Design and Stiffness Control of a Variable-Length Continuum Robot for Endoscopic Surgery

There is an increasingly popularity for the continuum robot in minimally invasive surgery(MIS), because of the compliance and dexterity. In the first place, a variable stiffness manipulator can resolve the two contradictions of the demands for predominant flexibility and strong payload capacity. In the second place, to control the continuum robot more precisely and avoid the collision between robot and human body, real-time tracking of the shape of the continuum robot is of great significance. A new type of flexible manipulator with variable stiffness is proposed which can track the bending shape timely. The low-melting-point-alloy (LMPA) is used to realize the variable stiffness and shape detection for the flexible manipulator. The concept design for a single module is put forward. Then the stiffness control method and finite element simulation, the method of shape detection are presented. Moreover, the presented method of shape detection is evaluated by experiments.

Stiffness variation is useful in soft robots, especially for continuum manipulators which have a high slenderness ratio. Softness intrinsically gives robots high flexibility of movement, but stiffness gives the robots enough carrying capacity. Many types of continuum manipulators can change their stiffness; however, the both large-range and fast-response stiffness variation has not been realized. In this work, an omnidirectional steering flexible manipulator with large-range and fast-response stiffness variation was designed and fabricated. It was composed of a nested structure with a stiffness variation layer, a tendon-driven layer, and a transport channel. The stiffness variation was achieved by the phase transition of LMPA (Low-Melting Point Alloy) with a melting point of 50 °C. Heating and cooling to the LMPA were performed by a tubular spring-like copper tube embedding in the LMPA. The tube not only acts as a skeleton of the manipulator, but also the material and structure of it bring the fast heat exchange. The motion of the manipulator was driven by tendons going through the holes of a threaded spring-like elastic skeleton which is flexible still can appropriately balance the self-weight of the manipulator. Continuum manipulators with one and two omnidirectional segments were fabricated to show the performance of movement and stiffness variation. Each segment is of 15 cm length and with diameter of 21 mm. The test shows that the stiffness of the manipulator has a factor of 45 variations in 15 seconds, and the stiffness variation is adequate to complete some challenging tasks like screw tightening and loosing.

The design and analysis of continuum robots have consistently been a prominent research focus in the field of mechanics. However, portable continuum robots with minimal spatial occupancy, which have great potential for applications such as search and rescue, are scarcely available. This paper presents a novel helical-coiled multi-segment flexible continuum robot featuring helical deployment and compact design, with an integrated framework for structural design, kinematic modeling, and experimental validation. The design of the helical-coiled multi-segment flexible continuum robot for unstructured environment detection, including a flexible body, an actuation module, a feed module, and a sensing module, is presented systematically. Kinematic models of both single- and multi-segment continuum robots were established based on the constant curvature model to analyze the parameter mapping relationship from the end-effector position and orientation to the driving inputs. Furthermore, the feedforward motion of the robot was examined, and an uncoiling strategy based on S-curve compensation was employed to complete the kinematic analysis. Finally, the accuracy of the kinematic model considering the active uncoiling feed motion was validated through experimental analysis, demonstrating the motion characteristics of the continuum robot. Altogether, this study provides a framework for the design and analysis of helical-coiled continuum robots.

Compliant joints are widely used in the structural design of 3D-printed continuum robots as their monolithic structure can greatly simplify the assembly process. However, some highly flexible compliant joints, such as the leaf-spring joints, still suffer from unstable rotation centers when interfered by external forces, which greatly reduces the motion stability of the constructed continuum robots. To cope with this problem, we propose a topology-optimization-based method in this paper to achieve efficient structural design of the complaint joints in continuum robots. With our method, the rotation stability of compliant joints can be improved without causing stress concentration problems. Experiments were also carried out to evaluate the bending performance of the 3D-printed continuum robots equipped with optimized compliant joints. Results demonstrated that, compared to continuum robots with the conventional leaf-spring joints, the optimized robots showed much less twisting deformation caused by out-of-plane loads, which exhibited the high rotation stability of the optimized joints. In future work, the proposed method can be further developed to achieve optimization of other mechanical properties of the compliant joints in continuum robots.

