This paper presents a practical time-optimal and smooth trajectory planning algorithm and then applies it to robot manipulators. The proposed algorithm uses the time-optimal theory based on the dynamics model to plan the robot’s motion trajectory, constructs the trajectory optimization model under the constraints of the geometric path and joint torque, and dynamically selects the optimal trajectory parameters during the solving process to prominently improve the robot’s motion speed. Moreover, the proposed algorithm utilizes the input shaping algorithm instead of the jerk constraint in the trajectory optimization model to achieve a smooth trajectory. The input shaping of trajectory parameters during postprocessing not only suppresses the residual vibration of the robot but also takes the signal delay caused by traditional input shaping into account. The combination of these algorithms makes the proposed time-optimal and smooth trajectory planning algorithm ensure absolute time optimality and achieve a smooth trajectory. The results of an experiment on a six-degree-of-freedom industrial robot indicate the validity of the proposed algorithm.

中文翻译：

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机器人机械手的时间最优和平滑轨迹规划

本文提出了一种实用的时间最优且平滑的轨迹规划算法，然后将其应用于机器人机械手。该算法利用基于动力学模型的时间最优理论规划机器人的运动轨迹，在几何路径和关节力矩约束下构建轨迹优化模型，并在求解过程中动态选择最优轨迹参数以突出提高机器人的运动速度。此外，所提出的算法利用输入整形算法代替轨迹优化模型中的jerk约束来实现平滑的轨迹。后处理时轨迹参数的输入整形不仅抑制了机器人的残余振动，而且还考虑了传统输入整形引起的信号延迟。这些算法的结合使得所提出的时间最优且平滑的轨迹规划算法保证绝对时间最优并实现平滑轨迹。六自由度工业机器人的实验结果表明了所提出算法的有效性。