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.

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In this work, a novel planar parallel continuum robot (PCR) is introduced, consisting of three kinematic chains that are coupled at a triangular end-effector platform and include tendon-actuated continuum segments. The kinematics of the resulting structure are derived by adapting the descriptions for conventional planar parallel manipulators to include constant curvature bending of the utilized continuous segments. To account for friction and non-linear material effects, a data-driven model is used to relate tendon displacements and curvature of the utilized continuum segments. A calibration of the derived kinematic model is conducted to specifically represent the constructed prototype. This includes the calibration of geometric parameters for each kinematic chain and for the end-effector platform.During evaluation, positioning repeatability of 1.0% in relation to one continuum segment length of the robot, and positioning accuracy of 1.4%, are achieved. These results are comparable to commonly used kineto-static modeling approaches for PCR. The presented model achieves high path accuracies regarding the robot's end-effector pose in an open-loop control scenario.

The use of continuous and flexible structures instead of rigid links and discrete joints is a growing field of robotics research. Recent work focuses on the inclusion of continuous segments in parallel robots to benefit from their structural advantages, such as a high dexterity and compliance. While some applications and designs of these novel parallel continuum robots have been presented, the field remains largely unexplored. Furthermore, an exact quantification of the kinematic advantages and disadvantages when using continuous structures in parallel robots is yet to be performed. In this paper, planar parallel robot designs using tendon actuated continuum robots instead of rigid links and discrete joints are proposed. Using the well known 3-RRR manipulator as a reference design, two parallel continuum robots are derived. Inverse and differential kinematics of these designs are modeled using constant curvature assumptions, which can be adapted for other actuation mechanisms than tendons. Their kinematic performances are compared to the conventional parallel robot counterpart. On the basis of this comparison, the advantages and disadvantages of using continuous structures in parallel robots are quantified and analyzed. Results show that parallel continuum robot can be kinematic equivalent and exhibit similar kinematic performances in comparison to conventional parallel robots depending on the chosen design.

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