Smooth trajectory generation and hybrid B-splines-quaternions based tool path interpolation for a 3T1R parallel kinematic milling robot

This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel kinematic milling robot. The proposed approach integrates B-spline and Quaternion interpolation techniques to manage decoupled position and orientation data points. The synchronization of orientation and...

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Vydáno v:	Precision engineering Ročník 95; s. 117 - 135
Hlavní autoři:	Akhbari, Sina, Mahboubkhah, Mehran
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.08.2025
Témata:	B-Spline unit quaternions Minimum jerk optimization Parallel kinematic robots Piece-wise beziers Smooth trajectory generation Tool path interpolation Minimum jerk optimization B-Spline unit quaternions Parallel kinematic robots Tool path interpolation Piece-wise beziers Smooth trajectory generation
ISSN:	0141-6359
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Popis
Shrnutí:	This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel kinematic milling robot. The proposed approach integrates B-spline and Quaternion interpolation techniques to manage decoupled position and orientation data points. The synchronization of orientation and arc-length-parameterized position data is achieved through the fitting of smooth piece-wise Bezier curves, which describe the non-linear relationship between path length and tool orientation, solved via sequential quadratic programming. By leveraging the convex hull properties of Bezier curves, the method ensures spatial and temporal separation constraints for multi-agent trajectory generation. Unit quaternions are employed for orientation interpolation, providing a robust and efficient representation that avoids gimbal lock and facilitates smooth, continuous rotation. Modifier polynomials are used for position interpolation. Temporal trajectories are optimized using minimum jerk, time-optimal piece-wise Bezier curves in two stages: task space followed by joint space, implemented on a low-cost microcontroller. Experimental results demonstrate that the proposed method offers enhanced accuracy, reduced velocity fluctuations, and computational efficiency compared to conventional interpolation methods. [Display omitted] •Bilayer smooth optimized trajectories reduces execution time, ensuring optimality while preserving kinematic feasibility.•Fusion of B-splines and unit quaternions for decoupled freeform tool path generation.•Effective synchronization of path length and tool spatial orientation.•Hybrid b-spline quaternion-based interpolation demonstrates high accuracy and computational efficiency.•Minimum jerk time-optimal method enables real-time execution on microcontrollers with negligible velocity fluctuations.
ISSN:	0141-6359
DOI:	10.1016/j.precisioneng.2025.04.020