Using the colored Yang–Baxter equation, the Lax pairs for the system with color parameters and periodic boundary conditions are derived. The explicit expressions of the Lax pairs for the six-vertex standard matrices...Using the colored Yang–Baxter equation, the Lax pairs for the system with color parameters and periodic boundary conditions are derived. The explicit expressions of the Lax pairs for the six-vertex standard matrices of both the Baxter and free-Fermion types are given.展开更多
由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力...由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力矩差和叶片重力矩分布产生的干涉关系,将装配平稳性、方向调整次数及更换装配工具的频次作为约束条件,设置干涉关系矩阵和适应度函数,以判断装配序列方案是否达到最佳;在装配方案达到最佳后,通过离散化萤火虫算法获取六自由度机器人装配序列最优解;根据该结果检测六自由度机器人碰撞结果,并采用优化随机树节点扩展控制及扩展能力检测的改进快速搜索随机树算法(Rapidly-exploring Random Tree,RRT*)来对所得装配序列进行调整修正,实现工业机器人六自由度装配序列规划下避障研究。实验结果证明:该方法可获取装配效率高、成本小的六自由度机器人装配序列;可以快速规划出最佳六自由度机器人避障路径,有效地避开障碍物,且精度较高、误差较小、实用性较强。展开更多
All solutions of Yang-Baxter equation with color parameters for six-vertex model are achieved by five solution transformations, three nondegenerate basic solutions and several degenerate basic solutions. It is shown t...All solutions of Yang-Baxter equation with color parameters for six-vertex model are achieved by five solution transformations, three nondegenerate basic solutions and several degenerate basic solutions. It is shown that all solutions of Yang-Baxter equation with spectral parameter for six-vertex model are obtainable from solutions of Yang-Baxter equation with color parameters for six-vertex model.展开更多
文摘Using the colored Yang–Baxter equation, the Lax pairs for the system with color parameters and periodic boundary conditions are derived. The explicit expressions of the Lax pairs for the six-vertex standard matrices of both the Baxter and free-Fermion types are given.
文摘由于六自由度机器人在装配序列规划中存在顶角叶片重力矩差难以保证、叶片重力矩分布不够均衡的问题,以至于避障过程中出现碰撞。为此,提出工业机器人六自由度装配序列规划下避障研究。通过分析六自由度机器人装配序列中,顶角叶片重力矩差和叶片重力矩分布产生的干涉关系,将装配平稳性、方向调整次数及更换装配工具的频次作为约束条件,设置干涉关系矩阵和适应度函数,以判断装配序列方案是否达到最佳;在装配方案达到最佳后,通过离散化萤火虫算法获取六自由度机器人装配序列最优解;根据该结果检测六自由度机器人碰撞结果,并采用优化随机树节点扩展控制及扩展能力检测的改进快速搜索随机树算法(Rapidly-exploring Random Tree,RRT*)来对所得装配序列进行调整修正,实现工业机器人六自由度装配序列规划下避障研究。实验结果证明:该方法可获取装配效率高、成本小的六自由度机器人装配序列;可以快速规划出最佳六自由度机器人避障路径,有效地避开障碍物,且精度较高、误差较小、实用性较强。
基金the Climbing-up Project, the National Natural Science Foundation of China the Natural Scientific Foundation of the Chinese Academy of Sciences
文摘All solutions of Yang-Baxter equation with color parameters for six-vertex model are achieved by five solution transformations, three nondegenerate basic solutions and several degenerate basic solutions. It is shown that all solutions of Yang-Baxter equation with spectral parameter for six-vertex model are obtainable from solutions of Yang-Baxter equation with color parameters for six-vertex model.
