发表机构
University of Tsukuba, Tsukuba, Japan（茨口大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对3自由度机器人操作器，提出基于综合格罗贝格系统的实量词消去法（CGS-QE），用于轨迹规划与验证。通过计算参数系统的CGS避免逐点重算格罗贝格基，提高效率，还能验证多种轨迹的逆运动学解，算法在Risa/Asir中实现。
AI 中文摘要
我们提出了一种用于3自由度机器人操作器轨迹规划与验证的算法及其实现。该方法使用基于综合格罗贝格系统（CGS）的实量词消去（QE），即CGS-QE方法。其主要优势在于轨迹规划和解决方案验证的效率，源于对CGS的有效利用。轨迹规划时通过格罗贝格基计算解决轨迹上各点的逆运动学问题，通过计算参数系统的CGS避免逐点重算。解决方案验证方面，CGS-QE方法可验证末端执行器轨迹上任意点的逆运动学解存在，还能验证由线段和三次自然样条组成的轨迹的解。算法在计算机代数系统Risa/Asir中实现。
英文摘要
We propose an algorithm and its implementation for trajectory planning and certification for 3-DOF robot manipulators. The method uses Real Quantifier Elimination (QE) based on Comprehensive Gröbner Systems (CGS), also known as the CGS-QE method. The main advantage of the proposed method is its efficiency in trajectory planning and solution certification. This efficiency comes from the effective use of the CGS. First, for trajectory planning, we solve the inverse kinematics problem at each point along the trajectory via Gröbner basis computation. This usually requires recalculating the Gröbner basis at every point, which is time-consuming. We avoid this by computing the CGS for a parametric system. Here, the end-effector coordinates are parameters. This approach streamlines the algorithm. Second, for solution certification, the CGS-QE method certifies that an inverse kinematics solution exists at any point along the end-effector's trajectory. Our method also certifies solutions for trajectories composed of line segments and cubic natural splines. The algorithm is implemented within the computer algebra system Risa/Asir.
