In continuum robotics, real-time robust shape estimation is crucial for planning and control tasks that involve physical manipulation in complex environments. In this paper, we present a novel stochastic observer-based shape estimation framework designed specifically for continuum robots. The shape state space is uniquely represented by the modal coefficients of a polynomial, enabled by leveraging polynomial curvature kinematics (PCK) to describe the curvature distribution along the arclength. Our framework processes noisy measurements from limited discrete position, orientation, or pose sensors to estimate the shape state robustly. We derive a novel noise-weighted observability matrix, providing a detailed assessment of observability variations under diverse sensor configurations. To overcome the limitations of a single model, our observer employs the Interacting Multiple Model (IMM) method, coupled with Extended Kalman Filters (EKFs), to mix polynomial curvature models of different orders. The IMM approach, rooted in Markov processes, effectively manages multiple model scenarios by dynamically adapting to different polynomial orders based on real-time model probabilities. This adaptability is key to ensuring robust shape estimation of the robot's behaviors under various conditions. Our comprehensive analysis, supported by both simulation studies and experimental validations, confirms the robustness and accuracy of our methods.

Grasp synergies represent a useful idea to reduce grasping complexity without compromising versatility. Synergies describe coordination patterns between joints, either in terms of position (joint angles) or effort (joint torques). In both of these cases, a grasp synergy can be represented as a low-dimensional manifold lying in the high-dimensional joint posture or torque space. In this article, we use the term mechanically realizable manifolds to refer to the subset of such manifolds (in either posture or torque space) that can be achieved via mechanical coupling of the joints in underactuated hands. We present a method to optimize the design parameters of an underactuated hand in order to shape the mechanically realizable manifolds to fit a predefined set of desired grasps. Our method guarantees that the resulting synergies can be physically implemented in an underactuated hand, and will enable the resulting hand to both reach the desired grasp postures and achieve quasi-static equilibrium while loading the grasps. We demonstrate this method on three concrete design examples motivated by a real use case, and evaluate and compare their performance in practice.

Currently, surgical continuum robots (CRs) are predominantly used as telemanipulators where modeling errors are overcome by the user. Such errors preclude their use for autonomous tasks. In this paper, we investigate the calibration of CRs with specific focus on capturing joint space errors due to homing offsets, assembly errors causing twist about the robot's backbone, and uncertainty in the equilibrium bending shapes of segments of these robots. A kinematic framework focusing on multibackbone CR is presented with emphasis on deriving calibration identification Jacobians. This framework captures the coupling between twist and the equilibrium shapes of a continuum segment as a function of its bending angle. To capture equilibrium shape variations as a function of bending, a homotopy of curves is defined and represented by respective modal coefficients. The estimation of the calibration parameters is cast as a nonlinear least-squares problem. The framework is validated by simulations and experimentally using a single-port access surgery robot. We believe this calibration framework will facilitate semiautomation of surgical tasks carried out by CRs.

In this work, we develop an approach for guiding robots to automatically localize and find the shapes of tumors and other stiff inclusions present in the anatomy. Our approach uses Gaussian processes to model the stiffness distribution and active learning to direct the palpation path of the robot. The palpation paths are chosen such that they maximize an acquisition function provided by an active learning algorithm. Our approach provides the flexibility to avoid obstacles in the robot's path, incorporate uncertainties in robot position and sensor measurements, include prior information about location of stiff inclusions while respecting the robot-kinematics. To the best of our knowledge this is the first work in literature that considers all the above conditions while localizing tumors. The proposed framework is evaluated via simulation and experimentation on three different robot platforms: 6-DoF industrial arm, da Vinci Research Kit (dVRK), and the Insertable Robotic Effector Platform (IREP). Results show that our approach can accurately estimate the locations and boundaries of the stiff inclusions while reducing exploration time.

Existing robots for multi-scale motion (MSM) are unsuitable for micro-surgery in deep surgical sites where miniaturization and traversal of often tortuous anatomical passageways is required. Also, new emerging surgical paradigms for natural orifice surgery and image-based diagnosis and guidance at the micro-scale level promise to provide accurate verification of tumor resection margins. To overcome the limitations of current robot architectures, and to enable image-based biopsy and micro-surgery in confined spaces, we present a new concept of continuum robots with equilibrium modulation (CREM). CREM robots are a modification of multi-backbone continuum robots that achieve micro-motion by using indirect actuation through modulation of their static equilibrium by change of the distribution of their cross-sectional flexural rigidity. As a first step towards modeling the micro-scale kinematics of these robots, solutions for micro-motion tracking are presented and verified to achieve tracking accuracies of better than 2μm. Preliminary evaluation of the micro-motion capabilities of a first prototype demonstrates motion resolutions at 1μm level and hysteresis of less than 10μm - despite the use of inexpensive actuators with significant backlash. Finally, a demonstration of a first effort at integrating such a robot with a custom-made optical coherence tomography (OCT) probe is presented.

