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Methods for inverse kinematics computation and path planning of a threedegree-of-freedom (DOF) manipulator using the algorithm for quantifierelimination based on Comprehensive Gr\"obner Systems (CGS), called CGS-QEmethod, are proposed. The first method for solving the inverse kinematicsproblem employs counting the real roots of a system of polynomial equations toverify the solution's existence. In the second method for trajectory planningof the manipulator, the use of CGS guarantees the existence of an inversekinematics solution. Moreover, it makes the algorithm more efficient bypreventing repeated computation of Gr\"obner basis. In the third method forpath planning of the manipulator, for a path of the motion given as a functionof a parameter, the CGS-QE method verifies the whole path's feasibility.Computational examples and an experiment are provided to illustrate theeffectiveness of the proposed methods.

Inverse kinematics and path planning of manipulator using real quantifier elimination based on Comprehensive Gr\"obner Systems