Journal of Bionic Engineering (2024) 21:821–841 https://doi.org/10.1007/s42235-023-00473-4 Controlling Tendons to Modulate Stifness of a Planar?to?Spatial Tendon?Driven Continuum Manipulator Under External Uncertain Forces 

Vipin Pachouri1  · Pushparaj Mani Pathak1

1 Indian Institute of Technology Roorkee, Roorkee 247667, India

AbstractContinuum manipulators (CM) are soft and fexible manipulators with large numbers of degrees of freedom and can perform complex tasks in an unstructured environment. However, their deformability and compliance can deviate distal tip under uncertain external interactions. To address this challenge, a novel tension-based control scheme has been proposed to modulate the stifness of a tendon-driven CM, reducing the tip position errors caused by uncertain external forces. To minimize the tip position error, a virtual spring is positioned between the deviated and the desired tip positions. The proposed algorithm corrects the manipulator deviated tip position, improving tension distribution and stifness profle, resulting in higher stifness and better performance. The corresponding task space stifness and condition numbers are also computed under diferent cases, indicating the efectiveness of the tension control scheme in modulating the manipulator's stifness. Experimental validation conducted on an in-house developed prototype confrms the practical feasibility of the proposed approach. 

Keywords Continuum arm · Hyper-redundant robots · Variable stifness manipulator · Tension-based control · Mechatronic systems