A spline-based approach to smooth and time-optimal trajectory generation for CNC machines with guaranteed kinematic constraints

In motion trajectory optimization of industrial machines, discrete points on a trajectory are typically considered for calculation. However, discrete constraints on grid points for calculation may violate the machine kinematic limits, inducing large tracking errors along a predefined geometric path. In contrast, increasing grid points enlarges the computational complexity. In this study, a method to achieve guaranteed kinematic constraints of a time-optimal trajectory is investigated. A cubic B-spline was used to parameterize the trajectory for acceleration and jerk continuity. The kinematic constraints were proposed based on spline control points and variable geometric derivatives using the convex hull and the local modification properties of the B-splines. The evaluation was performed with a jerk-constrained time-optimal trajectory generation approach by applying different geometric paths, kinematic limits, and problem grid sizes. The simulation results showed that the proposed method guaranteed smoothness and time optimality of the trajectory while satisfying kinematic constraints for all horizons. The experimental results with an industrial feed drive system validated that the proposed method provided a smoother trajectory, reducing the average tracking error by 12%.

Automated summary

In this study, a method to achieve guaranteed kinematic constraints of a time-optimal trajectory using cubic B-spline and convex hull was investigated. Both simulation and experimental results validate that the proposed method ensures trajectory smoothness and time optimality while satisfying motion constraints.