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.

翻译：提出采用基于完备Gröbner系统（CGS）的量词消去算法（即CGS-QE方法）实现三自由度机械臂逆运动学计算与路径规划的方法。第一种逆运动学求解方法通过计算多项式方程组实根数量验证解的存在性。第二种轨迹规划方法借助CGS保证逆运动学解的存在性，同时通过避免重复计算Gröbner基提升算法效率。第三种路径规划方法针对以参数函数形式给出的运动路径，利用CGS-QE方法验证整条路径的可行性。通过计算实例与实验验证了所提方法的有效性。