A Design and an Implementation of an Inverse Kinematics Computation in Robotics Using Real Quantifier Elimination based on Comprehensive Gr\"obner 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 Gr\"obner 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 Gr\"obner basis. Experimental results compared with our previous implementation are shown.Comment: 20 page

Inverse kinematics and path planning of manipulator using real quantifier elimination based on Comprehensive Gr\"obner 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 Gr\"obner 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 Gr\"obner 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.Comment: 26 pages. arXiv admin note: text overlap with arXiv:2111.0038

Face Memorization Using AIM Model for Mobile Robot and Its Application to Name Calling Function

We are developing a social mobile robot that has a name calling function using a face memorization system. It is said that it is an important function for a social robot to call to a person by her/his name, and the name calling can make a friendly impression of the robot on her/him. Our face memorization system has the following features: (1) When the robot detects a stranger, it stores her/his face images and name after getting her/his permission. (2) The robot can call to a person whose face it has memorized by her/his name. (3) The robot system has a sleep–wake function, and a face classifier is re-trained in a REM sleep state, or execution frequencies of information processes are reduced when it has nothing to do, for example, when there is no person around the robot. In this paper, we confirmed the performance of these functions and conducted an experiment to evaluate the impression of the name calling function with research participants. The experimental results revealed the validity and effectiveness of the proposed face memorization system