Two-Dimensional Shape and Distal Force Estimation for the Continuum Robot Based on Learning From the Proximal Sensors

Accurate shape sensing and distal contact force estimation of the flexible continuum robots remains challenging due to critical hysteresis profiles for modeling and the difficulties on sensor integration at their distal ends. This article proposes a learning-based approach to predict distal-tip interaction information by solely utilizing the sensory measurements from the proximal end. A workflow including multilayer perception (MLP) and long short-term memory (LSTM) was investigated to simultaneously estimate and predict the whole shape and distal contact force. Experiments were carried out on a typical single-section continuum robot to verify the effectiveness of the proposed method. The proposed method could achieve high accuracy of root mean square error (RMSE) = 0.26 N for force prediction and a relative error of less than 1.2% for shape estimation. Notably, the LSTM-based method could precisely identify the force hysteresis profile. In summary, the proposed framework could be applied to the cable-drive continuum robotic systems for precise contact force and shape feedback without requiring sensors at the distal tip.