Efficient and Scalable Inverse Kinematics for Continuum Robots

With their flexible nature, continuum robots offer hyper-redundancy regarding their workspace; their backbone can take many shapes upon a single tip position and orientation. Deciphering which backbone shape to use under certain conditions is crucial to their operation, especially given the rise in their use in industries such as inspection and repair, and minimally invasive surgery. This complexity increases when additional continuum robot sections are used. This paper presents a novel Piecewise Dual Quaternion (PDQ)-based algorithm for modeling continuum robots, demonstrating improved performance compared to the traditional pseudo-Inverse Jacobian (IJ) method. The proposed algorithm reduces computational complexity and increases convergence speed. We validate the algorithm through simulation studies, comparing its performance in terms of accuracy, frequency, and sequential backbone smoothness, for which a metric is defined. Furthermore, we assess the algorithm's scalability by extending the analysis to continuum robots with 4, 5, and 6 sections. The results indicate that the PDQ algorithm consistently outperforms the IJ method across various robot sections and paths, increasing the modeling frequency by an order of magnitude while maintaining tip accuracy. These findings have the potential to enable high precision of multi-section continuum robots and facilitate the use of haptic feedback sensors in practical applications