One of the goals of computer-aided surgery is to register intraoperative data to preoperative model of the anatomy, and hence add complementary information that can facilitate the task of surgical navigation. In this context, mechanical palpation can reveal critical anatomical features such as arteries and cancerous lumps which are stiffer than the surrounding tissue. This work uses position and force measurements obtained during mechanical palpation for registration and stiffness mapping. Prior approaches, including our own, exhaustively palpated the entire organ to achieve this goal. To overcome the costly palpation of the entire organ, a Bayesian optimization framework is introduced to guide the end effector to palpate stiff regions while simultaneously updating the registration of the end effector to an a priori geometric model of the organ, hence enabling the fusion of intraoperative data into the a priori model obtained through imaging. This new framework uses Gaussian processes to model the stiffness distribution and Bayesian optimization to direct where to sample next for maximum information gain. The proposed method was evaluated with experimental data obtained using a Cartesian robot interacting with a silicone organ model and an ex vivo porcine liver.

Surgeons often manually palpate tissue or organs in order to find tumors or other anatomical structures. Information about organ geometry and tissue stiffness gained from palpation can also be extremely useful in robotic surgery for diagnosis, surgical guidance, and registration to other preoperative information. However, it is not always easy to obtain, even if the robot is equipped with force sensors. This paper reports our approach for concurrent estimation of stiffness and surface geometry, using a continuous motion similar to a sweeping palpation motion used by surgeons. Our method relies on force data captured by a tactile sensor rigidly attached to an end-effector probe. We use Gaussian processes to simultaneously estimate geometry and stiffness. The method is not tied to any specific robotic platform and is consistent with a variety of palpation strategies. For simplicity, we discuss the results based on two different palpation primitives. This is our first step towards developing an adaptive high fidelity model reconstruction and path optimization technique.

Multi-backbone continuum robots have been demonstrated to possess wrench sensing capabilities by measuring the actuation load on each backbone and then using elaborate statics models. The ability to sense forces of interaction allows these robots to also control their interaction with the environment. In past studies, the force sensing models were subject to quasi-static assumptions. The goal of this paper is threefold: to update the wrench sensing model taking into account dynamic forces, to investigate the effect of these dynamic forces on the wrench sensing abilities of these robots and to present design atlases that help designers with the determination of critical dimensions ensuring bounded effect of dynamics on wrench sensing. The paper presents a simplified dynamics model using a Lagrangian formulation. This dynamics model is then used to update the wrench estimation model for a single-segment continuum robot. Finally, a set of normalized parameters is used to produce design atlases that help designers predict the effect of dynamics on the wrench estimation model. These results will allow improved performance in force sensing and control for multi-backbone continuum robots. Employing the methods presented in the paper, continuum robots, that have previously demonstrated excellent distal dexterity, will be able to control their force interaction with the anatomy better in future - thereby improving safety and the finesse of surgery.

Registering a surgical tool to an a priori model of the environment is an important first step in computer-aided surgery. In this paper we present an approach for simultaneous registration and stiffness mapping using blind exploration of flexible environments. During contact-based exploration of flexible environments, the physical interaction with the environment can induce local deformation, leading to erroneous registration if not accounted for. To overcome this issue, a new registration method called complementary model update (CMU), is introduced. By incorporating measurements of the contact force, and contact location, we minimize a unique objective function to cancel out the effect of local deformation. We are thus able to acquire the necessary registration parameters using both geometry and stiffness information. The proposed CMU method is evaluated in simulation and using experimental data obtained by probing silicone models and an ex vivo organ.

In this paper, we present the integration and preliminary evaluation of a novel Insertable Robotic Effectors Platform (IREP) for Single Port Access Surgery (SPAS). The unique design of the IREP includes planar parallel mechanisms, continuum snake-like arms, wire-actuated wrists, and passive flexible components. While this design has advantages, it presents challenges in terms of modeling, control, and telemanipulation. The complete master-slave resolved-rates telemanipulation framework of the IREP along with its actuation compensation is presented. Experimental evaluation of the capabilities of this new surgical system include bi-manual exchange of rings, pick-and-place tasks, suture passing and knot tying. Results show that the IREP meets the minimal workspace and dexterity requirements specified for laparoscopic surgery, it allows for dual-arm operations such as tool exchange and knot tying in confined spaces. Although it was possible to tie a surgeon's knot with minimal training, suture passing was difficult due to the limited axial rotation of the distal wrists.