Continuum robots have the advantages of agility and adaptability. However, existing continuum robots have limitations of low stiffness and complex motion modes, and the existing variable stiffness methods cannot achieve a wide range of stiffness changes and fast switching stiffness simultaneously. A continuum robot structure, switching stiffness method, and motion principle are proposed in this article. The continuum robot is made up of three segments connected in series. Each segment comprises multiple spherical joints connected in series, and the joints can be locked by their respective airbag. A valve controls each airbag, quickly switching the segment between rigidity and flexibility. The motion of the segments is driven by three cables that run through the robot. The segment steers only when it is unlocked. When a segment becomes locked, it acts as a rigid body. As a result, by locking and unlocking each segment in sequence, the cables can alternately drive all the segments. The stiffness variation and movement of the continuum robot were tested. The segment's stiffness varies from 36.89 to 1300.95 N/m and the stiffness switching time is 0.25-0.48 s. The time-sharing control mode of segment stiffness and motion is validated by establishing a specific test platform and a mathematical model. The continuum robot's flexibility is demonstrated by controlling the fast bending of different segments sequentially.

In the field of robots, soft continuum robots have strong adaptability, and rigid continuum robots have large carrying capacity, but they all have some limitations. The purpose of this paper is to solve the problems of small carrying capacity of soft continuum robots and low safety of rigid continuum robots. Based on the combined action of particle jamming and fiber jamming, we use the good fluidity of spherical particles and the rigidity of spherical particles to realize the flexibility and rigidity of the robot, and put forward the requirement of flexible contact and rigid bearing. According to the large range variable stiffness actual demand, a self-locking soft continuum robot with large range variable stiffness based on the jamming phenomenon is proposed, and the principle of large range variable stiffness is explained. Then the model experiment prototype is designed and manufactured. Based on the model, the combination elastomer is defined. The basic unit is constructed and the theoretical analysis is carried out, and the equivalent of the combination elastomer stiffness model is obtained. Finally, an experimental test system is built. Through the experiment and simulation of variable stiffness, the stiffness change of combination elastomer is obtained, and the specific situation of bearing capacity change is recorded. This study provides a new method to achieve a wide range of stiffness changes, and builds a bridge from soft continuum robots to rigid continuum robots.

Soft robots are increasingly being explored and developed in various settings that demand safe and adaptable interactions between robots and their environments. In addition, soft robots exhibit passive compliant behavior and generate continuous deformations when engaging with the environment. This imposes challenges on achieving active, on-demand interaction force control, especially when feedback force-sensing devices are not available. Consequently, there is a need to explore new model-based force control paradigms for soft robots. In this article, we propose a (quasi-)static force control approach for soft robots based on compliance modeling, avoiding the necessity for feedback control loops or extensive training data collection. The proposed approach can deliver contact force control along three Cartesian axes when the robot is actuated into various configurations. The compliance matrix is derived from the robot configuration, which allows the calculation of desired deflection displacements needed to generate on-demand forces. The resulting force control is achieved by solving inverse kinematics problems based on these deflection displacements. The efficacy of our proposed controller is validated through experiments with both one- and two-segment pneumatic-driven soft continuum robots. The results demonstrate effective static force control performance, with mean control errors below 5% of the desired peak forces.

Continuum Robots The cover illustrates three continuum robots accessing a nuclear facility through pipes, with a pneumatically actuated robot manipulating a radioactive component, a tendon-driven continuum robot performing a laser machining task on it, and a concentric tube robot monitoring the operation. In article number 2200367, recent advances, current limitations, and open challenges in the design, modeling, and control of continuum robots are discussed by Matteo Russo, Dragos Axinte, and colleagues.

Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progress has been made in the mechanical design and dynamic modeling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modeled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils, or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot’s shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5 mm and 0.016° in simulation or 3.3 mm and 0.035° for unloaded configurations and 6.2 mm and 0.041° for loaded ones during experiments, when using discrete pose measurements.

In order to improve the environmental adaptability and interaction stability of industrial robotic arms, a flexible joint with variable damping and stiffness based on magnetorheological (MR) technology was proposed. The mechanical models for variable stiffness and damping of MR flexible joint were established, and the relationship between cam surface and variable stiffness element was derived based on the energy method. Subsequently, the variation patterns of equivalent stiffness and damping of the prototype under different excitations were experimentally tested, and the test results show that its mechanical properties meet the design requirements. To further verify the performance of the MR flexible joint on the robotic arm, we setup a collision buffering test system and investigated the buffering performance of the system under different working conditions. The buffering test results indicate that when the current of variable stiffness element is 2.0 A, the peak collision acceleration of the system after installing the MR flexible joint decreases by about 40.19% compare with the rigid collision.

