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Soft robots can undergo large elastic deformations and adapt to complex shapes. However, they lack the structural strength to withstand external loads due to the intrinsic compliance of fabrication materials (silicone or rubber). In this paper, we present a novel stiffness modulation approach that controls the robot's stiffness on-demand without permanently affecting the intrinsic compliance of the elastomeric body. Inspired by concentric tube robots, this approach uses a Nitinol tube as the backbone, which can be slid in and out of the soft robot body to achieve robot pose or stiffness modulation. To validate the proposed idea, we fabricated a tendon-driven concentric tube (TDCT) soft robot and developed the model based on Cosserat rod theory. The model is validated in different scenarios by varying the joint-space tendon input and task-space external contact force. Experimental results indicate that the model is capable of estimating the shape of the TDCT soft robot with an average root mean square error (RMSE) of 0.90~mm and an average tip error of 1.49~mm. Simulation studies demonstrate that the Nitinol backbone insertion can enhance the kinematic workspace and reduce the compliance of the TDCT soft robot by 57.7%. Two case studies (object manipulation and soft laparoscopic photodynamic therapy) are presented to demonstrate the potential application of the proposed design.

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Contact force is one of the most significant feedback for robots to achieve accurate control and safe interaction with environment. For continuum robots, it is possible to estimate the contact force based on the feedback of robot shapes, which can address the difficulty of mounting dedicated force sensors on the continuum robot body with strict dimension constraints. In this paper, we use local curvatures to estimate the magnitude and location of single or multiple contact forces based on Cosserat rod theory. We validate the proposed method in a thin elastic tube and calculate the curvatures via Fiber Bragg Grating (FBG) sensors or image feedback. For the curvature feedback obtained from multicore FBG sensors, the overall force magnitude estimation error is $0.062 \pm 0.068$ N and the overall location estimation error is $3.51 \pm 2.60$ mm. For the curvature feedback obtained from image, the overall force magnitude estimation error is $0.049 \pm 0.048$ N and the overall location estimation error is $2.75 \pm 1.71$ mm. The results demonstrate that the curvature-based force estimation method is able to accurately estimate the contact force.