Capability verification and error source investigation of external force sensing methods of continuum robot

This paper studies mainly error sources of current external force sensing algorithms and presents external force sensing algorithms of continuum robots using superelastic NiTi backbones. Axial compression is deliberately taken into consideration in analytical dynamics for facilitating the later analysis of error sources. The analytical dynamics of multibackbone continuum robots is established by Lagrange equation in a simple and concise manner. Experiments show that the stress–strain relationship is significantly different with or without external force, and we provide some insights into the feasibility and limitations of dynamic model. Then, an extend intrinsic force sensing algorithm (EIFS) and an external force observer based on generalized momentum method (EFOGM) are developed. Both of them only depend on joint-level information. The effectiveness of both force sensing algorithms is validated by simulations and experiments. Mean absolute error of EIFS using real-time axial strain is 0.0980 N, while mean absolute error of EFOGM using real-time axial strain is 0.0977 N, respectively. Experiments show that the main sources of force sensing algorithm error are: (1) the estimated external force compensates the force part caused by axial compression and (2) model error from nonlinear stress–strain relationship of cable tension-induced deformation and external force-induced deformation under the loading and unloading force stage.