Real-time time-optimal continuous multi-axis trajectory planning using the trajectory index coordination method

Real-time time-optimal trajectory planning exists in a wide range of applications such as computer numerical control (CNC) manufacturing, robotics and autonomous vehicles. Generally, the methods to generate time-optimal trajectory can be categorized as non-real-time methods and real-time methods. Non-real-time methods such as direct optimization method tend to generate time-optimal trajectory through nonlinear or linear programming while it is computationally prohibitive for high frequency real-time applications. Current real-time methods are computationally efficient but either deal with the sparse waypoint trajectories or sacrifice the time optimality a lot. This paper innovatively proposed a time-optimal switching trajectory index coordination (TOS-TIC) framework to solve the real-time time-optimal planning problem for continuous multi-axis trajectories. The proposed method is able to generate time-optimal trajectory for continuous geometric paths while considering the axial velocity and acceleration constraints. The time-optimality of the trajectory planned by TOS-TIC is nearly the same as the offline planned optimal results. Meanwhile, the proposed method is computationally efficient for even 5kHz real-time applications. The main idea of TOS-TIC is coordinating several one-axis time-optimal switching controls to generate a modified control that decreases the state deviation from the desired trajectory. Several comparative experiments are carried out on an industrial biaxial linear motor stage. And the experimental results consistently verify that the proposed TOS-TIC real-time planner generates faster trajectory compared with the real-time lookahead method. In addition, the trajectory running time and final tracking error of the proposed method are nearly the same as the offline direct optimization method.