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

Bendali, Nadir; Scalera, Lorenzo; Sundaram, Arunachalam; Said, Abderrezak; Gasparetto, Alessandro

Abstract

This paper introduces a novel approach for planning smooth trajectories of robotic manipulators byleveraging multiquadric radial basis functions (MQRBFs). 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-RBFtrajectory approach is compared with alternative state-of-the-art trajectory planning techniques, such as fifth-order Bsplines 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.

• Journal Article Type: Article
• Acceptance Date: May 12, 2025
• Online Publication Date: May 15, 2025
• Publication Date: May 12, 2025
• Deposit Date: May 16, 2025
• Publicly Available Date: May 19, 2025
• Journal: Nonlinear Dynamics
• Print ISSN: 0924-090X
• Electronic ISSN: 1573-269X
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s11071-025-11248-3
• Keywords: Interpolation techniques · MQ-RBF · Robotics · Time-jerk optimization · Trajectory planning
• Publisher URL: https://link.springer.com/article/10.1007/s11071-025-11248-3?utm_source=rct_congratemailt&utm_medium=email&utm_campaign=oa_20250515&utm_content=10.1007/s11071-025-11248-3#citeas
• Additional Information: Received: 8 February 2025; Accepted: 12 April 2025; First Online: 15 May 2025; : ; : Not applicable; : Not applicable; : Not applicable; : Not applicable