2023/05/21 by Mizuki Yoshizawa, Yoshizawa, Mizuki, Akira Terui +3 · 2 citations
Computer Science · Engineering · #13P15 #68W30 #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Robotic Mechanisms and Dynamics #Robotics (cs.RO) #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2305.12451
openalex publication_date 2023/05/21 · openalex created_date 2023/05/24 · openalex updated_date 2026/07/28
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.