Tendon actuation is one of the most prominent actuation principles for continuum robots. To date, a wide variety of modelling approaches has been derived to describe the deformations of tendon-driven continuum robots. Motivated by the need for a comprehensive overview of existing methodologies, this work summarizes and outlines state-of-the-art modelling approaches. In particular, the most relevant models are classified based on backbone representations and kinematic as well as static assumptions. Numerical case studies are conducted to compare the performance of representative modelling approaches from the current state-of-the-art, considering varying robot parameters and scenarios. The approaches show different performances in terms of accuracy and computation time. Guidelines for the selection of the most suitable approach for given designs of tendon-driven continuum robots and applications are deduced from these results.

No abstract

Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is 0.43% and the proposed static model is 3.25% w.r.t. robot length. The average computation time is 0.56 ms for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from 8.6% to 5.1% w.r.t. robot length, while using 30 observations for training.

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.

We propose a segment design that combines two distinct characteristics of tendon-driven continuum robots, i.e. variable length and non-straight tendon routing, into a single segment by enabling rotation of its backbone. As a result, this segment can vary its helical tendon routing and has four degrees-of-freedom, while maintaining a small-scale design with an overall outer diameter of 7 mm thanks to an extrinsic actuation principle. In simulation and on prototypes, we observe improved motion capabilities, as evidenced by position redundancy and follow-the-leader deployment along spatially tortuous paths. To demonstrate the latter on a physical prototype, a simple, yet effective area-based error measure for follow-the-leader deployment is proposed to evaluate the performance. Furthermore, we derive a static model which is used to underpin the observed motion capabilities. In summary, our segment design extends previous designs with minimal hardware overhead, while either archiving similar accuracy in position errors and planar follow-the-leader deployment, or exhibiting superior motion capabilities due to position redundancy and spatial follow-the-leader deployment.