The continuum robot is a new type of bionic robot which is widely used in the medical field. However, the current structure of the continuum robot limits its application in the field of minimally invasive surgery. In this paper, a bio-inspired compound continuum robot (CCR) combining the concentric tube continuum robot (CTR) and the notched continuum robot is proposed to design a high-dexterity minimally invasive surgical instrument. Then, a kinematic model, considering the stability of the CTR part, was established. The unstable operation of the CCR is avoided. The simulation of the workspace shows that the introduction of the notched continuum robot expands the workspace of CTR. The dexterity indexes of the robots are proposed. The simulation shows that the dexterity of the CCR is 1.472 times that of the CTR. At last, the length distribution of the CCR is optimized based on the dexterity index by using a fruit fly optimization algorithm. The simulations show that the optimized CCR is more dexterous than before. The dexterity of the CCR is increased by 1.069 times. This paper is critical for the development of high-dexterity minimally invasive surgical instruments such as those for the brain, blood vessels, heart and lungs.

Model-based control for continuum robots is often based on the piecewise constant curvature (PCC) assumption. However, the actual physical motions of continuum robots deviate significantly from this assumption, posing challenges to achieving the desired stability and accuracy in control. In this article, a real-time model-based data-driven controller is designed to enhance the precision and stability of continuum robots. An algorithm is designed to construct the static model of the cable-driven continuum robots. A real-time data-based kinematics model is formulated based on the static model, and the multistate motions of the robot are described in this model. A nonlinear control strategy is proposed based on the data-based kinematics model. Validation through simulations and experiments demonstrates the method’s robust stability and impressive precision, achieving a positioning accuracy of 0.0318 mm and a tracking accuracy of 0.0434 mm. This article provides a general paradigm for model-based control of continuum robots, which is crucial to the advancement of this industry.

The compound continuum robot employs both concentric tube components and cable-driven continuum components to achieve its complex motions. Nevertheless, the interaction between these components causes coupling, which inevitably leads to reduced accuracy. Consequently, researchers have been striving to mitigate and compensate for this coupling-induced error in order to enhance the overall performance of the robot. This paper leverages the coupling between the components of the compound continuum robot to accomplish specific surgical procedures. Specifically, the internal concentric tube component is utilized to induce motion in the cable-driven external component, which generates coupled motion under the constraints of the cable. This approach enables the realization of high-precision surgical operations. Specifically, a kinematic model for the proposed robot is established, and an inverse kinematic algorithm is developed. In this inverse kinematic algorithm, the solution of a highly nonlinear system of equations is simplified into the solution of a single nonlinear equation. To demonstrate the effectiveness of the proposed approach, simulations are conducted to evaluate the efficiency of the algorithm. The simulations conducted in this study indicate that the proposed inverse kinematic (IK) algorithm improves computational speed by a significant margin. Specifically, it achieves a speedup of 2.8 × 10³ over the Levenberg–Marquardt (LM) method. In addition, experimental results demonstrate that the coupled-motion system achieves high levels of accuracy. Specifically, the repetitive positioning accuracy is measured to be 0.9 mm, and the tracking accuracy is 1.5 mm. This paper is significant for dealing with the coupling of the compound continuum robot.

The notched continuum robot (NCR), characterized by its compact size and excellent mechanical properties, is extensively used in the design of minimally invasive surgical robots. However, integrating sensors into the NCR in a limited surgical environment is challenging. Using drive state for force estimation is a promising method that relies on the accurate modeling of the NCR. This article proposes a sensor-free force estimation method for the NCR. The method establishes an accurate static model of the NCR based on the beam constraint model (BCM). Subsequently, cable length changes are introduced as constraints into the static model, enabling sensor-free force estimation. The proposed static model demonstrates good accuracy, with results from 28 experiments showing an average position error of 1.23 mm, accounting for 2.48% of the robot's total length. Based on the accurate static model, the average estimation error of the proposed force estimation method is 7.41 mN. Compared to models using traditional assumptions, the proposed force estimation method in this article also demonstrates a significant improvement.

Concentric tube robots (CTRs) are a promising prospect for minimally invasive surgery due to their inherent compliance and ability to navigate in constrained environments. Existing mechanics-based kinematic models typically neglect friction, clearance, and torsion between each pair of contacting tubes, leading to large positioning errors in medical applications. In this paper, an improved kinematic modeling method is developed. The effect of clearance on tip position during concentric tube assembly is compensated by the database method. The new kinematic model is mechanic-based, and the impact of friction moment and torsion on tubes is considered. Integrating the infinitesimal torsion of the concentric tube robots eliminates the errors caused by the interaction force between the tubes. A prototype is built, and several experiments with kinematic models are designed. The results indicate that the error of tube rotations is less than 2 mm. The maximum error of the feeding experiment does not exceed 0.4 mm. The error of the new modeling method is lower than that of the previous kinematic model. This paper has substantial implications for the high-precision and real-time control of concentric tube robots.

Combining different types of continuum manipulators is a potential strategy to overcome the limitations of continuum manipulators. In this paper, a high-accuracy hybrid continuum manipulator (HCM) consisting of a notch continuum manipulator section and a concentric tube manipulator section is proposed. The static model of the manipulator is established, and an optimization algorithm of the manipulator has been carried out to enhance the precision of the kinematic model. This algorithm can optimize the accuracy of the model while retaining the high computational speed. Then, three different modes, namely the trajectory planning mode, operation mode, and hybrid mode are introduced to cater to distinct surgical requirements. The mechanical structure of the HCM is specifically designed to realize the modes above. The experimental results demonstrate a repetition positioning error of 0.4745 mm and an operation error of 1.7801 mm. The kinematic model error of the optimized manipulator was reduced by 77.4% compared to its pre-optimization state. Finally, the feasibility of the manipulator is demonstrated through function testing experiments. The proposed manipulator design provides a more versatile and adaptable solution to meet the diverse requirements of surgical procedures.