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This paper presents the theoretical analysis and the experimental validation of the force sensing capabilities of continuum robots. These robots employ superelastic NiTi backbones and actuation redundancy. The paper uses screw theory to analyze the limitations and provide geometric interpretation to the sensible wrenches. The analysis is based on the singular value decomposition of the Jacobian mapping between the configuration space and the twist space of the end effector. The results show that the sensible wrenches belong to a 2-D screw system and the insensible wrenches belong to a 4-D screw system. The theory presented in this paper is validated through simulations and experiments. It is shown that the force sensing errors have an average of 0.34 g with a standard deviation of 0.83 g. Another experiment of generating the stiffness map of a silicone strip suggests possible medical application of palpation for tumor detection. The presented study allows force sensing in challenging environments where placing force sensors at the distal end of a robot is not possible due to limitations such as size and MRI compatibility.
Xu et al. (Sun,) studied this question.