Discrete Cosserat Approach for Multisection Soft Manipulator Dynamics

Nowadays, the most adopted model for the design and control of soft robots is the piecewise constant curvature model, with its consolidated benefits and drawbacks. In this work, an alternative model for multisection soft manipulator dynamics is presented based on a discrete Cosserat approach, in which the continuous Cosserat model is discretized by assuming a piecewise constant strain along the soft arm. As a consequence, the soft manipulator state is described by a finite set of constant strains. This approach has several advantages with respect to the existing models. First, it takes into account shear and torsional deformations, which are both essential to cope with out-of-plane external loads. Furthermore, it inherits desirable geometrical and mechanical properties of the continuous Cosserat model, such as intrinsic parameterization and greater generality. Finally, this approach allows to extend to soft manipulators, the recursive composite-rigid-body and articulated-body algorithms, whose performances are compared through a cantilever beam simulation. The soundness of the model is demonstrated through extensive simulation and experimental results.

I. Introduction

Since the beginning of research in the field of soft robotics, many researchers have contributed in the development of mathematical modeling approaches that could be able to describe the kinematics and dynamics of such infinite degrees of freedom robots. However, addressing the requirements imposed by robotic applications is still a challenge [1], [2]. In order to meet the standards achieved in traditional rigid robotics, a model for soft robotics should be, at the same time, computational inexpensive and sufficiently accurate. It should be able to shed light on the mathematical submodels, encompass them in a unified framework, and provide a systematic modeling procedure, regardless of the specific application. Such a modeling framework is the necessary condition for developing the physical designs and control architectures of these new soft robots as well as their task-related motions and path planning.