Then , the minimum - time trajectory planning ( mttp ) for single manipulator is investigated . mttp with dynamic model constrains is presented in detail . then a algorithm of dynamic searching time - optimal trajectory based on phase - plane techniques is proposed and simulated 其次,研究了沿指定路径单臂最优时间轨迹规划,先详细介绍考虑动力学模型的最小时间轨迹精确解法,然后提出了一种基于相平面动态搜索时间近似最优轨迹的方法,并将该算法进行了仿真实验。