In teleoperation tasks, communication delays between master and slave sides negatively affect the stability and transparency of closed loop system, and make it difficult to maintain a desired contact force. In order to improve the performance of contact force control in teleoperation under large time delays, a shared compliant control method is proposed in this paper. On the master side, the operator issues a desired contact force command according to the feedback of the contact stiffness identified on line besides motion commands. And on the slave side, a local contact force controller is designed using an adaptive Smith predictor, so as to shares control load with the operator. Experimental results show that this method can improve the force control performance, lower the difficulty of operation, and help the operator complete contact tasks with proper forces.In teleoperation tasks, communication delays between master and slave sides negatively affect the stability and transparency of closed loop system, and make it difficult to maintain a desired contact force. In order to improve the performance of contact force control in teleoperation under large time delays, a shared compliant control method is proposed in this paper. On the master side, the operator issues a desired contact force command according to the feedback of the contact stiffness identified on line besides motion commands. And on the slave side, a local contact force controller is designed using an adaptive Smith predictor, so as to shares control load with the operator. Experimental results show that this method can improve the force control performance, lower the difficulty of operation, and help the operator complete contact tasks with proper forces.

Continuum robots, characterized by their hyper-redundant and flexible structures, have gained significant attention in fields such as minimally invasive surgery, remote inspection, and soft manipulation. Their complex design and highly nonlinear kinematic behavior present substantial modeling and control challenges. This paper presents a complete framework encompassing the design, modeling, and inverse kinematics solution for a novel two-segment, tendon-driven continuum robot utilizing an elastic spring backbone for enhanced compliance and structural simplicity. A constant curvature forward kinematic model is presented. Subsequently, an efficient numerical approach for solving the challenging inverse kinematics problem is introduced by adapting the Jacobian-based Newton-Raphson method and incorporating the Moore-Penrose Pseudoinverse. This strategy effectively manages the robot's redundancy, ensuring smooth and reliable trajectory generation. Experimental verification confirms the robot's feasibility, demonstrating that the system successfully navigates along the trajectories computed by the inverse kinematics, thus validating the reasonableness of the kinematic model and ensuring seamless and smooth operation. These findings provide a robust foundation for improving motion planning of simple continuum robot platforms in practical applications.

The quadruped robot can achieve stable locomotion with contact force control. The crucial technique of it is to convert the control of the center of mass (COM) to the control of supporting legs. In this paper, we propose a force distribution and control strategy based on model decomposition and optimal contact constrains for the quadruped robot with trotting gait. The quadruped robot can be modeled as a virtual planar seven-link and a virtual planar three-link under the supposition that the control of the COM is decoupled. Meanwhile, an optimal contact constraint will be proposed and the desired contact force can be found. The simulation and experiment results show that the robot can track the desired trajectories exactly and steadily.

SUMMARYThis paper addresses the problem of contact force control for multiple contacts distributed over multiple links in a robot. This is of importance when performing complex tasks in unstructured environment, particularly in humanoid robot applications. The proposed multicontact control framework provides a new way of defining the operational space coordinates, which facilitates the specification of multiple contact control. The contact force space on multiple links is constructed as an operational space for the highest priority task. Motion control, given lower priority, can be executed using the rest of degree of freedom within the null-space of the force control. The dynamic control structure, then, provides a means to control each contact force and motion independently. This dynamic decoupling enables each contact force controller to utilize linear control theories. In particular, the contact force controllers adopt full state feedback control and estimation methods to produce robust performance with respect to modeling and parameter uncertainties. The effectiveness of the multiple contact control framework was demonstrated using a PUMA560 manipulator, with multiple contacts on the end-effector and third link. The demonstrated tasks involved controlling each of the contact forces with null-space motion.

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction. This compliance reduces the risk of damage to the manipulated object and its surroundings. However, continuum robots possess theoretically infinite degrees of freedom, and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints. Describing these complex deformations is the main challenge in modeling continuum robots. In this study, we investigated a novel variable curvature modeling method for continuum robots, considering external forces and positional constraints. The robot configuration curve is described using the developed mechanical model, and then the robot is fitted to the curve. A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model. The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load. This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.