphic landscape of flufenamic acid for Z′ = 1 structures, resulting in the successful identification of all three experimentally resolved polymorphs within reasonable computational time.

scholarly journals Biclique Cryptanalysis on the Full Crypton-256 and mCrypton-128

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Junghwan Song ◽  
Kwanhyung Lee ◽  
Hwanjin Lee
Keyword(s):  
Computational Complexity ◽  
Bipartite Graph ◽  
Time Complexity ◽  
Computational Time

Biclique cryptanalysis is an attack which reduces the computational complexity by finding a biclique which is a kind of bipartite graph. We show a single-key full-round attack of the Crypton-256 and mCrypton-128 by using biclique cryptanalysis. In this paper, 4-round bicliques are constructed for Crypton-256 and mCrypton-128. And these bicliques are used to recover master key for the full rounds of Crypton-256 and mCrypton-128 with the computational complexities of 2253.78and 2126.5, respectively. This is the first known single-key full-round attack on the Crypton-256. And our result on the mCrypton-128 has superiority over known result of biclique cryptanalysis on the mCrypton-128 which constructs 3-round bicliques in terms of computational time complexity.

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