Kinetostatic Path Planning for Continuum Robots By Sampling on Implicit Manifold

Continuum robots (CR) offer excellent dexterity and compliance in contrast to rigid-link robots, making them suitable for navigating through, and interacting with, confined environments. However, the study of path planning for CRs while considering external elastic contact is limited. The challenge lies in the fact that CRs can have multiple possible configurations when in contact, rendering the forward kinematics not well-defined, and characterizing the set of feasible robot configurations as non-trivial. In this paper, we propose to solve this problem by performing quasi-static path planning on an implicit manifold. We model elastic obstacles as external potential fields and formulate the robot statics in the potential field as the extremal trajectory of an optimal control problem obtained by the first-order variational principle. We show that the set of stable robot configurations is a smooth manifold diffeomorphic to a submanifold embedded in the product space of the CR actuation and base internal wrench. We then propose to perform path planning on this manifold using AtlasRRT*, a sampling-based planner dedicated to planning on implicit manifolds. Simulations in different operation scenarios were conducted and the results show that the proposed planner outperforms Euclidean space planners in terms of success rate and computational efficiency.Comment: 7 pages, 4 figures, submitted to IEEE ICRA 202

Task and Configuration Space Compliance of Continuum Robots via Lie Group and Modal Shape Formulations

Continuum robots suffer large deflections due to internal and external forces. Accurate modeling of their passive compliance is necessary for accurate environmental interaction, especially in scenarios where direct force sensing is not practical. This paper focuses on deriving analytic formulations for the compliance of continuum robots that can be modeled as Kirchhoff rods. Compared to prior works, the approach presented herein is not subject to the constant-curvature assumptions to derive the configuration space compliance, and we do not rely on computationally-expensive finite difference approximations to obtain the task space compliance. Using modal approximations over curvature space and Lie group integration, we obtain closed-form expressions for the task and configuration space compliance matrices of continuum robots, thereby bridging the gap between constant-curvature analytic formulations of configuration space compliance and variable curvature task space compliance. We first present an analytic expression for the compliance of a single Kirchhoff rod. We then extend this formulation for computing both the task space and configuration space compliance of a tendon-actuated continuum robot. We then use our formulation to study the tradeoffs between computation cost and modeling accuracy as well as the loss in accuracy from neglecting the Jacobian derivative term in the compliance model. Finally, we experimentally validate the model on a tendon-actuated continuum segment, demonstrating the model's ability to predict passive deflections with error below 11.5\% percent of total arc length

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multisegment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic methods. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6%-8% (4-6 mm) mean error for the Ritz-Galerkin method in static cases and 16%-20% (12-14 mm) mean error for the Ritz method in dynamic cases, in planar and general three-dimensional motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation, and control applications

Stiffness Imaging With a Continuum Appendage: Real-Time Shape and Tip Force Estimation From Base Load Readings

In this paper, we propose benefiting from load readings at the base of a continuum appendage for real-time forward integration of Cosserat rod model with application in configuration and tip load estimation. The application of this method is successfully tested for stiffness imaging of a soft tissue, using a 3-DOF hydraulically actuated braided continuum appendage. Multiple probing runs with different actuation pressures are used for mapping the tissue surface shape and directional linear stiffness, as well as detecting non-homogeneous regions, e.g. a hard nodule embedded in a soft silicon tissue phantom. Readings from a 6-axis force sensor at the tip is used for comparison and verification. As a result, the tip force is estimated with 0.016-0.037 N (7-20%) mean error in the probing and 0.02-0.1 N (6-12%) in the indentation direction, 0.17 mm (14%) mean error is achieved in estimating the surface profile, and 3.4-15 [N/m] (10-16%) mean error is observed in evaluating tissue directional stiffness, depending on the appendage actuation. We observed that if the appendage bends against the slider motion (toward the probing direction), it provides better horizontal stiffness estimation and better estimation in the perpendicular direction is achieved when it bends toward the slider motion (against the probing direction). In comparison with a rigid probe, ≈ 10 times smaller stiffness and ≈ 7 times larger mean standard deviation values were observed, suggesting the importance of a probe stiffness in estimation the tissue stiffness

Closed Loop Force Control of In-Situ Machining Robots using Audible Sound Features

