Smooth and time-optimal S-curve trajectory planning for automated robots and machines

Abstract In this paper, a smooth and time-optimal S-curve trajectory planning method is proposed to meet the requirements of high-speed and ultra-precision operation for robotic manipulators in modern industrial applications. This method utilizes a piecewise sigmoid function to establish a jerk profile with suitably chosen phase durations such that the generated trajectories are infinitely continuously differentiable under the given constraints on velocity, acceleration and jerk. All the trajectory parameters are derived with an analytical algorithm to ensure an acceptable computational cost. This S-curve model achieves a greater efficiency than the trigonometric models, while avoiding the high complexity presented by conventional high order polynomial models. The trade-off between efficiency and smoothness can be modulated by the limit value of the snap (the derivative of jerk), this feature is advantageous for adapting to different task requirements. Furthermore, a synchronization strategy is suggested to coordinate multi-axis motions, enabling the full capabilities of the actuators to be exploited. The feasibility and practicality of the proposed approach is evaluated by the simulation and experimental studies in comparison with other benchmark techniques in the literature.