Real-Time Shape Estimation for Concentric Tube Continuum Robots with a Single Force/Torque Sensor

Shape-sensing in real-time is a key requirement for the development of advanced algorithms for concentric tube continuum robots when safe interaction with the environment is important e.g., for path planning, advanced control, and human-machine interaction. We propose a real-time shape-estimation algorithm for concentric tube continuum robots based on the force-torque information measured at the tubes’ basis. It extends a shape estimation algorithm for elastic rods based on discrete Kirchhoff rod theory. For simplicity and efficiency of calculation, we combine it with a model under piece-wise constant curvature assumption, in which we model a concentric tube continuum robot as a combination of segments of planar constant curvatures lying on different equilibrium planes. We evaluate our approach for a single and two combined additively manufactured tubes and achieve an estimation frequency of 333 Hz for two combined tubes with a mean deviation along the backbone of the tubes of 1.91–5.22 mm.

On a consistent rod theory for a linearized anisotropic elastic material II. Verification and parametric study

We have derived a rod theory by an asymptotic reduction method for a straight and circular rod composed of linearized anisotropic material in part I of this series. In the current work, we first verify the derived rod theory through five benchmark Saint-Venant’s problems. Then, under a specific loading condition (line force at the lateral surface with two clamped ends), we apply the rod theory to conduct a parametric study of the effects of elastic moduli on the deformation of a rod composed of four types of anisotropic materials including cubic, transversely isotropic, orthotropic, and monoclinic materials. Analytical solutions for the displacement, axial twist angle, stress, and principal stress have been obtained and a systematic investigation of the effects of elastic moduli on these quantities is conducted, which is the main feature of this paper. It is found that these elastic moduli arise in a certain form and in a certain order in the solutions, which gives information about how to appropriately choose moduli to adjust the deformation. Among the four anisotropic materials, it turns out that the monoclinic material presents the most remarkable mechanical behavior owing to the existence of a coupling coefficient: it yields coupled leading-order rod equations, non-trivial axial twist angle, non-negligible transverse shear deformation, and a more adjustable principal stress along the axis.

Dynamics and path tracking of continuum robotic arms using data-driven identification tools

In this paper, forward/inverse dynamics of a continuum robotic arm is developed using a data-driven approach, which could tackle uncertainties and extreme nonlinearities to obtain reliable solutions. By establishing a direct mapping between the actuator and task spaces, the unnecessary mappings of actuator-to-configuration then configuration-to-task are eliminated, to reduce extra computational cost. The proposed approach is validated through simulation (based on Cosserat rod theory) and experimental tests on RoboArm. Next, path tracking in the presence/absence of obstacles as well as load carrying maneuver are investigated. Finally, the obtained results concerning repeatability, scalability, and disturbance rejection performance of the approach are discussed.

FBG-Based Estimation of External Forces Along Flexible Instrument Bodies

A variety of medical treatment and diagnostic procedures rely on flexible instruments such as catheters and endoscopes to navigate through tortuous and soft anatomies like the vasculature. Knowledge of the interaction forces between these flexible instruments and patient anatomy is extremely valuable. This can aid interventionalists in having improved awareness and decision-making abilities, efficient navigation, and increased procedural safety. In many applications, force interactions are inherently distributed. While knowledge of their locations and magnitudes is highly important, retrieving this information from instruments with conventional dimensions is far from trivial. Robust and reliable methods have not yet been found for this purpose. In this work, we present two new approaches to estimate the location, magnitude, and number of external point and distributed forces applied to flexible and elastic instrument bodies. Both methods employ the knowledge of the instrument’s curvature profile. The former is based on piecewise polynomial-based curvature segmentation, whereas the latter on model-based parameter estimation. The proposed methods make use of Cosserat rod theory to model the instrument and provide force estimates at rates over 30 Hz. Experiments on a Nitinol rod embedded with a multi-core fiber, inscribed with fiber Bragg gratings, illustrate the feasibility of the proposed methods with mean force error reaching 7.3% of the maximum applied force, for the point load case. Furthermore, simulations of a rod subjected to two distributed loads with varying magnitudes and locations show a mean force estimation error of 1.6% of the maximum applied force.

Conveyance of texture signals along a rat whisker

Neuronal activities underlying a percept are constrained by the physics of sensory signals. In the tactile sense such constraints are frictional stick–slip events, occurring, amongst other vibrotactile features, when tactile sensors are in contact with objects. We reveal new biomechanical phenomena about the transmission of these microNewton forces at the tip of a rat’s whisker, where they occur, to the base where they engage primary afferents. Using high resolution videography and accurate measurement of axial and normal forces at the follicle, we show that the conical and curved rat whisker acts as a sign-converting amplification filter for moment to robustly engage primary afferents. Furthermore, we present a model based on geometrically nonlinear Cosserat rod theory and a friction model that recreates the observed whole-beam whisker dynamics. The model quantifies the relation between kinematics (positions and velocities) and dynamic variables (forces and moments). Thus, only videographic assessment of acceleration is required to estimate forces and moments measured by the primary afferents. Our study highlights how sensory systems deal with complex physical constraints of perceptual targets and sensors.

Coupled Time-Domain Hydro-Elastic Simulation for Submerged Floating Tunnel Under Wave Excitations

We develop a fully-coupled time-domain hydro-elasticity model for the Submerged Floating Tunnel (SFT) based on the Discrete-Module-Beam (DMB) method. Frequency-domain simulation based on 3D potential theory results in multibody’s hydrodynamic coefficients and excitation forces for tunnel sections. Subsequently, we build the time-domain model with the multibody Cummins equation and external stiffness matrix from the Euler-Bernoulli and Saint-Venant torsion theories. We establish the mooring line model with rod theory and couple components with translational springs at their respective connection locations. We then compare the dynamic motions, wave forces, and mooring tensions between the present and Morison-equation-based elastic models under regular wave excitations at different submergence depths. The present model is especially important for the shallowly submerged tunnel in which the Morison model shows exaggerated motions, especially at high-frequency range.

Modeling and Fabrication of Soft Actuators Based on Fiber-Reinforced Elastomeric Enclosures

Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between the deformation of soft actuators and external factors such as pressure would enable rapid designs based on specific requirements, such as flexible, compliant endoscopes. An effective model is demonstrated that predicts the deformation of a soft actuator based on the virtual work principle and the geometrically exact Cosserat rod theory. The deformation process is analyzed for extension, bending, and twisting modules. A new manufacturing method is then introduced. Through any combination of modules, the soft actuator can have a greater workspace and more dexterity. The proposed model was verified for various fiber-reinforced elastomeric enclosures. There is good agreement between the model analysis and the experimental data, which indicates the effectiveness of the model.