Abstract-- T endon-actuated concentric tube mechanisms combine the advantages of tendon-driven continuum robots and concentric tube robots while addressing their respective limitations. They overcome the restricted degrees of freedom often seen in tendon-driven designs, and mitigate issues such as snapping instability associated with concentric tube robots. However, a complete and general mechanical model for these systems remains an open problem. The model allows each tube to twist and elongate while enforcing a shared centerline for bending. We validate the proposed framework through experiments with two-tube and three-tube assemblies under various tendon routing configurations, achieving tip prediction errors < 4% of the robot's total length. We further demonstrate the model's generality by applying it to existing robots in the field, where maximum tip deviations remain around 5% of the total length. This model provides a foundation for accurate shape estimation and control of advanced tendon-actuated concentric tube robots. Minimally invasive surgical interventions have revolutionized modern medicine by reducing patient trauma, shortening recovery times, and improving procedural outcomes. However, accessing deep-seated anatomical targets, such as the spine, brain, or vasculature, poses significant challenges due to the confined, and deformable nature of biological tissues. While highly accurate in structured environments, traditional rigid-link robotic systems often lack the flexibility and compliance required to safely navigate these constrained anatomical spaces.

Spinal cord stimulation (SCS) electrodes are traditionally placed in the dorsal epidural space to stimulate the dorsal column fibers for pain therapy. Recently, SCS has gained attention in restoring gait. However, the motor fibers triggering locomotion are located in the ventral and lateral spinal cord. Currently, SCS electrodes are steered manually, making it difficult to navigate them to the lateral and ventral motor fibers in the spinal cord. In this work, we propose a helically micro-machined continuum robot that can bend in a helical shape when subjected to actuation tendon forces. Using a stiff outer tube and adding translational and rotational degrees of freedom, this helical continuum robot can perform follow-the-leader (FTL) motion. We propose a kinematic model to relate tendon stroke and geometric parameters of the robot's helical shape to its acquired trajectory and end-effector position. We evaluate the proposed kinematic model and the robot's FTL motion capability experimentally. The stroke-based method, which links tendon stroke values to the robot's shape, showed inaccuracies with a 19.84 mm deviation and an RMSE of 14.42 mm for 63.6 mm of robot's length bending. The position-based method, using kinematic equations to map joint space to task space, performed better with a 10.54 mm deviation and an RMSE of 8.04 mm. Follow-the-leader experiments showed deviations of 11.24 mm and 7.32 mm, with RMSE values of 8.67 mm and 5.18 mm for the stroke-based and position-based methods, respectively. Furthermore, end-effector trajectories in two FTL motion trials are compared to confirm the robot's repeatable behavior. Finally, we demonstrate the robot's operation on a 3D-printed spinal cord phantom model.

As soft continuum manipulators characterize terrific compliance and maneuverability in narrow unstructured space, low stiffness and limited dexterity are two obvious shortcomings in practical applications. To address the issues, a novel asymmetric coaxial antagonistic tubular robot (CATR) arm with high stiffness has been proposed, where two asymmetrically patterned metal tubes were fixed at the tip end with a shift angle of 180{\deg} and axial actuation force at the other end deforms the tube. Delicately designed and optimized steerable section and fully compliant section enable the soft manipulator high dexterity and stiffness. The basic kinetostatics model of a single segment was established on the basis of geometric and statics, and constrained optimization algorithm promotes finding the actuation inputs for a given desired task configuration. In addition, we have specifically built the design theory for the slits patterned on the tube surface, taking both bending angle and stiffness into account. Experiments demonstrate that the proposed robot arm is dexterous and has greater stiffness compared with same-size continuum robots. Furthermore, experiments also showcase the potential in minimally invasive surgery.

Concentric Tube Robots (CTRs) have been proposed to operate within the unstructured environment for minimally invasive surgeries. In this letter, we consider the operation scenario where the tubes travel inside the channels with a large clearance or large curvature, such as aortas or industrial pipes. Accurate kinematic modeling of CTRs is required for the development of advanced control and sensing algorithms. To this end, we extended the conventional CTR kinematics model to a more general case with large tube-to-tube clearance and large centerline curvature. Numerical simulations and experimental validations are conducted to compare our model with respect to the conventional CTR kinematic model. In the physical experiments, our proposed model achieved a tip position error of 1.53 mm in the 2D planer case and 4.36 mm in 3D case, outperforming the state-of-the-art model by 71% and 66%, respectively.

This paper presents a novel multi-axis force-sensing approach in robotic minimally invasive surgery with no modification to the surgical instrument. Thus, it is adaptable to different surgical instruments. A novel 6-axis optical force sensor, with local signal conditioning and digital electronics, was mounted onto the proximal shaft of a da Vinci EndoWrist instrument. A new cannula design comprising an inner tube and an outer tube was proposed. The inner tube is attached to the cannula interface to the robot base through a compliant leaf spring with adjustable stiffness. It allows bending of the instrument shaft due to the tip forces. The outer tube mechanically filters out the body forces from affecting the instrument bending behavior. A mathematical model of the sensing principle was developed and used for model-based calibration. A data-driven calibration based on a shallow neural network architecture comprising a single 5-nodes hidden layer and a 5x1 output layer is discussed. Extensive testing was conducted to validate that the sensor can successfully measure the lateral forces and moments and the axial torque applied to the instruments distal end within the desired resolution, accuracy, and range requirements.