Continuum robots are kinematically redundant and their dynamic models are highly nonlinear. This study aims to overcome this difficulty by presenting a more practical dynamic model of a certain class of continuum robots called cable-driven continuum robot (CDCR). Firstly, the structural design of a CDCR with two rotational degrees of freedom (DOF) is introduced. Then, the kinematic models are derived according to the constant curvature assumption. Considering the complexity of the kinetic energy expression, it has been approximated by the well-known Taylor expansions. This case corresponds to weak bending angles within the specified bending angle range of the robot. On the other hand, due to the low weight of the CDCR components, the gravitational energy effects can be neglected compared to those stemmed from the elastic energy. Thereafter, the corresponding dynamic model is established using Euler-Lagrange method. Static and dynamic models have been illustrated by examples. This analysis and dynamic model development have been compared with the existing scientific literature. The obtained results shown that the consistency and the efficiency of accuracy for real-time have been carried out. However, the dynamic modeling of CDCR with more than 2-DOF leads to a more complex mathematical expression, and cannot be simplified by adopting the similar assumptions and methodology used in the case of 2-DOF.
Continuum robot modeling is a research topic that focuses on ways to develop kinematic models while respecting some kinematics specificity as well as mechanical properties of such class of robots. The purpose of this article is to present a new alternative approach for solving inverse kinematic models for multi-sections of continuum manipulators. To achieve this work, it is assumed that each constitutive section is curved in a circular arc shape with an inextensible central structure axis. At first, the article presents a solution of an inverse kinematic model for one bending section and details some adopted methodologies, based on the identical inverse kinematic model of parallel robots, used for computation of the links’ length. The latter allows concatenating between multiple platforms to realize a bending section. The inverse kinematic model of the multi-section manipulator is then developed using a modular concept where the endpoint coordinates of each bending section are determined using a metaheuristic method. Finally, to validate the proposed approach, some simulation and experimental studies have been carried out on the Compact Bionic Handling Arm. From this investigation, it was found that the multiple test results show the ability of the developed metaheuristic approach to avoid obstacles and to adopt a real-time implementation with multi-section configuration. On the other hand, this type of concept can enable to model all continuum robots with multiple bending sections.
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