The Kinematics of Containment for N-Dimensional Ellipsoids

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Sipu Ruan ◽  
Jianzhong Ding ◽  
Qianli Ma ◽  
Gregory S. Chirikjian
Keyword(s):  
Motion Planning ◽  
Lower Bounds ◽  
Convex Bodies ◽  
Practical Applications ◽  
Constraint Equations ◽  
Specific Configuration ◽  
Different Shapes ◽  
2D And 3D ◽  
Planning Problems ◽  
Simple Convex

Knowing the set of allowable motions of a convex body moving inside a slightly larger one is useful in applications such as automated assembly mechanisms, robot motion planning, etc. The theory behind this is called the “kinematics of containment (KC).” In this article, we show that when the convex bodies are ellipsoids, lower bounds of the KC volume can be constructed using simple convex constraint equations. In particular, we study a subset of the allowable motions for an n-dimensional ellipsoid being fully contained in another. The problem is addressed in both algebraic and geometric ways, and two lower bounds of the allowable motions are proposed. Containment checking processes for a specific configuration of the moving ellipsoid and the calculations of the volume of the proposed lower bounds in the configuration space (C-space) are introduced. Examples for the proposed lower bounds in the 2D and 3D Euclidean space are implemented, and the corresponding volumes in C-space are compared with different shapes of the ellipsoids. Practical applications using the proposed theories in motion planning problems and parts-handling mechanisms are then discussed.

Lower Bounds of the Allowable Motions of One N-Dimensional Ellipsoid Contained in Another

2018 ◽  
Author(s):  
Sipu Ruan ◽  
Gregory S. Chirikjian ◽  
Jianzhong Ding
Keyword(s):  
Closed Form ◽  
Lower Bounds ◽  
Automated Assembly ◽  
First Order ◽  
Order Algebraic ◽  
Specific Configuration ◽  
Different Shapes ◽  
2D And 3D ◽  
Minkowski Difference

This paper studies the representations of a subset of the allowable motions for an N-dimensional ellipsoid inside another slightly larger ellipsoid without collision based on the idea of the Kinematics of Containment. As an extension to the previous work on the closed-form lower bounds, this paper proposes another two lower bounds based on the first-order algebraic condition of containment and the closed-form Minkowski difference between two ellipsoids respectively. Querying processes for a specific configuration of the moving ellipsoid and the calculations of the volume of the proposed lower bounds in configuration space (C-space) are introduced. Examples for the proposed lower bounds in 2D and 3D Euclidean space are implemented and the corresponding motion volumes in C-space are compared with different shapes of the ellipsoids. Finally a case study of the application on automated assembly is introduced.

scholarly journals Adversarial Actor-Critic Method for Task and Motion Planning Problems Using Planning Experience

2019 ◽  
Vol 33 ◽  
pp. 8017-8024 ◽  
Author(s):  
Beomjoon Kim ◽  
Leslie Pack Kaelbling ◽  
Tomás Lozano-Pérez
Keyword(s):  
Motion Planning ◽  
Vector Representation ◽  
Search Trees ◽  
Training Set ◽  
Fixed Length ◽  
Different Shapes ◽  
Robot Task ◽  
High Level ◽  
Robot Configurations ◽  
Planning Problems

We propose an actor-critic algorithm that uses past planning experience to improve the efficiency of solving robot task-and-motion planning (TAMP) problems. TAMP planners search for goal-achieving sequences of high-level operator instances specified by both discrete and continuous parameters. Our algorithm learns a policy for selecting the continuous parameters during search, using a small training set generated from the search trees of previously solved instances. We also introduce a novel fixed-length vector representation for world states with varying numbers of objects with different shapes, based on a set of key robot configurations. We demonstrate experimentally that our method learns more efficiently from less data than standard reinforcementlearning approaches and that using a learned policy to guide a planner results in the improvement of planning efficiency.

