Tendon driven continuum robots are often considered to navigate through and operate in cluttered environments. While their compliance allows them to conform safely to obstacles, it leads them also to buckle under tendon actuation. In this article, we perform for the first time an extensive elastic stability analysis of these robots for arbitrary planar designs. The buckling phenomena are investigated and analyzed using bifurcation diagrams, complementing the current state of the art and adding new knowledge about robots composed of$n$spacer disks. We show the existence of multiple robot configurations with different shapes, achievable with the same actuation inputs. A global stability criterion is also established, which links the critical tendon force, until which the robot is stable to the design parameters. Finally, the buckling phenomena are used to actively soften the robot for a better compromise between compliance and payload. An open loop control strategy is proposed, which can theoretically decrease the stiffness to zero, while maintaining the same robot shape. Experimentally, the robot is made four times more compliant than it is nominally using tendon actuation only.

Tendon-driven continuum robots show promise for use in surgical applications as they can assume complex configurations to navigate along tortuous paths. However, to achieve these complex robot shapes, multiple segments are required as each robot segment can bend only with a single constant curvature. To actuate these additional robot segments, multiple tendons must typically be added on-board the robot, complicating their integration, robot control, and actuation. This work presents a method of achieving two curvatures in a single tendon-driven continuum robot segment through use of a novel magnetic locking mechanism. Thus, the need for additional robot segments and actuating tendons is eliminated. The resulting two curvatures in a single segment are demonstrated in two and three dimensions. Furthermore, the maximum magnetic field required to actuate the locking mechanism for different robot bending angles is experimentally measured to be 6.1 mT. Additionally, the locking mechanism resists unintentional unlocking unless the robot assumes a 0° bending angle and a magnetic field of 18.1 mT is applied, conditions which are not typically reached during routine use of the system. Finally, addressable actuation of two locking mechanisms is achieved, demonstrating the capability of producing multiple curvatures in a single robot segment.

Due to the continuous and flexible nature of continuum robot backbones and the infinite number of parameters required to represent them in configuration space, modeling them accurately and in real-time is challenging. While the constant curvature assumption provides a simple alternative, it is limited in its capabilities as it cannot account for external tip forces. In cases where the backbone deviates from the constant curvature backbone, Euler curves are an interesting alternative for modeling continuum robots. In this paper, we show that a linear approximation of the backbone curvature is sufficiently accurate for estimating the shape of a robot subject to external tip forces. Next, we propose a numerical static model for tendon-driven continuum robots experiencing in-plane external tip forces. In this model, we use Euler arc splines to circumvent the limitations of standard numerical integration schemes required to calculate these curves. The system reduces to solving two nonlinear equations, allowing fast approximation of the backbone shape. The proposed model is validated experimentally on a robot prototype. Average tip error of 3.07% of the robot length is obtained for an average computation time of 0.51 ms.