Craniosynostosis involves premature fusion of the cranial sutures resulting in abnormal skull morphology and elevated intracranial pressure. Surgical intervention is necessary to correct the skull shape and to allow for unrestricted brain growth. This study presents a novel snake robot designed for minimally invasive cranial osteotomies featuring two articulating bending segments. The end-effector comprises a bone-punch for bone-cutting, a dural and scalp retractor, as well as channels for an endoscope and an instrument. The robot's bending mechanism is driven by tendons and utilizes geared linkages to facilitate a smooth curved shape. Pre-tensioned antagonistic tendons allow the robot to modulate its stiffness to adapt to external loads. A follow-the-leader algorithm was implemented to guide the robot along a skull cutting path. Experimental results demonstrated that at maximum bending of$60^{\circ}$for segment 1 and$90^{\circ}$for segment 2 there was a$15.9^{\circ}$and$11.5^\circ$error, respectively. Position errors ranged from 2.5 to 21.5 mm when tracing a curved path. The tool increased stiffness with tendon pre-tensioning from 20–100 N during bent configurations$q_{1}$and$q_{2}$for segments 1 and 2, respectively, at$[q_{1},q_{2}]=[0^{\mathrm{o}},30^{\mathrm{o}}]$and$[30^{\circ},60^{\circ}]$. Tip deflection reduced from 0.42 to 0.03 cm and 0.37 to 0.10 cm during axial loading and from 11.40 to 3.88 cm and 3.62 to 0.48 cm during radial loading for each configuration, respectively. Ex vitro trials demonstrated the robots ability to perform simulated osteotomies on skull models to 68–73% of desired path lengths with a maximum deviation of 8 mm.

Concentric tube robots (CTRs) hold great potential for minimally invasive surgery, offering flexibility, small diameters, and the ability to navigate within complex anatomical structures. While machine learning models have been increasingly used to predict the kinematics of CTRs, there is a lack of an established framework for evaluating generative inverse kinematic models, which are able to solve the inverse kinematic problem by providing various joint solutions for a desired end position. In this study, we introduce a workspace-based measure to assess the diversity of solutions produced by three generative models: an invertible neural network (INN), a conditional invertible neural network (cINN), and a conditional variational autoencoder (cVAE). We find that all three models record similar end position errors (3-6 mm) on dexterous subsets of the workspace, but that a cINN outperforms the others in generating diverse solutions using a workspace-based 1-Wasserstein distance by at least 2.38 standard deviations. To further test the applicability of these models, we integrate the best-performing cINN into a CTR controller and demonstrate the first use of a generative CTR model with real-time teleoperation under task-based constraints.