An approach based on multiquadric radial basis functions for smooth trajectory planning of robotic manipulators with kinematic constraints

Abstract This paper introduces a novel approach for planning smooth trajectories of robotic manipulators by leveraging multiquadric radial basis functions (MQ-RBFs). The proposed approach aims to achieve optimal trajectories by minimizing a multi-objective function that accounts for both time and jerk optimization. The MQ-RBF interpolation technique ensures that the trajectory meets velocity, acceleration, and jerk limits, while ensuring jerk continuity. Comparative evaluations are conducted in two cases: with and without optimization. In the first case, the MQ-RBF interpolation approach is compared with various RBF interpolation models. In the second case, the MQ-RBF trajectory approach is compared with alternative state-of-the-art trajectory planning techniques, such as fifth-order B-splines and trigonometric spline functions, for generating optimal time-jerk trajectories for 6-joint robotic manipulators using optimization algorithms. Numerical and experimental results demonstrate the superior performance of the proposed technique in efficiently planning smooth trajectories compared to existing trajectory planning approaches and validate its effectiveness across various scenarios.