An analytical differential kinematics-based method for controlling tendon-driven continuum robots

This paper presents a study on miniature continuum robots which can bend continuously along their length and can be constructed to be more than one section to increase their degrees of freedom. This study is concerned with providing the kinematics and the dynamics of the robot. The kinematic equations is provided by Piece-wise constant curvature (PCC) assumption which is based on curve geometry. The Dynamics of the robot are provided by the analysis of the Lagrangian equation. Next, three control strategies are applied on a two-section continuum robot model using MATLAB Simulink environment to demonstrate the effectiveness of each control loop. The three control strategies are Proportional Derivative (PD) control, Fuzzy Logic Control (FLC), and Sliding Mode Control (SMC). The simulation results show an advantage in performance for the intelligent controller (FLC) and the nonlinear robust control (SMC) over the PD control.

Due to the outstanding compliance and dexterity, continuum robot have great advantages in confined space applications, especially in minimally invasive surgery (MIS). However, the vascular environment is complicated and tortuous, it is necessary to preoperative motion planning and navigation for a continuum robot. A cable-driven continuum robot is proposed, and the mapping relationship among the driven space, joint space and task space, as well as the decoupling algorithm are analyzed based on piecewise constant curvature assumption. Moreover, a navigation method is presented to achieve semi-autonomous interventional surgery based on the vascular constraints by using the backbone cure method. Finally, by using the prototype, the interventional simulations and experiments for a simulated glass blood vessel are developed to validate the feasibility and maneuverability of the proposed model and navigation method. The established motion model and navigation method can be used as a motion control and navigation reference.

Tendon-driven continuum robots possess versatile application capabilities and have a robust design. The actuation of such robots with non-straight tendons that wrap around the backbone, described by a variable function, offers a lot of untapped potentials. While it has been shown that these continuum robots are able to take up complex shapes using only one actuated segment, the merits of non-straight tendon routing have not been quantified in terms of workspace and motion. In this paper, we show that one additional helically routed tendon can greatly benefit the robot's reachable workspace. For instance, the reachable workspace of a one-segment robot with 3 conventional straight tendons increases by 400 % by adding one helically routed tendon. Furthermore, the dexterity of such a continuum robot is improved, i.e. motion sequences to avoid obstacles or to twine an object for grasping. For the first time, the potential of tendon-driven continuum robots with two segments and helically routed tendons is investigated. The general findings on the merits of helical tendon routing are supported with both simulation and experimental results.

PurposeContinuum robots modeling, be it from a hard or soft class, is giving rise to several challenges compared with rigid robots. These challenges are mainly due to kinematic redundancy, dynamic nonlinearity and high flexibility. This paper aims initially at designing a hard class of continuum robots, namely, cable-driven continuum robot (CDCR) and equally at developing their kinematic and dynamic models.Design/methodology/approachFirst, the CDCR prototype is constructed, and its description is made. Second, kinematic models are established based on the constant curvature assumption and inextensible bending section. Third, by using the Lagrange method, the dynamic model is derived under some simplifications and based on the kinematic equations, in which the flexible backbone’s elasticity modulus was identified experimentally. Finally, the static model of the CDCR is also derived based on the dynamic model.FindingsNumerical examples are carried out using Matlab software to verify the static and dynamic models. Moreover, the static model is validated by comparing the simulation’s results to the real measurements that have been provided with satisfactory results.Originality/valueTo reduce the complexity of the dynamic model’s expressions and avoid the numerical singularity when the bending angle is close to zero, some simplifications have been taken, especially for the kinetic energy terms, by using the nonlinear functions approximation. Hence, the main advantage of this analytical-approximate solution is that it can be applied in the bending angle that ranges up to 2p with reasonable errors, unlike the previously proposed techniques. Furthermore, the resulting dynamic model has, to some extent, the proprieties of simplicity, accuracy and fast computation time. Ultimately, the obtained results from the simulations and real measurements demonstrate that the considered CDCR’s static and dynamic models are feasible.

Tendon-driven continuum robots offer exceptional flexibility and slenderness, making them particularly suitable for inspection and maintenance in constrained and unstructured environments as well as robotic surgery. However, their control remains challenging due to nonlinear behavior, limited sensory feedback, and a significant kinematic dissimilarity from existing controllers. These challenges make continuum robots, similarly to endoscopes, their non-robotic counterparts, require a cost- and time-expensive training for users who operate them in such critical environments. This paper addresses this point by designing and implementing a custom, user-friendly control interface for a tendon-driven continuum robot, leveraging principles from both robotics and gaming to enhance intuitiveness and accessibility. After developing a custom graphical user interface, a prototype has been manufactured to evaluate system performance in a dedicated testing environment. Twelve participants have attempted a timed navigation task using the proposed interface, with data collected to assess usability and control accuracy. Results confirmed the feasibility and effectiveness of the system: users were able to navigate the robot through the course with minimal training. Participant feedback is then analyzed to identify meaningful directions for improvement.