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

scholarly journals HMCTS-OP: Hierarchical MCTS Based Online Planning in the Asymmetric Adversarial Environment

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 719
Author(s):  
Lina Lu ◽  
Wanpeng Zhang ◽  
Xueqiang Gu ◽  
Xiang Ji ◽  
Jing Chen
Keyword(s):  
Computational Complexity ◽  
State Space ◽  
Planning Horizon ◽  
Search Space ◽  
Monte Carlo Tree Search ◽  
Practical Applications ◽  
Online Planning ◽  
Planning Framework ◽  
Planning Methods ◽  
Planning Problems

The Monte Carlo Tree Search (MCTS) has demonstrated excellent performance in solving many planning problems. However, the state space and the branching factors are huge, and the planning horizon is long in many practical applications, especially in the adversarial environment. It is computationally expensive to cover a sufficient number of rewarded states that are far away from the root in the flat non-hierarchical MCTS. Therefore, the flat non-hierarchical MCTS is inefficient for dealing with planning problems with a long planning horizon, huge state space, and branching factors. In this work, we propose a novel hierarchical MCTS-based online planning method named the HMCTS-OP to tackle this issue. The HMCTS-OP integrates the MAXQ-based task hierarchies and the hierarchical MCTS algorithms into the online planning framework. Specifically, the MAXQ-based task hierarchies reduce the search space and guide the search process. Therefore, the computational complexity is significantly reduced. Moreover, the reduction in the computational complexity enables the MCTS to perform a deeper search to find better action in a limited time. We evaluate the performance of the HMCTS-OP in the domain of online planning in the asymmetric adversarial environment. The experiment results show that the HMCTS-OP outperforms other online planning methods in this domain.

INFLUENCE OF SOME GEOMETRICAL PARAMETERS ON THE CHARACTERISTICS OF PREFILMING TWIN-FLUID ATOMIZATION

2014 ◽  
Vol 38 (3) ◽  
pp. 391-404
Author(s):  
Jiafeng Yao ◽  
Shinji Furusawa ◽  
Akimaro Kawahara ◽  
Michio Sadatomi
Keyword(s):  
Great Influence ◽  
Geometrical Parameters ◽  
Porous Fiber ◽  
Spray Characteristics ◽  
Fiber Ring ◽  
Practical Applications ◽  
Internal Mixing ◽  
Mixing Chamber ◽  
Liquid Atomization ◽  
Different Shapes

Geometries are considered to have a great influence on the spray characteristics of atomizers. In the present study, we studied a prefilming twin-fluid atomizer patented by Sadatomi and Kawahara (2012), in which liquid atomization is implemented by supplying compressed air alone into an internal mixing chamber, and water is automatically sucked by the negative pressure induced by an orifice. In the experiments, we studied spray characteristics influenced by the geometrical parameters, such as orifices in different opening area ratios and different shapes, porous rings with different porous diameters, and different atomizer sizes. Higher spray performance can be obtained by a small sized atomizer with a circular orifice in opening area ratio of 0.429 and a porous fiber ring with porosity of 25 μm. The present results provide a significant guidance for practical applications with different requirements of spray characteristics.

scholarly journals Maximizing the Coverage of Roadmap Graph for Optimal Motion Planning

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
Jae-Han Park ◽  
Tae-Woong Yoon
Keyword(s):  
Motion Planning ◽  
Industry 4.0 ◽  
Industrial Robot ◽  
Efficient Solutions ◽  
Industrial Robots ◽  
Optimal Motion ◽  
Optimal Motion Planning ◽  
Planning Problems ◽  
Complex Planning ◽  
Satisfactory Quality

Automated motion-planning technologies for industrial robots are critical for their application to Industry 4.0. Various sampling-based methods have been studied to generate the collision-free motion of articulated industrial robots. Such sampling-based methods provide efficient solutions to complex planning problems, but their limitations hinder the attainment of optimal results. This paper considers a method to obtain the optimal results in the roadmap algorithm that is representative of the sampling-based method. We define the coverage of a graph as a performance index of its optimality as constructed by a sampling-based algorithm and propose an optimization algorithm that can maximize graph coverage in the configuration space. The proposed method was applied to the model of an industrial robot, and the results of the simulation confirm that the roadmap graph obtained by the proposed algorithm can generate results of satisfactory quality in path-finding tests under various conditions.

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