Gentleflow: A time-synchronized optimization approach for online trajectory generation with gentle torque control for manipulators

This paper proposes Gentleflow, a time-synchronized online trajectory generation (OTG) method for smooth torque control in multi-joint manipulators. The proposed method generates synchronized joint trajectories while satisfying velocity, acceleration, and jerk constraints. It can start from arbitrary initial states and efficiently guide the system toward the desired target state. Unlike traditional methods, Gentleflow not only explicitly incorporates jerk constraints into the synchronization process, but also proactively tightens the allowable jerk bounds below the original constraint values, in order to suppress torque rate variations and achieve smoother trajectory transitions. This refined jerk treatment significantly contributes to smoother motion profiles and improved compliance. Extensive experimental validation was conducted on a 6-DOF industrial robot to demonstrate the effectiveness of Gentleflow and the importance of jointly minimizing jerk and optimizing motor torque for time-synchronized multi-joint motion. The experiments included abrupt target-switching motions, multi-stage sequential assembly tasks, and repetitive long-distance movements. Performance was compared with Ruckig and the minimum-acceleration-peak synchronization method. Real-world end-effector vibration measurements show that Gentleflow substantially reduces vibrations during high-speed motions, resulting in smoother, more compliant, and repeatable trajectories, providing strong evidence of its practical advantages for complex robotic tasks.