Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study.

This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm.

Soft continuum manipulators are characterized by low stiffness that allows safe operation in unstructured environments but introduces underactuation. In addition, soft materials such as silicone rubber, which are commonly used for soft manipulators, are characterized by nonlinear stiffness, while pneumatic actuation can result in nonlinear damping. Consequently, achieving accurate control of these systems in the presence of disturbances is a challenging task. This article investigates the model-based adaptive control for soft continuum manipulators that have nonlinear uniform stiffness and nonlinear damping, that bend under the effect of internal pressure, and that are subject to time-varying disturbances. A rigid-link model with virtual elastic joints is employed for control purposes within the port-Hamiltonian framework. The effects of disturbances and model uncertainties are estimated adaptively. A nonlinear controller that regulates the tip orientation of the manipulator and that compensates the effects of disturbances and of model uncertainties is then constructed by using an energy shaping passivity-based approach. Stability conditions are discussed highlighting the beneficial role of nonlinear damping. The effectiveness of the controller is assessed with simulations and with experiments on a soft continuum manipulator prototype.

Concentric tube robots offer the capability of follow-the-leader motion, which is desirable when navigating in cluttered environments, such as in minimally invasive surgery or in-situ inspections. The follow-the-leader capabilities identified in the existing literature, however, are limited to trajectories with piecewise constant-curvature segments or piecewise helical segments. A complete study of follow-the-leader kinematics is, therefore, relevant to determine the full potential of these robots, and clarify an open question. In this paper, a general analysis of follow-the-leader motion is presented, and a closed-form solution to the complete set of trajectories where follow-the-leader is possible under the assumption of no axial torsion of the tubes composing the robot is derived. For designs with constant-stiffness tubes, the precurvatures required are found to be either circumference arcs, helices, or deformed helices with exponentially varying curvature magnitude. The analysis developed also elucidates additional motions of interest, such as the combination of follow-the-leader motion in a robot segment with general maneuvers in another part. To determine the applicability of the assumption regarding the tubes’ torsion, the general equilibrium of the robot designs of interest is considered, and a closed-form solution to torsion in two-tube robots with helical precurvatures is derived. Criteria to select a desired torsional behavior are then extracted. This enables one to identify stable trajectories where follow-the-leader is possible, for potential application to minimally invasive surgery. An illustrative case study involving simulation and experiment is conceived using one of these trajectories, and the results are reported, showcasing the research.

This paper presents a new 6 DOF soft robotic manipulator intended for colorectal surgery. The manipulator, based on a novel design that employs an inextensible tube to limit axial extension, is shown to maximize the force exerted at its tip and the bending angle, the latter being measured with a soft sensing skin. Manufacturing of the prototype is achieved with a lost-wax silicone-casting technique. The kinematic model of the manipulator, its workspace, and its manipulability are discussed. The prototype is evaluated with extensive experiments, including pressure-deflection measurement with and without tip load, and lateral force measurements with and without the soft sensing skin to assess hysteresis. The experimental results indicate that the prototype fulfils the key design requirements for colorectal surgery: (i) it can generate sufficient force to perform a range of laparoscopic tasks; (ii) the workspace is commensurate with the dimensions of the large intestine; (iii) the soft sensing skin only results in a marginal reduction of the maximum tip rotation within the range of pressures and external loads relevant for the chosen application.

This letter introduces a novel hybrid manipulator composed of two pneumatically-actuated soft segments and a tendon-driven continuum segment, connected in series. The soft segments enhance the mobility of the tendon-driven manipulator, enabling functionalities such as triangulation while maintaining low tool stiffness, making it suitable for endoluminal surgery in the lower gastrointestinal tract. A key advantage of this design is the implementation of a model-based controller and an observer-based contact force estimation method, which estimates external forces based on the configuration and actuation of the soft segments. This approach is experimentally compared to a tendon tension sensing methodology, known as intrinsic force sensing. The experiments include typical lifting and pushing tasks, along with realistic operations on ex-vivo porcine intestinal tissue. The results demonstrate the feasibility of the proposed approach in surgical applications and its advantages over intrinsic force sensing, achieving an average 15.8% reduction in normalized RMSE among all tasks.