中文摘要：

提出基函数叠加与粒子群优化（PSO）相结合的振动抑制轨迹规划方法．首先推导了各关节变量与模态坐标的关系，采用正弦一梯形函数作为基函数构造各关节的角速度，其中基函数的系数和幅值为待定参数；然后将末端振动最小化轨迹规划转换为待定参数的优化问题，并采用PSO算法获得待定参数的最优值；最后以双杆刚柔混合机械臂为例开展仿真研究．仿真结果表明，所提出的方法大大减小了机械臂末端的残留振动．

英文摘要：

A trajectory planning method of combing the basis functions superposition and particle swarm optimization is proposed to suppress the vibration. Firstly, the relationship between the state variables of each joint and the modal coordinates of the flexible body is derived. Then, sinusoidal-trapezoidal functions are used as basis functions to construct joint angular velocities. The coefficients and amplitudes of the basis functions are considered as the parameters of the joint rate functions to be determined. Then, the vibration minimized trajectory planning problem is transformed into an optimization problem of the unknown parameters. And the PSO algorithm is utilized to search the optimal parameters. Finally, a two-link rigid- flexible hybrid manipulator is taken as the example and simulation study is performed. Simulation results show that the proposed method largely reduces the residual vibration of the end-effector.