提出了高速Delta并联机器人拾放操作轨迹的一种实现及优化的方法。在笛卡儿空间中利用Lamé曲线平滑竖直运动与水平运动之间的直角过渡部分，确定运动轨迹形状。用高阶多项式运动特性对一维曲线弧位移进行三维规划，获得运动轨迹插补点的位置、速度和加速度信息。通过Delta机器人运动学模型和动力学模型将笛卡儿空间内的轨迹信息映射到机器人关节空间，以关节电动机的近似输出能量函数为目标优化Lamé曲线的参数。在试验样机平台上进行测试，测量不同Lamé曲线参数的运动轨迹在运动停止后机构残余振动的情况，通过比较验证了参数优化后的轨迹具有良好的实际性能，能够获得满足实践要求的轨迹曲线。

A method of trajectory planning for high-speed Delta parallel robots in pick-and-place operations is presented. The transitions between the vertical and horizontal segments of the operation trajectory are smoothed with Lamé curves, thus determining the overall shape of the trajectory in Cartesian space. High order polynomials are adopted to plan the one-dimensional displacement along the curve and generate the position, velocity, acceleration information necessary for the interpolation points. Trajectory information in Cartesian space is mapped back to the joint space by using the Delta robot’s kinematics and dynamics models. In order to optimize the Lamé curve’s geometric parameters, an energy-like function based on joint torques and angular rates is thus defined. The trajectories planned are finally tested on an experimental platform. The residual vibrations as the robot’s end-effector reaches the terminal are recorded and then compared under different Lamé curve parameters. These results verify that the optimized trajectory has a better performance practically. The planning method discussed could lead to trajectories which satisfy operational requirements.