scholarly journals Kinodynamic Planning in the Configuration Space via Admissible Velocity Propagation

2013 ◽  
Author(s):  
Quang-Cuong Pham ◽  
Stéphane Caron ◽  
Yoshihiko Nakamura
Keyword(s):  
Configuration Space ◽  
Admissible Velocity

scholarly journals Admissible velocity propagation: Beyond quasi-static path planning for high-dimensional robots

2016 ◽  
Vol 36 (1) ◽  
pp. 44-67 ◽  
Author(s):  
Quang-Cuong Pham ◽  
Stéphane Caron ◽  
Puttichai Lertkultanon ◽  
Yoshihiko Nakamura
Keyword(s):  
Path Planning ◽  
Configuration Space ◽  
Geometric Constraints ◽  
High Dimensional ◽  
Planning Problem ◽  
Admissible Velocity ◽  
Velocity Decomposition ◽  
Powerful Approach ◽  
Planning Problems ◽  
Fundamental Requirement

Path-velocity decomposition is an intuitive yet powerful approach to addressing the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler steps: first, a path is found in the configuration space that satisfies the geometric constraints (path planning), and second, a time-parameterization of that path satisfying the kinodynamic constraints is found. A fundamental requirement is that the path found in the first step must be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints during the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm – Admissible Velocity Propagation – which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path, while respecting the system’s kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

Computing Model for Vibratory Digging-Out of Sugar Beet Roots

2014 ◽  
Vol 1 (2) ◽  
pp. 52-60
Author(s):  
V. Bulgakov ◽  
V. Adamchuk ◽  
H. Kaletnyk
Keyword(s):  
Differential Equations ◽  
Sugar Beet ◽  
Vertical Plane ◽  
Forward Motion ◽  
Admissible Velocity ◽  
Beet Root ◽  
Optimum Speed ◽  
Analytical Research ◽  
Sugar Beet Root ◽  
The Given

The new design mathematical model of the sugar beet roots vibration digging-out process with the plowshare vibration digging working part has been created. In this case the sugar beet root is simulated as a solid body , while the plowshare vibration digging working part accomplishes fl uctuations in the longitudinal - vertical plane with the given amplitude and frequency in the process of work . The aim of the current research has been to determine the dependences between the design and kinematic parameters of the sugar beet roots vibra- tion digging-out technological process from soil , which provide the ir non-damage. Methods . For the aim ac- complishment, the methods of design mathematical models constructing based on the classical laws of me- chanics are applied. The solution of the obtained differential equations is accomplished with the PC involve- ment. Results . The differential equations of the sugar beet root’s motion in course of the vibration digging-out have been comprised . They allow to determine the admissible velocity of the vibration digging working part’s forward motion depending on the angular parameters of the latter. In the result of the computational simula- tion i.e., the solution of the obtained analytical dependence by PC, the graphic dependences of the admissible velocity of plowshare v ibration digging working part’s forward motion providing the extraction of the sugar beet root from soil without the breaking-off of its tail section have been determined. Conclusions . Due to the performed analytical research , it has been established that γ = 13 ... 16 ° , β = 20 ... 30 ° should be considered as the most reasonable values of γ and β angles of the vibration digging working part providing both its forward motion optimum speed and sugar beet root digging-out from the soil without damage . On the ground of the data obtained from the analytical rese arch, the new vibration digging working parts for the sugar beet roots have been designed; also the patents of Ukraine for the inventions have been obtained for them.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

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 Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

ADD-RRV for motion planning in complex environments

Robotica ◽  
2021 ◽  
pp. 1-18
Author(s):  
Peng Cai ◽  
Xiaokui Yue ◽  
Hongwen Zhang
Keyword(s):  
Principal Component Analysis ◽  
Motion Planning ◽  
Configuration Space ◽  
Principal Component ◽  
Component Analysis ◽  
Planning Method ◽  
Complex Environments ◽  
Local Configuration ◽  
Narrow Passage

Abstract In this paper, we present a novel sampling-based motion planning method in various complex environments, especially with narrow passages. We use online the results of the planner in the ADD-RRT framework to identify the types of the local configuration space based on the principal component analysis (PCA). The identification result is then used to accelerate the expansion similar to RRV around obstacles and through narrow passages. We also propose a modified bridge test to identify the entrance of a narrow passage and boost samples inside it. We have compared our method with known motion planners in several scenarios through simulations. Our method shows the best performance across all the tested planners in the tested scenarios.

scholarly journals Notes on cluster algebras and some all-loop Feynman integrals

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Qinglin Yang
Keyword(s):  
Configuration Space ◽  
Strong Evidence ◽  
Wilson Loop ◽  
Cluster Algebra ◽  
Cluster Algebras ◽  
Gauge Invariant ◽  
Feynman Integrals ◽  
Cluster Function ◽  
Invariant Description ◽  
Cluster Configuration

Abstract We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $$ {D}_2\simeq {A}_1^2 $$ D 2 ≃ A 1 2 , we show that penta-box ladder has an alphabet of D3 ≃ A3 and provide strong evidence that the alphabet of seven-point double-penta ladders can be identified with a D4 cluster algebra. We relate the symbol letters to the u variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop d log representation, which allows us to predict higher-loop alphabet recursively; by applying it to certain eight-point and nine-point double-penta ladders, we also find D5 and D6 cluster functions respectively.

scholarly journals Safe Path Planning Algorithms for Mobile Robots Based on Probabilistic Foam

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4156
Author(s):  
Luís B. P. Nascimento ◽  
Dennis Barrios-Aranibar ◽  
Vitor G. Santos ◽  
Diego S. Pereira ◽  
William C. Ribeiro ◽  
...  
Keyword(s):  
Path Planning ◽  
Mobile Robots ◽  
Configuration Space ◽  
Autonomous Robot ◽  
Breadth First Search ◽  
Propagation Process ◽  
Robot Systems ◽  
And Performance ◽  
Safe Path ◽  
High Clearance

The planning of safe paths is an important issue for autonomous robot systems. The Probabilistic Foam method (PFM) is a planner that guarantees safe paths bounded by a sequence of structures called bubbles that provides safe regions. This method performs the planning by covering the free configuration space with bubbles, an approach analogous to a breadth-first search. To improve the propagation process and keep the safety, we present three algorithms based on Probabilistic Foam: Goal-biased Probabilistic Foam (GBPF), Radius-biased Probabilistic Foam (RBPF), and Heuristic-guided Probabilistic Foam (HPF); the last two are proposed in this work. The variant GBPF is fast, HPF finds short paths, and RBPF finds high-clearance paths. Some simulations were performed using four different maps to analyze the behavior and performance of the methods. Besides, the safety was analyzed considering the new propagation strategies.

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