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Towards Trajectory Planning of a Robot Manipulator with Computer Algebra using Bézier Curves for Obstacle Avoidance 10

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Towards Trajectory Planning of a Robot Manipulator with Comp...

10th International Symposium on Symbolic Computation in Software Science - Work in Progress Workshop, SCSS 2024 WiP

作者： Hatakeyama, Ryo Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

This paper discusses the trajectory planning of a robot manipulator with computer algebra. In the operation of robot manipulators, it is important to make the trajectory of the end effector so that it does not collide with obstacles. For this purpose, we have proposed a method of generating a method of trajectory planning using cubic spline curves. However, the method has the disadvantage that the trajectory may not be included in the feasible region of the manipulator, thus an extra test for the inclusion of the curve is needed. In this paper, we propose a new method of generating a trajectory using Bézier curves, which is guaranteed to be included in the feasible region. © 2024 CEUR-WS. All rights reserved.

关键词： Trajectories

An Optimized Path Planning of Manipulator with Spline Curves Using Real Quantifier Elimination Based on Comprehensive Gröbner Systems 10

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An Optimized Path Planning of Manipulator with Spline Curves...

10th International Symposium on Symbolic Computation in Software Science - Work in Progress Workshop, SCSS 2024 WiP

作者： Shirato, Yusuke Oka, Natsumi Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and orientation of the end-effector. Furthermore, the path planning problem seeks a trajectory between two points. Traditional approaches in computer algebra have utilized Gröbner basis computations to solve these problems, offering a global solution but at a high computational cost. To overcome the issue, the present authors have proposed a novel approach that employs the Comprehensive Gröbner System (CGS) and CGS-based quantifier elimination (CGS-QE) methods to efficiently solve the inverse kinematics problem and certify the existence of solutions for trajectory planning. This paper extends these methods by incorporating smooth curves via cubic spline interpolation for path planning and optimizing joint configurations using shortest path algorithms to minimize the sum of joint configurations along a trajectory. This approach significantly enhances the manipulator's ability to navigate complex paths and optimize movement sequences. © 2024 CEUR-WS. All rights reserved.

关键词： Inverse kinematics

Solving Estimation Problems Using Minimax Polynomials and Gröbner Bases 10

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Solving Estimation Problems Using Minimax Polynomials and Gr...

10th International Symposium on Symbolic Computation in Software Science - Work in Progress Workshop, SCSS 2024 WiP

作者： Kuramochi, Kenta Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

We propose a method for solving the speech direction estimation problem by computer algebra. The method is based on the function approximation using the minimax polynomial. The minimax polynomial is obtained by an iterative method called the Remez exchange algorithm, in which Gröbner bases computation is employed. We present an effective way to compute the minimax polynomial using Gröbner bases. © 2024 CEUR-WS. All rights reserved.

关键词： Iterative methods

HARADA’S CONJECTURE II FOR THE FINITE GENERAL LINEAR GROUPS AND UNITARY GROUPS

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arXiv 2023年

作者： Masahiro, Sugimoto Doctoral Program in Mathematics Degree Programs in Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Japan

K. Harada conjectured for any finite group G, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when G is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently *** Codes 20C15 Copyright © 2023, The Authors. All rights reserved.

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Exploring 3D Reconstruction with Drone Images: Advances and Challenges in Urban Environments 50

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Exploring 3D Reconstruction with Drone Images: Advances and ...

50th Annual Conference of the IEEE Industrial Electronics Society, IECON 2024

作者： Miranda Baldivieso, Thiago João da Silva Batista, Taise Grazielle Chagas, Fabio Suim Rodrigues Velho, Luiz Carlos Pacheco Ferreira Rosa, Paulo Fernando Defense Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil State Institute of the Environment Inea RJ Rio de Janeiro Brazil Department of Science and Industry systems University of South-Eastern Norway Kongsberg Norway Department of Computer Graphics Institute for Pure and Applied Mathematics Rio de Janeiro Brazil Electrical Engineering Graduate Program Military Institute of Engineering Rio de Janeiro Brazil

ISBN: (纸本)9781665464543

This working-in-progress paper aims to present a three-dimensional reconstruction using aerial images in different environments. The experiments were conducted with aircraft in both external and internal settings, starting with image acquisition, followed by the application of specific photogrammetry software-both commercial and open-source-and concluding with a qualitative evaluation of the results. © 2024 IEEE.

关键词： Aerial photography

PRIKRY-TYPE FORCINGS AFTER COLLAPSING A HUGE CARDINAL

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arXiv 2022年

作者： Tsukuura, Kenta Doctoral Program in Mathematics Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan

Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's conjecture, polarized partition relations, and transfer principles for chromatic numbers of graphs. In this paper, we study these in the case of the successors of singular cardinals. In particular, we show that Prikry forcing preserves the centeredness of ideals but kills the layeredness. We also study (Equation presented) in the extension by Prikry forcing at µ.MSC Codes 03E35, 03E40, 03E55 Copyright © 2022, The Authors. All rights reserved.

关键词： Combinatorial mathematics

PRIKRY-TYPE FORCING AND THE SET OF POSSIBLE COFINALITIES

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arXiv 2022年

作者： Tsukuura, Kenta Doctoral Program in Mathematics Degree Programs in Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan

It is known that the set of possible cofinalities pcf(A) has good properties if A is a progressive interval of regular cardinals. In this paper, we give an interval of regular cardinals A such that pcf(A) has no good properties in the presence of a measurable cardinal, or in generic extensions by Prikry-type *** Codes 03E04, 03E35, 03E55 Copyright © 2022, The Authors. All rights reserved.

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THE EXTENT OF SATURATION OF INDUCED IDEALS

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arXiv 2022年

作者： Tsukuura, Kenta Doctoral Program in Mathematics Degree Programs in Pure and Applied Sciences Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan

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Strongly damped wave equations with mass-like terms of the logarithmic-Laplacian

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arXiv 2022年

作者： Piske, Alessandra Charão, Ruy Coimbra Ikehata, Ryo Graduate Program in Pure and Applied Mathematics Department of Mathematics Federal University of Santa Catarina Florianopolis88040-900 Brazil Department of Mathematics Division of Educational Sciences Graduate School of Humanities and Social Sciences Hiroshima University Higashi-Hiroshima739-8524 Japan

We consider strongly damped wave equations with logarithmic mass-like terms with a parameter θ ∈ (0, 1]. This research is a part of a series of wave equations that was initiated by Charão-Ikehata [6], Charão-D’Abbicco-Ikehata considered in [5] depending on a parameter θ ∈ (1/2, 1) and Piske-Charão-Ikehata [26] for small parameter θ ∈ (0, 1/2). We derive a leading term as t → ∞ of the solution, and by using it, a growth and a decay property of the solution itself can be precisely studied in terms of L2-norm. An interesting aspect appears in the case of n = 1, roughly speaking, a small θ produces a diffusive property, and a large θ gives a kind of singularity, expressed by growth *** Codes Primary 35B4, 35L05, Secondaryn 35B20, 35R12, 35S05 © 2022, CC BY.

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