Continuum robot, unlike conventional rigid-link robots, has numerous numbers of degrees of freedom, enabling it to be applied for confined space works, such as minimally invasive surgery, safe robot/objective interactions, and in-situ aero-engine detection. This study presented a cable-driven continuum robot with twin-pivot structure, which poses smaller diameter-length-ratio and torsion resistance ability compared with conventional single-pivot structure, as well as the kinematics and shape estimation. The kinematics model of the twin-pivot continuum robot is established based on the assumption of piecewise constant curvature, with which the mapping between driving space and operation space are presented. Finally, a prototype of continuum robot system with single section is constructed to verify the validation of the kinematics model and study the shape estimation. Based on the constructed prototype, the shape estimation of the continuum robot with different payloads is performed. The comparative results suggest that relative error is less than 5% for total length of the single section without payload, verifying the validity of the kinematics model. The comparison between the results with different payloads indicate that the increasing payload will increase the relative error.

Continuum robots (CRs) have been developed for maxillary sinus surgery (MSS) in recent years. However, due to the anatomically curved and narrow pathway of the maxillary sinus and the deformable characteristics of the CR, it is still a challenge to accurately approach the target in the sinus. Thus, the CR-assisted MSS demands further research, whether in robotic system design or in reliable motion control. A continuum robotic system integrated with essential instruments and sensors for MSS is developed, and the path tracking control of the designed CR is studied. The differential kinematic model of the CR is constructed. By analyzing the potential problem of the traditional Jacobian-based control, an iterative Jacobian transpose-based closed-loop control method is proposed to improve the path tracking performance. To validate the design of the CR and the effectiveness of the proposed control scheme, different groups of experiments are performed. With the proposed method, the path tracking performance of the CR is improved. Compared with the open-loop Jacobian transpose-based control method, the path tracking error of the proposed method is much less. The maxillary sinus phantom tests are conducted to verify the reachability of the designed CR. Given the reference path from the nostril to the target in the maxillary sinus phantom, experiments show a mean error of 0.96mm. The designed CR is slender, flexible, and able to smoothly approach the target in a tortuous and constrained environment without colliding with or damaging the surrounding tissue. The designed continuum robotic system and the proposed iterative Jacobian transpose-based closed-loop control strategy have great potential for MSS. The limitations of the proposed method are also discussed.

Tendon-driven continuum robots (TDCRs) have the potential to be used in minimally invasive surgery and industrial inspection, where the robot must navigate narrow and confined spaces. We propose a model predictive controller (MPC) to leverage the non-linear kinematics and redundancy of TDCRs for whole-body collision avoidance, with real-time capabilities for hanadling inputs at 30 Hz. Key to our method's effectiveness is the integration of a nominal piecewise constant curvature (PCC) model for efficient computation of feasible trajectories, with a local feedback controller to handle modeling uncertainties and disturbances. Our experiments in simulation show that our MPC outperforms conventional Jacobian-based controller in position tracking, particularly under disturbances and user-defined shape constraints, while also allowing the incorporation of control limits. We further validate our method on a hardware prototype, showcasing its potential for enhancing the safety of teleoperation.

Tendon-driven continuum robots are compliant and capable of assuming complex curves, making them ideal for minimally invasive surgery in confined spaces with obstacles. These robots can achieve an infinite family of curves, determined by both actuation and design considerations, such as the tendon routing paths of tendons along the robot. Design optimization of surgical continuum robots has been studied (see [1] for review), but the idea of variable and complex tendon routing is newer, and although it has been modeled [2], it has yet to be used to design a practical surgical device. For tendon-driven continuum robots in general, design optimization has thus far focused on multi-segment robots that use straight (i.e. parallel to the backbone) segments of different lengths, where tendons terminate at various arclengths along the robot [3], [4]. The ad- vantage of designing with nonlinearly routed tendons is the potential to enable a much more expressive family of shapes during actuation [2]. However, it has thus far been challenging to design nonlinear tendons because one is working in an infinite design space with mechanics- based models that require solving differential equations to compute robot kinematics. Toward solving this problem, this paper presents a new tendon routing parameterization for tendon-driven robots and leverages it to optimize the routings for a de- sign objective drawn from a practical neurosurgical ap- plication: choroid plexus cauterization for hydrocephalus [5]. This application was an early motivating example in the development of concentric tube robots, extended in [6], although physical size, achievable curvatures, and stiffness constraints have thus far limited practical fabrication of the robots designed in simulation. The endoscopic approach to choroid plexus cauterization requires maneuvering through tight spaces in the ven- tricles, which is challenging with traditional constant curvature endoscopes (see Fig.1). Further, even in “suc- cessful” procedures, surgeons often want to cauterize more of the choroid plexus than they can currently reach and simply settle for what they can reach. Thus, a robot with nonlinear tendon routing that can access more of the choroid plexus would be a valuable tool.

