Related Experiment Video
Updated: Oct 8, 2025
06:35
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
8.2K
Parametrized topological complexity of poset-stratified spaces
1Institute of Social Sciences, School of Humanities and Social Sciences, Academic Assembly, Shinshu University, 3-3-1 Asahi, Matsumoto, Nagano 390-8621 Japan.
Journal of Applied and Computational Topology
|December 27, 2021
Summary
This study introduces motion planning algorithms for fiberwise spaces, crucial for robot navigation. It computes parametrized topological complexity to minimize boundary crossings in robot motion planning.
Area of Science:
- Algebraic Topology
- Robotics
- Computational Geometry
Background:
- Parametrized motion planning algorithms are essential for robot navigation in complex environments.
- Topological complexity quantifies the difficulty of motion planning without crossing boundaries.
Purpose of the Study:
- To study parametrized motion planning algorithms for fiberwise spaces over a poset.
- To compute the parametrized topological complexity of these spaces.
Main Methods:
- Investigating algorithms that assign paths within a space decomposed into subspaces indexed by a poset.
- Developing methods to ensure paths do not cross boundaries between these subspaces.
Main Results:
- The parametrized topological complexity is determined.
- This complexity is shown to be one less than the minimum number of local algorithms required for non-cross-border motion planning.
Conclusions:
- The findings provide a theoretical framework for designing efficient robot motion planning strategies.
- This work contributes to understanding the relationship between topological complexity and practical motion planning algorithms.
Related Concept Videos
01:18Castigliano's Theorem
578
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
578
01:15Routh-Hurwitz Criterion I
357
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
357
01:19Routh-Hurwitz Criterion II
461
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
461
01:12Theorems of Pappus and Guldinus: Problem Solving
832
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
832
01:14Stability of structures
269
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
269
01:14Castigliano's Theorem: Problem Solving
805
The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam...
805