A Sensor-Free Force Estimation Method for Notched Continuum Surgical Robot

The notched continuum robot (NCR), characterized by its compact size and excellent mechanical properties, is extensively used in the design of minimally invasive surgical robots. However, integrating sensors into the NCR in a limited surgical environment is challenging. Using drive state for force estimation is a promising method that relies on the accurate modeling of the NCR. This article proposes a sensor-free force estimation method for the NCR. The method establishes an accurate static model of the NCR based on the beam constraint model (BCM). Subsequently, cable length changes are introduced as constraints into the static model, enabling sensor-free force estimation. The proposed static model demonstrates good accuracy, with results from 28 experiments showing an average position error of 1.23 mm, accounting for 2.48% of the robot's total length. Based on the accurate static model, the average estimation error of the proposed force estimation method is 7.41 mN. Compared to models using traditional assumptions, the proposed force estimation method in this article also demonstrates a significant improvement.