arXiv subjects

Masahiko Mikawa

Publications and source records attributed to Masahiko Mikawa.

10 recordsLinked to original sources

arXiv2026

Trajectory Planning and Certification for 3-DOF Robot Manipulators Using Real Quantifier Elimination Based on Comprehensive Gröbner Systems

We propose an algorithm and its implementation for trajectory planning and certification for 3-DOF robot manipulators. The method uses Real Quantifier Elimination (QE) based on Comprehensive Gröbner Systems (CGS), also known as the CGS-QE method. The main advantage of the proposed method is its efficiency in trajectory planning and solution certification. This efficiency comes from the effective use of the CGS. First, for trajectory planning, we solve the inverse kinematics problem at each point along the trajectory via Gröbner basis computation. This usually requires recalculating the Gröbner basis at every point, which is time-consuming. We avoid this by computing the CGS for a parametric system. Here, the end-effector coordinates are parameters. This approach streamlines the algorithm. Second, for solution certification, the CGS-QE method certifies that an inverse kinematics solution exists at any point along the end-effector's trajectory. Our method also certifies solutions for trajectories composed of line segments and cubic natural splines. The algorithm is implemented within the computer algebra system Risa/Asir.

cs.RO↗

arXiv2025

Inverse Kinematics for a 6-Degree-of-Freedom Robot Manipulator Using Comprehensive Gröbner Systems

We propose an effective method for solving the inverse kinematic problem of a specific model of 6-degree-of-freedom (6-DOF) robot manipulator using computer algebra. It is known that when the rotation axes of three consecutive rotational joints of a manipulator intersect at a single point, the inverse kinematics problem can be divided into determining position and orientation. We extend this method to more general manipulators in which the rotational axes of two consecutive joints intersect. This extension broadens the class of 6-DOF manipulators for which the inverse kinematics problem can be solved, and is expected to enable more efficient solutions. The inverse kinematic problem is solved using the Comprehensive Gröbner System (CGS) with joint parameters of the robot appearing as parameters in the coefficients to prevent repetitive calculations of the Gröbner bases. The effectiveness of the proposed method is shown by experiments.

cs.RO↗

arXiv2025

An Effective Trajectory Planning and an Optimized Path Planning for a 6-Degree-of-Freedom Robot Manipulator

An effective method for optimizing path planning for a specific model of a 6-degree-of-freedom (6-DOF) robot manipulator is presented as part of the motion planning of the manipulator using computer algebra. We assume that we are given a path in the form of a set of line segments that the end-effector should follow. We also assume that we have a method to solve the inverse kinematic problem of the manipulator at each via-point of the trajectory. The proposed method consists of three steps. First, we calculate the feasible region of the manipulator under a specific configuration of the end-effector. Next, we aim to find a trajectory on the line segments and a sequence of joint configurations the manipulator should follow to move the end-effector along the specified trajectory. Finally, we find the optimal combination of solutions to the inverse kinematic problem at each via-point along the trajectory by reducing the problem to a shortest-path problem of the graph and applying Dijkstra's algorithm. We show the effectiveness of the proposed method by experiments.

cs.RO↗

arXiv2025

Exploring Interactive Simulation of Grass Display Color Characteristic Based on Real-World Conditions

Recent research has focused on incorporating media into living environments via color-controlled materials and image display. In particular, grass-based displays have drawn attention as landscape-friendly interactive interfaces. To develop the grass display, it is important to obtain the grass color change characteristics that depend on the real environment. However, conventional methods require experiments on actual equipment every time the lighting or viewpoint changes, which is time-consuming and costly. Although research has begun on simulating grass colors, this approach still faces significant issues as it takes many hours for a single measurement. In this paper, we explore an interactive simulation of a grass display color change characteristic based on real-world conditions in a virtual environment. We evaluated our method's accuracy by simulating grass color characteristics across multiple viewpoints and environments, and then compared the results against prior work. The results indicated that our method tended to simulate the grass color characteristics similar to the actual characteristics and showed the potential to do so more quickly and with comparable accuracy to the previous study.

cs.GR↗

arXiv2024

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

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.

