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Continuum manipulators have found several applications in surgical interventions like endoscopy, laparoscopy, and as end‐effectors for surgical robots. Continuum manipulators coupled with magnetic actuation can be precisely maneuvered inside the human body. Recently, variable stiffness manipulators (VSMs) have been introduced for enhanced dexterity and safe navigation. This study presents a new design of a magnetically actuated VSM based on shape memory polymer (SMP) springs. The VSM has a silicone backbone enclosed within a spring made of SMP that can change in length with stiffness change that is triggered by Joule heating. The stiffness and thermal characteristics of the VSM are studied using analytical models and experiments. Subsequently, a one‐segment VSM and a two‐segment VSM having outer diameters of 9 and 10 mm and lengths of 15 and 25 mm, respectively, capable of extending to four times their length are designed. The VSM can be deployed in a compact form and extended to achieve variable bending curvatures in soft and rigid states, which can facilitate instrument insertion and reduce operation invasiveness. Potential clinical applications are demonstrated by incorporating miniature camera, biopsy tool, and laser optical fiber in the working channel of the VSM and coupled with robotic magnetic actuation. This work presents a new deployable variable stiffness manipulator (VSM) based on shape memory polymer (SMP) springs. The VSM exhibits variable stiffness and variable bending curvatures at variable working lengths. The shape locking ability of the VSM is coupled with magnetic actuation to facilitate instrument insertion, stably deploy surgical tools, and enhance maneuverability to reach difficult‐to‐access surgical sites safely.

Continuum manipulators (CM) are soft and flexible manipulators with large numbers of degrees of freedom and can perform complex tasks in an unstructured environment. However, their deformability and compliance can deviate distal tip under uncertain external interactions. To address this challenge, a novel tension-based control scheme has been proposed to modulate the stiffness of a tendon-driven CM, reducing the tip position errors caused by uncertain external forces. To minimize the tip position error, a virtual spring is positioned between the deviated and the desired tip positions. The proposed algorithm corrects the manipulator deviated tip position, improving tension distribution and stiffness profile, resulting in higher stiffness and better performance. The corresponding task space stiffness and condition numbers are also computed under different cases, indicating the effectiveness of the tension control scheme in modulating the manipulator's stiffness. Experimental validation conducted on an in-house developed prototype confirms the practical feasibility of the proposed approach.

Robotic manipulators are widely used for precise operation in the medical field. Vibration suppression control of robotic manipulators has become a key issue affecting work stability and safety. In this paper an optimal trajectory planning control method to suppress the vibration of a variable-stiffness flexible manipulator considering the rigid-flexible coupling is proposed. Through analyzing the elastic deformation of the variable-stiffness flexible manipulator, a distributed dynamic physical model of the flexible manipulator is constructed based on the Hamilton theory. Based on the mathematical model of the system, the design of the vibration damping controller of the flexible manipulator is proposed, and the control system with nonlinear input is considered for numerical analysis. According to the boundary conditions, the vibration suppression effect of the conventional and the variable-stiffness flexible manipulator is compared. The motion trajectory of the variable-stiffness flexible manipulator and compare the vibration response from different trajectories. Then, with minimum vibration displacement, minimum energy consumption and minimum trajectory tracking deviation as performance goals, the trajectory planning of the variable-stiffness flexible manipulator movement is carried out based on the cloud adaptive differential evolution (CADE) optimization algorithm. The validity of the proposed trajectory planning method is verified by numerical simulation.

