An Offline‐Cascade‐Online Learning‐Based Algorithm for Distal Trajectory Estimation of Medical Continuum Manipulators

This work proposes an offline‐cascade‐online (OCO) estimation algorithm, achieving the distal trajectory estimation in unstructured working space and with long‐term visual occlusion. The OCO estimation algorithm cascades a backpropagation (BP)‐based offline learning network and a radial basis function (RBF)‐based online learning network, realizing the prior estimation and error compensation, respectively. The BP network is pretrained offline based on the data collected in free spaces, while the RBF network could be updated online by the least squares method with the historical data in unstructured working spaces to avoid the local optimum problem. Furthermore, a modified loss function consisting of three terms is proposed for the RBF network to improve the estimated distal trajectories’ accuracy, smoothness, and stability in complex unstructured environments. Experimental results indicate that the proposed OCO estimation algorithm achieves a high level of accuracy, with an average relative estimation error of 1.36% in two types of unstructured environments with visual occlusion. Meanwhile, the accuracy of the proposed algorithm is improved by more than 30% in the trajectory estimation of two consecutive loops, demonstrating its outstanding online learning ability. Moreover, experiments on another type of continuum manipulator have also validated its high transferability and strong robustness.