Estimating Contact Forces Along the Continuum Robot Considering Actuation

Perceiving the body contact force along the continuum surgical robot can reduce iatrogenic injuries and improve surgical accuracy. Therefore, this article presents a curvature profile-based method for continuum robots deformed by actuation to estimate the external contact force. A kinematic model of a continuum robot under driving force was established based on the Cosserat rod theory to derive the theoretical curvature under the interaction of external contact force and robot driving force. Then, a curvature sensor based on fiber Bragg grating (FBG) was designed to acquire the discrete curvature of the robotic center curve. The external contact state was estimated by minimizing the least squares loss function between the theoretical curvature of the kinematic model and the measured curvature. Finally, a discrete Gaussian approximation function was constructed to parameterize the external contact information, improving the estimation strategy’s generalization ability. The point loading experiments show that the proposed method has a root mean square error (RMSE) of 0.024 N for force estimation and an RMSE of 6.4 mm for position estimation. The average RMSE between the theoretical curvature and the measured curvature in the x- and y-direction is 0.282 and 0.21 m $^{-{1}}$ , respectively. The error results indicate that the proposed contact force estimation can effectively estimate the contact information of the external environment.