In flexible endoscopy, the endoscope needs to be sufficiently flexible to go through the tortuous paths inside the human body and meanwhile be stiff enough to withstand external payloads without unwanted tip bending during operation. Thus, an endoscope whose stiffness can be adjusted on command is needed. This paper presents a novel variable-stiffness manipulator. The manipulator (Ø15 mm) has embedded thermoplastic tubes whose stiffness is tunable through temperature. Temperature is adjusted through joule heat generated by the electrical current supplied to the stainless steel coils and an active air-cooling mechanism. Tests and modeling were conducted to characterize the performance of the design. The manipulator has a high stiffness-changing ratio (22) between rigid and flexible states while that of its commercial Olympus counterpart is only 1.59. The active cooling time is 11.9 s while that of passive ambient cooling is 100.3 s. The thermal insulation layer (Aerogel) keeps the temperature of the outer surface within the safe range (below 41 °C). The models can describe the heating and cooling processes with root mean square errors ranging from 0.6 to 1.3 °C. The results confirm the feasibility of a variable-stiffness endoscopic manipulator with high stiffness-changing ratio, fast mode-switching, and safe thermal insulation.

This paper presents a continuum manipulator inspired by the anatomical characteristics of the elephant trunk. Specifically, the manipulator mimics the conoid profile of the elephant trunk, which helps to enhance its strength. The design features two concentric parts: inner pneumatically actuated bellows and an outer tendon-driven helical spring. The tendons control the omnidirectional bending of the manipulator, while the fusion of the pneumatic bellows with the tendon-driven spring results in an antagonistic actuation mechanism that provides the manipulator with variable stiffness and extensibility. This paper presents a new design for extensible manipulator and analyzes its stiffness and motion characteristics. Experimental results are consistent with theoretical analysis, thereby demonstrating the validity of the theoretical approach and the versatile practical mechanical properties of the continuum manipulator. The impressive extensibility and variable stiffness of the manipulator were further demonstrated by performing a pin-hole assembly task.

The robot‐assisted flexible access surgery represented by the emerging robot‐assisted flexible endoscopy (FE) and natural orifice transluminal endoscopic surgery demands flexible and continuum manipulators instead of the rigid and straight instruments in the traditional minimally invasive surgery (MIS). These flexible manipulators are required to advance through the tortuous and narrow anatomic paths via natural orifices for dexterous diagnostic examination and therapeutic operations. Therefore, developing flexible endoscopic manipulators with the capacity of snake‐like movements for flexible access and variable stiffness regulation for operations to address these flexible access surgical difficulties is demanding but remains challenging. To address such challenges, herein, it is proposed that a novel distal continuum joint based on the hybrid pneumatic and cable‐driven approach achieves variable stiffness capacity, excellent bending characteristics in both flexible and rigid states, satisfactory motion consistency and shape‐locking ability during the rigid‐flexible transition, and relatively high loading capacity for flexible gastrointestinal endoscopic robots. Characterization experiments validate these performances, and phantom and ex vivo experiments have been performed to demonstrate the feasibility and effectiveness for FE. The presented method demonstrates an effective and practical approach to enabling continuum robots with both flexible access and tunable stiffness capacity and supports a convenient extension for MIS applications. Herein, it is proposed that a novel distal continuum joint based on the hybrid pneumatic and cable‐driven approach achieves excellent bending characteristics in both flexible and rigid states, variable stiffness, and high loading capacity for flexible gastrointestinal endoscopy. The presented method demonstrates an effective and practical approach for flexible endoscopic robots to achieve flexibility for access and rigidity for operation.

Soft manipulators have garnered significant research attention in recent years due to their flexibility and adaptability. However, the inherent flexibility of these manipulators imposes limitations on their load-bearing capacity and stability. To address this, this study compares various variable stiffness technologies and proposes a novel design concept: leveraging the phase-change characteristics of low-melting-point alloys (LMPAs) with distinct melting points to fulfill the variable stiffness requirements of soft manipulators. The pneumatic structure of the manipulator is fabricated via 3D-printed molds and silicone casting. The manipulator integrates a pneumatic working chamber, variable stiffness chambers, heating devices, sensors, and a central channel, achieving multi-stage variable stiffness through controlled heating of the LMPAs. A steady-state temperature field distribution model is established based on the integral form of Fourier’s law, complemented by finite element analysis (FEA). Subsequently, the operational temperatures at which the variable stiffness mechanism activates, and the bending performance are experimentally validated. Finally, stiffness characterization and kinematic performance experiments are conducted to evaluate the manipulator’s variable stiffness capabilities and flexibility. This design enables the manipulator to switch among low, medium, and high stiffness levels, balancing flexibility and stability, and provides a new paradigm for the design of soft manipulators.

