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 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.