Detecting, measuring and controlling the forces between cutting tools and machined components is essential in circumstances where direct position control (e.g. depth of cut, feed speed, etc.) is inaccurate and/or impossible. This paper explores the use of airborne sound signals that result from the machining process to control the cutting force in closed loop for generating accurate machined features when performing in-situ robotic repair of complex installations. The sound signals during indentation at various cutting forces are analysed and used to calibrate a remotely mounted microphone sensor and signal processing control system. The power spectral density of the audible sound is used to estimate tool cutting force and the sound intensity used in turn to estimate the resulting process energy. The described controller uses intensity of sound to mitigate the e_ects of resonance with workpiece natural frequencies while controlling the spindle velocity of the tool based on the dominant audible frequency. The performance of the controller is validated using a representative test rig and demonstrated using a robotic arm to machine thin Ni-Cr-Co alloy cantilever beams with a miniature air-driven grinding tool. Results from the test rig show that such a sound-based control approach can achieve consistent cutting forces with an accuracy of 0.08 N. The robot arm is shown to be capable of grinding features of consistent depth (to within 0.05 mm) on beams with surface defects of unde_ned shape using only the sound of the process for closed loop force control

An Online Model-Free Adaptive Tracking Controller for Cable-Driven Medical Continuum Manipulators

Continuum manipulators have demonstrated promising potential for flexible access and complicated operation and thus have been emerging and introduced in robot-assisted flexible endoscopy. However, due to their inherent structural compliance and strong nonlinearities, developing an accurate and robust control framework remains challenging. This paper proposes a model-free control method based on the Model-Free Adaptive Control (MFAC) algorithm to accomplish the trajectory tracking for two kinds of continuum manipulators by solely utilizing the robotic system’s real-time input/output data. The presented controller discretizes and dynamically linearizes the motion process of the continuum actuator to obtain a dynamic linearization data (DLD) model. This DLD model can be derived from a pseudo-partial derivative (PPD) matrix updated based on the I/O measurement data for the iterative operation. The stability of the presented MFAC controller can be mathematically guaranteed in theory to provide generality, and the control framework demonstrates a low computational cost and real-time control capability. The superior performance of the presented controller is firstly validated in MATLAB simulations and then compared with the other two controllers. Through experimental validation on two kinds of continuum manipulators, the model-free control framework shows high tracking accuracy and good robustness against the system uncertainty and external disturbances, as well as high transferability

Design and validation of a novel fuzzy-logic-based static feedback controller for tendon-driven continuum robots

10.13039/100013406-Aerospace Technology Institute; 10.13039/501100000266-Engineering and Physical Sciences Research Council

NOVEL SENSOR PLATFORMS BASED ON FABRY-PEROT RESONATORS FOR APPLICATIONS IN ENVIRONMENTAL GEOPHYSICS

Fabry-Perot resonator sensors have been widely used for various physical and chemical measurements owing to their unique advantages over traditional sensors such as high measurement resolution, mechanically robust, and distributed sensing capabilities. This dissertation focuses on the development of robust fiber optic microwave sensors based on Fabry-Perot resonator mechanism for real-time applications in environmental geophysics. Firstly, a novel Extrinsic Fabry-Perot Interferometer (EFPI)-based fiber-optic sensor for force measurement using a pre-buckled beam was demonstrated. The axial displacement is transferred and amplified to a horizontal deflection at the middle of the buckled beam, leading to a relatively significant change in the Fabry-Perot cavity length. The force measurement range and the size of the sensor can be easily reconfigured by adjusting the size of the beam, enabling force measurement for different scenarios. Secondly, a self-compensated inclinometer with a wide dynamic range and high measurement resolution based on two hollow coaxial cable Fabry-Perot resonators (HCC-FPRs) was reported. By tracking the shift of the resonance wavelength of the HCC-FPR, two HCC-FPRs are used in the inclinometer design, which enables the inclinometer to achieve self-compensation for variations in environmental factors. Thirdly, a Polyvinyl Alcohol (PVA) film-assisted open-ended hollow coaxial cable Fabry-Perot resonator was proposed for highly sensitive embeddable soil moisture measurements. The invented sensor platform could be reconfigured to detect chemical contaminants in soil by changing the functional films in the active zone of the sensor --Abstract, p. i

Challenges of continuum robots in clinical context: a review

With the maturity of surgical robotic systems based on traditional rigid-link principles, the rate of progress slowed as limits of size and controllable degrees of freedom were reached. Continuum robots came with the potential to deliver a step change in the next generation of medical devices, by providing better access, safer interactions and making new procedures possible. Over the last few years, several continuum robotic systems have been launched commercially and have been increasingly adopted in hospitals. Despite the clear progress achieved, continuum robots still suffer from design complexity hindering their dexterity and scalability. Recent advances in actuation methods have looked to address this issue, offering alternatives to commonly employed approaches. Additionally, continuum structures introduce significant complexity in modelling, sensing, control and fabrication; topics which are of particular focus in the robotics community. It is, therefore, the aim of the presented work to highlight the pertinent areas of active research and to discuss the challenges to be addressed before the potential of continuum robots as medical devices may be fully realised