This paper presents a method for comprehensive 6D estimation of tip wrench for generally deflected static elastic rods. Current methods for load estimation are restricted to estimating lateral (point or distributed) forces for (quasi-)planar deformation; estimation of tangential force and moment, i.e., the full 6D wrench, remains largely unreliable due to the ill-posed nature of the problem. To address this challenge, this paper begins by proposing a high-fidelity static rod model that leverages Koopman Operator theory. Building on this model and utilizing shape feedback, a computationally efficient three-step wrench estimator is proposed: (i) a Koopman-UKF local moment observer, (ii) a static equilibrium solver, and (iii) a rod model propagator. Then, a 2D wrench screw system, identified as the insensible wrench in the initial estimation, elucidates error sources and informs strategies to enhance accuracy by incorporating additional feedback, such as the rod tip material frame and base axial force. Ultimately, the framework delivers accurate 6D tip wrench estimation with quantified uncertainty. Simulation and experimental evaluations validate its effectiveness, demonstrating mean errors of$53.14\,$mN (1.94%) and$2.65\,$mNm (7.18%) for a$159\,$mm-long Nitinol tube undergoing complex out-of-plane deformations, outperforming three replicated state-of-the-art methods. Additionally, its applicability to more complex continuum robots is demonstrated through load estimation on a Parallel Continuum Robot.

This paper presents an uncertainty-aware shared control and calibration method for micromanipulation using a digital microscope and a tool-mounted, multi-joint robotic arm, integrating real-time human intervention with a visual-motor policy. Our calibration algorithm leverages co-manipulation control to calibrate the hand-eye transformation without requiring knowledge of the kinematics of the microtool mounted on the robot while remaining robust to camera intrinsics errors. Experimental results show that the proposed calibration method achieves a 39.6% improvement in accuracy over established methods. Additionally, our control structure and calibration method reduces the time required to reach single-point targets from 5.74 s (best conventional method) to 1.91 s, and decreases trajectory tracking errors from 392 μm to 40 μm. These findings establish our method as a robust solution for improving reliability in high-precision biomedical micromanipulation.

Continuum manipulators can accomplish various tasks in confined spaces, benefiting from their compliant structures and improved dexterity. Confined and unstructured spaces may require both enhanced stiffness of a continuum manipulator for precision and payload, as well as compliance for safe interaction. Thus, studies have been consistently dedicated to design continuum or articulated manipulators with tunable stiffness to adapt to different operating conditions. This paper presents a continuum manipulator with independently tunable stiffness where the stiffness variation does not affect the movement of the manipulator's end-effector. Moreover, the proposed continuum manipulator is found to have analytical inverse kinematics. The design concept, analytical kinematics, system construction and experimental characterizations are presented. The results showed that the manipulator's stiffness can be increased up to 3.61 times of the minimal value, demonstrating the effectiveness of the proposed idea.

Fruitful developments on continuum robots have been witnessed in recent years due to their movements and manipulation capabilities in confined spaces. Due to the nature that a continuum robot has an infinite number of DoFs (Degrees of Freedom), majority of the existing systems deployed abundant actuators such that the robot can be controlled in separately modeled and actuated segments with constant or variable curvature. As the shape of a continuum robot is always jointly determined by its actuation and the interactions from the environment, it is hence worth exploring the opposite approach that how a task can be accomplished with a minimal number of actuators. This paper presents the first step of such an investigation where a slim 3-actuator continuum robot is actuated to reach different spatial locations under gravity. As the gravity greatly affects the robot's shape, a monocular camera, together with two UKFs (Unscented Kalman Filters), was used to concurrently estimate the robot's shape and the feature depth. Then the estimated shape can be used in updating the kinematics model of the robot to achieve motion control. Experiments were conducted to validate the effectiveness of the proposed shape estimation, which promises the motion control implementation in the near future work.