Wrench Estimation and Friction Compensation Using Multiple Shooting Method for Tether Units Augmented to Remote Tendon-Driven Continuum Robots

Remote-actuated mechanisms that employ tendon sheaths or tether units can transmit mechanical force without directly connecting the actuators to the mechanism, but suffer from undesirable side effects like mechanical friction and induced external wrench disturbances on the distal side of the mechanism. In this work, a multiple shooting method is proposed as a superior method to the single shooting method to solve the Cosserat rod boundary value problems, to obtain the states of the system. With that, numerical experiments are provided to demonstrate the difficulty of solving these boundary value problems, simultaneously showing the validity of the proposed approach. 2D reconstruction experiments were conducted to show shape reconstruction capabilities. In addition, friction loss and 6-degree-of-freedom wrench estimations were also experimentally validated with the proposed mathematical model with 0.1679N and 0.0401Nm for root-mean-squared error (RMSE) force estimation and torque estimation error, respectively, while achieving a 3% mean absolute percentage steady-state friction estimation error. Finally, a modified resolved rate controller was applied to steer a remote tendon-driven continuum robot to compensate for friction loss for 3.1-m long tether units.