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Continuum robots are a type of robotic device that are characterized by their flexibility and dexterity, thus making them ideal for an active endoscope. Instead of articulated joints they have flexible backbones that can be manipulated remotely, usually through tendons secured onto structures attached to the backbone. This structure makes them lightweight and ideal to be miniaturized for endoscopic applications. However, their flexibility poses technical challenges in the modeling and control of these devices, especially when closed-loop control is needed, as is the case in medical applications. There are two main approaches in the modeling of continuum robots, the first is to theoretically model the behavior of the backbone and the interaction with the tendons, while the second is to collect experimental observations and retrospectively apply a model that can approximate their apparent behavior. Both approaches are affected by the complexity of continuum robots through either model accuracy/computational time (theoretical method) or missing complex system interactions and lacking expandability (experimental method). In this work, theoretical and experimental descriptions of an endoscopic continuum robot are merged. A simplified yet representative mathematical model of a continuum robot is developed, in which the backbone model is based on Cosserat rod theory and is coupled to the tendon tensions. A robust numerical technique is formulated that has low computational costs. A bespoke experimental facility with precise automated motion of the backbone via the precise control of tendon tension, leads to a robust and detailed description of the system behavior provided through a contactless sensor. The resulting facility achieves a real-world mean positioning error of 3.95% of the backbone length for the examined range of tendon tensions which performs favourably to existing approaches. Moreover, it incorporates hysteresis behavior that could not be predicted by the theoretical modeling alone, reinforcing the benefits of the hybrid approach. The proposed workflow is theoretically grounded and experimentally validated allowing precise prediction of the continuum robot behavior, adhering to realistic observations. Based on this accurate estimation and the fact it is geometrically agnostic enables the proposed model to be scaled for various robotic endoscopes.

Passive rotors are often limited in rotational speed due to bearing constraints, stability and excessive vibration levels. To address the vibration issue, Active Magnetic Bearings (AMBs) levitating the rotor with a magnetic field can be used. They offer a clearance and variable stiffness and damping to the rotor support, which help to mitigate greatly the vibration issue. However, they are also limited at large rotational speed because of the high frequency control force required to levitate the rotor safely. To overcome the frequency limitation, a dual AMBs/internal bending control concept is investigated with associated modelling and control algorithms. This approach is examined in simulation with a 19 kg rotor running up to 10,000 RPM, where three resonance frequencies are present at 2700, 5300, and 9300 RPM, with the first resonant frequency being the most strongly excited. Using internal rotor bending control, a maximum radial displacement of 15 μm for the rotor mid-point is achieved, which gives a reduction in vibration amplitude of 45% compared to the case of no control. Variations of the algorithm are presented and discussed, showing the potential of the proposed approach.

An initial deterministic mathematical model for the dynamic motion of a simple pressurised liquid film bearing is derived and utilised to evaluate the possibility of bearing contact for thin film operation. For a very thin film bearing the flow incorporates a Navier slip boundary condition as parametrised by a slip length that in general is subject to significant variability and is difficult to determine with precision. This work considers the formulation of a modified Reynolds equation for the pressurised liquid flow in a highly rotating coned bearing. Coupling of the axial motion of the stator is induced by prescribed axial oscillations of the rotor through the liquid film. The bearing gap is obtained from solving a nonlinear second-order non-autonomous ordinary differential equation, via a mapping solver. Variability in the value of the slip length parameter is addressed by considering it as a random variable with prescribed mean and standard deviation. The method of derived distributions is used to exactly quantify the impact of variability in the slip length with a parametric study investigating the effect of both the deterministic and distribution parameters on the probability of contact. Additionally, as the axial rotor oscillations also have a random aspect due to possible varying excitations of the system, the probability of contact is investigated for both random amplitude of the periodic rotor oscillations and random slip length, resulting in a two parameter random input problem. The probability of contact is examined to obtain exact solutions and evaluate a range of bearing configurations.