As soft, continuum robots see increasing areas of application, many scenarios have arisen where it is necessary to consider the geometric shape of the robot. The current approaches to robot kinematics, such as the piecewise constant-curvature (PCC) model, are effective in representing simple overall robot geometry and estimating the end-effector state, but they are less intuitive for planning robots that involve complex geometries. In this work, we propose a solution to the geometric design problem by a two-part approach: a freeform spline defines a “shape curve” that describes the overall geometry of the robot, and then a “kinematic curve” composed of shapes that are feasible to replicate with continuum robots is fitted to the shape curve. As an implementation of this approach, we specifically explore the application of piecewise cubic Bezier curves in designing the shape curve of the robot, and pairs of arcs to construct the kinematic curves. Finally, the approach is applied to a tip-extension “vine” robot that is designed and fabricated to “grow” along a designed path and access the top surface of an obstacle.

Constrained visual predictive control of tendon-driven continuum robots

This paper presents the inverse kinematic analysis of a planar bio-inspired soft robot in a discrete task space using artificial intelligence (AI). The soft robot manipulator comprises a stack of hydraulically amplified dielectric elastomer actuators, which exhibit snap-through instability, resulting in a discrete robot task space. The model simulates the manipulator with a series of adjustable-length rods connected with revolute joints and satisfies the piecewise constant curvature (PCC) requirement for each robot segment. The discrete task space of the robot was estimated using the Monte Carlo method. The inverse kinematic analysis was carried out through genetic algorithm optimization with an embedded forward kinematic model to minimize the error for both the position and the orientation of the robot's end-effector. We analyze the fully controlled robot at each discrete segment, and we compare the results with the reduced complexity model obtained by grouping the actuator in sets of different sizes. The algorithm showed excellent results and can potentially be used in the analysis of similar soft manipulators with discrete task spaces.

This paper proposes a novel decentralized approach to kinematic control of soft segmented continuum robots based on a consensus strategy. The robots under consideration deform in a plane according to a multi-segment Piecewise Constant Curvature (PCC) kinematic model in which each segment is represented as an equivalent rigid-link Revolute-Prismatic-Revolute (RPR) mechanism. In our approach, we assume that each segment of the robot is equipped with sensors to measure joint variables in its local coordinate frame and can communicate with its two adjacent segments. Our consensus-based decentralized control strategy provides an alternative to conventional control methods, which solve the inverse kinematic problem by using computationally intensive numerical methods to calculate the robot's Jacobian matrix at each time instant. We investigate the stability and convergence properties of proposed controllers for position regulation and trajectory tracking tasks and provide theoretical guarantees on the controllers' performance. We evaluate the controllers in simulation for scenarios in which the robot's tip must reach a certain position or follow a specified trajectory. We compare the performance of the position regulator for different controller gains, and we find that a simulated 15-link robot can track a complex reference trajectory with an average root-mean-square error of only 0.16% of the robot's initial length.

Accomplishing a task with telerobotics typically involves a combination of operator control/supervision and a `script' of preprogrammed commands. These commands usually assume that the location of various objects in the task space conform to some internal representation (database) of that task space. The ability to quickly and accurately verify the task environment against the internal database would improve the robustness of these preprogrammed commands. In addition, the on-line initialization and maintenance of a task space database is difficult for operators using Cartesian coordinates alone. This paper describes the interactive scene analysis module (ISAM) developed to provide task space database initialization and verification utilizing 3-D graphic overlay modeling, video imaging, and laser radar based range imaging. Through the fusion of task space database information and image sensor data, a verifiable task space model is generated providing location and orientation data for objects in a task space. This paper also describes applications of the ISAM in the Intelligent Systems Research Laboratory (ISRL) at NASA Langley Research Center, and discusses its performance relative to representation accuracy and operator interface efficiency.

Chapter 3 - PID Control in Task Space