High-speed motions performed by industrial machines can induce severe vibrations that degrade the positioning accuracy and efficiency. To address this issue, this paper proposes a novel motion profile design method utilizing a sinusoidal jerk model to generate fast and smooth motions with low vibrations. The expressions for the acceleration, velocity, and displacement were obtained through successive integrations of the continuous jerk profile. A minimum-time solution with actuator limits was formulated based on an analysis of the critical constraint conditions. Differing from previous studies, the current study introduces an analytical optimization procedure for the profile parameters to minimize both the motion duration and excitation frequency contents corresponding to the system pole. By examining the correlation between the input motion profiles and system responses, the conditions for vibration elimination were identified, highlighting the significance of specific time intervals in controlling the vibration amplitude. Numerical and experimental studies were conducted to validate the effectiveness of the proposed method. The comparative results illustrate that this method outperforms existing baseline techniques in terms of smoothness and vibration attenuation. The residual-vibration level and settling time are significantly reduced with the optimized sinusoidal jerk profile, even in the presence of modeling errors, contributing to higher productivity.

Industrial parts are increasingly being designed to be more lightweight in modern manufacturing for energy saving and material cost reduction. However, the high-speed motion of flexible systems tends to excite severe residual vibrations that result in positioning accuracy degradation and loss of productivity. This study proposes a closed-form trajectory optimization method for vibration suppression based on trapezoidal velocity profiles, which are most widely used in industrial robots and machines. First, the formulation and minimum time solution under actuator limits of the motion profile are defined. Then, the relationship between the trajectory parameters and the vibration response is investigated. It is shown that residual vibration can be eliminated by properly tuning the acceleration/deceleration switching times according to the natural frequency. Based on the derived vibration suppression conditions, a tuning procedure for time parameters compliant with actuator limits is established to generate fast and precise movement. A main advantage of the proposed method is easy implementation for general machines without requiring extra computational resources or modification to the control system. The effectiveness and practicality of the proposed approach are verified through experiments conducted on a robot. The experimental results show that the optimized trajectory achieves superior residual vibration reduction performance.

Planning efficient trajectories is an essential task in most automated robotic applications. The execution time and smoothness are usually important considerations for economic and safety reasons. A novel method to generate a trigonometric frequency central pattern generator trajectory is presented in this paper for cyclic point-to-point tasks of industrial robotic manipulators. The proposed method is biologically motivated by the concept of central pattern generator, which is a special neural circuit underlying most rhythmic activities in living beings. A modified central pattern generator model with simple network structure is developed for yielding the desired joint trajectories of robots. An important property of this technique lies in the fact that stable online trajectory transition between different paths is enabled by simply adjusting the central pattern generator control parameters. Moreover, kinematic constraints of the robot can be taken into account for optimizing the robot motion instead of setting a priori the execution time. Two examples of the pick-and-place operation, which is a typical cyclic point-to-point task, are used to illustrate the validity of the method. The results of simulation indicate that the proposed method is capable of producing smooth and time-optimal trajectories, which have also been compared with those yielded by other trajectory planning approaches found in the scientific literature.