Development of inverse static model of continuum robots based on absolute nodal coordinates formulation for large deformation applications

Abstract

AbstractContinuum robotics has emerged as a prominent trend within the robotics field for about two decades. Nevertheless, motion analysis of continuum robots based on dynamic modelling remains severely limited. In the realm of continuum robots, it is obvious that simplified theoretical models or first-order approximations utilizing springs and dampers are insufficient for capturing the dynamics of soft-bodied structures. This inadequacy is especially apparent in applications involving significant deformations in 3D space, continuous actuation, and interface effects. In this regard, the development of precise theoretical models is crucial. Within this particular framework, the paper presents the absolute nodal coordinates formulation (ANCF) to construct the kinematic models of continuum robots. The transformation between the structural, body, and element coordinate systems, as well as the derivation of the generalized external forces and moments using the principle of virtual work and the velocity gradient tensor, are demonstrated. Additionally, it proceeds to develop the strain measures required for the computation of the elastic forces of elements with circular cross sections, ultimately enabling the construction of the Forward Static Model (FSM) of continuum robots. A procedure based on B-spline surface geometry is proposed to figure out the robot shapes in space and generate the necessary nodal coordinates and gradients of ANCF elements. Finally, the inverse static model (ISM) of the ANCF-B-spline generated structure is presented using an iterative solution approach. The effectiveness of the proposed model is evaluated by the analysis of numerical examples. According to the numerical results, it can be inferred that the ANCF method well captures the modelling aspects of continuum robots. The results obtained from the FSM demonstrate a high level of accuracy, moreover, the driving forces based on the ISM provide, from a practical standpoint, satisfactory results.