cs.RO↗

arXiv2024

ProgrammableGrass: A Shape-Changing Artificial Grass Display Adapted for Dynamic and Interactive Display Features

There are various proposals for employing grass materials as a green landscape-friendly display. However, it is difficult for current techniques to display smooth animations using 8-bit images and to adjust display resolution, similar to conventional displays. We present ProgrammableGrass, an artificial grass display with scalable resolution, capable of swiftly controlling grass color at 8-bit levels. This grass display can control grass colors linearly at the 8-bit level, similar to an LCD display, and can also display not only 8-bit-based images but also videos. This display enables pixel-by-pixel color transitions from yellow to green using fixed-length yellow and adjustable-length green grass. We designed a grass module that can be connected to other modules. Utilizing a proportional derivative control, the grass colors are manipulated to display animations at approximately 10 [fps]. Since the relationship between grass lengths and colors is nonlinear, we developed a calibration system for ProgrammableGrass. We revealed that this calibration system allows ProgrammableGrass to linearly control grass colors at 8-bit levels through experiments under multiple conditions. Lastly, we demonstrate ProgrammableGrass to show smooth animations with 8-bit grayscale images. Moreover, we show several application examples to illustrate the potential of ProgrammableGrass. With the advancement of this technology, users will be able to treat grass as a green-based interactive display device.

cs.GR↗

arXiv2023

Inverse kinematics and path planning of manipulator using real quantifier elimination based on Comprehensive Gröbner Systems

Methods for inverse kinematics computation and path planning of a three degree-of-freedom (DOF) manipulator using the algorithm for quantifier elimination based on Comprehensive Gröbner Systems (CGS), called CGS-QE method, are proposed. The first method for solving the inverse kinematics problem employs counting the real roots of a system of polynomial equations to verify the solution's existence. In the second method for trajectory planning of the manipulator, the use of CGS guarantees the existence of an inverse kinematics solution. Moreover, it makes the algorithm more efficient by preventing repeated computation of Gröbner basis. In the third method for path planning of the manipulator, for a path of the motion given as a function of a parameter, the CGS-QE method verifies the whole path's feasibility. Computational examples and an experiment are provided to illustrate the effectiveness of the proposed methods.

cs.RO↗

arXiv2023

A Design and an Implementation of an Inverse Kinematics Computation in Robotics Using Real Quantifier Elimination based on Comprehensive Gröbner Systems

The solution and implementation of the inverse kinematics computation of a three degree-of-freedom (DOF) robot manipulator using an algorithm for real quantifier elimination with Comprehensive Gröbner Systems (CGS) are presented. The method enables us to verify if the given parameters are feasible before solving the inverse kinematics problem. Furthermore, pre-computation of CGS and substituting parameters in the CGS with the given values avoids the repetitive computation of Gröbner basis. Experimental results compared with our previous implementation are shown.

cs.RO↗

arXiv2022

Dynamic Grass Color Scale Display Technique Based on Grass Length for Green Landscape-Friendly Animation Display

Recently, public displays such as liquid crystal displays (LCDs) are often used in urban green spaces, however, the display devices can spoil green landscape of urban green spaces because they look like artificial materials. We previously proposed a green landscape-friendly grass animation display method by controlling a pixel-by-pixel grass color dynamically. The grass color can be changed by moving a green grass length in yellow grass, and the grass animation display can play simple animations using grayscale images. In the previous research, the color scale was mapped to the green grass length subjectively, however, this method has not achieved displaying the grass colors corresponding to the color scale based on objective evaluations. Here, we introduce a dynamic grass color scale display technique based on a grass length. In this paper, we developed a grass color scale setting procedure to map the grass length to the color scale with five levels through image processing. Through the outdoor experiment of the grass color scale setting procedure, the color scale can correspond to the green grass length based on a viewpoint. After the experiments, we demonstrated a grass animation display to show the animations with the color scale using the experiment results.

cs.GR↗

arXiv2020

Solving System of Nonlinear Equations with the Genetic Algorithm and Newton's Method

An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm for guessing the rough location of the roots, then it uses the advantage of a good rate of convergence of Newton's method. An effective application of the method for the positioning problem of multiple small rovers proposed for the use in asteroid exploration is shown.

math.NA↗