A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

Abstract.: Investigations on control and optimization of continuum manipulators have resulted in a number of kinematic and dynamic modeling approaches each having their own advantages and limitations in various applications. In this paper, a comparative study of five main methods in the literature for kinematic, static and dynamic modeling of continuum manipulators is presented in a unified mathematical framework. The five widely used methods of Lumped system dynamic model, Constant curvature, two-step modified constant curvature, variable curvature Cosserat rod and beam theory approach, and series solution identification are re-viewed here with derivation details in order to clarify their methodological differences. A comparison between computer simulations and experimental results using a STIFF-FLOP continuum manipulator is presented to study the advantages of each modeling method.

Abstract-There is an emerging trend towards soft robotics due to its extended manipulation capabilities compared to traditionally rigid robot links, showing promise for an extended applicability to new areas. However, as a result of the inherent property of soft robotics being less rigid, the ability to control/obtain higher overall stiffness when required is yet to be further explored. In this paper, an innovative design is introduced which allows varying the stiffness of a continuum silicon-based manipulator and proves to have potential for applications in Minimally Invasive Surgery. Inspired by muscular structures occurring in animals such as the octopus, we propose a hybrid and inherently antagonstic actuation scheme. In particular, the octopus makes use of this principle activating two sets of muscles -longitudinal and transverse musclesthus, being capable of controlling the stiffness of parts of its arm in an antagonistic fashion. Our designed manipulator is pneumatically actuated employing chambers embedded within the robot's silicone structure. Tendons incorporated in the structure complement the pneumatic actuation placed inside the manipulator's wall to allow variation of overall stiffness. Experiments are carried out by applying an external force in different configurations while changing the stiffness by means of the two actuation mechanisms. Our test results show that dual, antagonistic actuation increases the load bearing capabilities for soft continuum manipulators and thus their range of applications.

Various methods based on hyperelastic assumptions have been developed to address the mathematical complexities of modelling motion and deformation of continuum manipulators. Here, we propose a quasi-static approach for 3D modelling and real-time simulation of a pneumatically actuated soft continuum robotic appendage to estimate the contact forces and the overall pose. Our model can incorporate external load at any arbitrary point on the body and deliver positional and force propagation information along the entire backbone. In line with the proposed model, the effectiveness of elasticity vs. hyperelasticity assumptions (Neo-Hookean and Gent) are investigated and compared. Experiments are carried out with and without external load, and simulations are validated across a range of Young's moduli. Results show best conformity with Hooke's model for limited strains with about 6% average normalized error of position; and a mean absolute error of less than 0.08N for force applied at the tip and on the body; demonstrating high accuracy in estimating the position and the contact forces.