Attitude interpolation of B-spline curve based on modified Rodrigues parameters

To improve the continuity of robot’s attitude interpolation, a method is proposed to swiftly create a seamless quaternion spline curve by mapping a quaternion rotation space to a three-dimensional(3D) space spline interpolation curve using modified Rodrigues parameters. Initially, a function based on the modified Rodrigues parameters is formulated to facilitate the mapping from the quaternion space to 3D one. Subsequently, a cubic quasi-uniform B-spline interpolation theory in the 3D space is employed to construct the interpolation function, ensuring that it passes through specified key attitude interpolation points and achieves C2 continuity of the attitude interpolation curve. Consequently, the accuracy and smoothness of the proposed method for quaternion multi-attitude interpolation are verified with simulations. The results demonstrate that this method achieves smooth interpolation between multiple attitude quaternions. Furthermore, this approach is characterized by its simple construction function, ease of implementation, intuitive nature, and comprehensibility, thus providing valuable insights for smooth quaternion spline-curve interpolation.