Cable-driven manipulators, characterized by slender arms, dexterous motion, and controllable stiffness, have great prospects for application to capture on-orbit satellites. However, it is difficult to achieve effective motion planning and stiffness control of cable-driven manipulators because of the coupled relationships between cable lengths, joint angles, and reaction forces. Therefore, a convolutional dynamic-jerk-planning algorithm is devised for impedance control of variable-stiffness cable-driven manipulators. First, a variable-stiffness cable-driven manipulator with universal modules and rotary quick-change modules is designed to overcome difficulties related to disassembly, installation, and maintenance. Second, a convolutional dynamic-jerk-planning algorithm is devised to overcome the discontinuity and shock problems of the manipulator’s velocity during intermittent control processes. The algorithm can also make acceleration smooth by setting jerk dynamically, reducing acceleration shock and ensuring the stable movement of the cable-driven manipulator. Third, the stiffness of the cable-driven manipulator is further optimized by compensating for the position and velocity of drive cables by employing position-based impedance control. Finally, the prototype of the variable-stiffness cable-driven manipulator is developed and tested. The convolutional dynamic-jerk-planning algorithm is used to plan the desired velocity curves for velocity control experiments of the cable-driven manipulator. The results verify that the algorithm can improve the acceleration smoothness, thereby making movement smooth and reducing vibrations. Furthermore, stiffness control experiments verify that the cable-driven manipulator has ideal variable stiffness capabilities.

During constant-force operations in complex marine environments, underwater manipulators are affected by hydrodynamic disturbances and unknown, time-varying environment stiffness. Under classical impedance control (IC), this often leads to large transient contact forces and steady-state force errors, making high-precision compliant control difficult to achieve. To address this issue, this study proposes a Bayesian recursive least-squares-based fuzzy adaptive impedance control (BRLS-FAIC) strategy with displacement correction for underwater manipulators. Within a position-based impedance-control framework, a Bayesian Recursive Least Squares (BRLS) stiffness identifier is constructed by incorporating process and measurement noise into a stochastic regression model, enabling online estimation of the environment stiffness and its covariance under noisy, time-varying conditions. The identified stiffness is used in a displacement-correction law derived from the contact model to update the reference position, thereby removing dependence on the unknown environment location and reducing steady-state force bias. On this basis, a three-input/two-output fuzzy adaptive impedance tuner, driven by the force error, its rate of change, and a stiffness-perception index, adjusts the desired damping and stiffness online under amplitude limitation and first-order filtering. Using an underwater manipulator dynamic model that includes buoyancy and hydrodynamic effects, MATLAB simulations are carried out for step, ramp, and sinusoidal stiffness variations and for planar, inclined, and curved contact scenarios. The results show that, compared with classical IC and fuzzy adaptive impedance control (FAIC), the proposed BRLS-FAIC strategy reduces steady-state force errors, shortens force and position settling times, and suppresses peak contact forces in variable-stiffness underwater environments.

Variable admittance control is commonly used for a collaborative robot to achieve the compliant or accurate cooperation according to human’s intention. However, existing research seldom investigates such a human-robot collaboration coupled with an extra environment with unknown stiffness. If the end-effector that is guided by a human with various intended motion contacts the unknown environment, the interaction might become unstable. Additionally, current research for this physical human-robot-environment interaction use two force sensors to address the issue, and hence the cost of the robot is likely to increase and it reduces the flexibility to many applications. Therefore, in this paper, we address the issue of physical human-robot interaction coupled with an extra environment whose stiffness is unknown. To achieve this, the condition of robot admittance is rigorously proved in accordance with different human intended motion and environmental stiffness. Moreover, a variable admittance control scheme is proposed based on human intention, environmental force and environment stiffness using the combination of a force sensor and a force observer. Simulation and experiments are conducted to demonstrate the effectiveness of the proposed control scheme.