Dual-Objective Optimization of G³-Continuous Quintic B-Spline Trajectories for Robotic Ultrasonic Testing

To address the challenges of unstable motion and insufficient detection accuracy in robotic scanning trajectories, particularly under high curvature and irregular shape conditions during ultrasonic testing of complex free-form surface workpieces, this paper proposes a G³ continuous trajectory planning and optimization method based on quintic B-spline curves. First, the scanning trajectory of the robot is represented by a parametric curve, with explicit expressions for position, velocity, acceleration, and jerk derived in the form of quintic B-splines. These expressions ensure continuity in position, velocity, acceleration, and jerk (C³/G³ continuity), thus maintaining high-order geometric continuity and motion stability of the trajectory. Second, to achieve the dual optimization objectives of trajectory smoothness and surface fitting, this paper constructs a composite objective function that incorporates both the integral of acceleration squared and the surface fitting error. The smoothness index is weighted by the sum of the square integrals of the second and third derivatives of the trajectory, thereby suppressing high-order oscillations, while the fitting index is based on the mean square error between the robot end-effector path and the target surface. Finally, a numerical optimization algorithm is utilized to solve the objective function, resulting in an optimal scanning trajectory that ensures both motion stability and fitting accuracy, while maintaining G³ continuity. Simulation and experimental results demonstrate that this method effectively mitigates trajectory mutations and oscillations, enabling efficient and high-precision automatic ultrasonic testing, and provides a reliable trajectory planning strategy for online non-destructive testing of complex curved workpieces.