Dynamic modeling of soft continuum manipulators using lie group variational integration

Abstract

This paper presents the derivation and experimental validation of algorithms for modeling and estimation of soft continuum manipulators using Lie group variational integration. Existing approaches are generally limited to static and quasi-static analyses, and are not sufficiently validated for dynamic motion. However, in several applications, models need to consider the dynamical behavior of the continuum manipulators. The proposed modeling and estimation formulation is obtained from a discrete variational principle, and therefore grants outstanding conservation properties to the continuum mechanical model. The main contribution of this article is the experimental validation of the dynamic model of soft continuum manipulators, including external torques and forces (e.g., generated by magnetic fields, friction, and the gravity), by carrying out different experiments with metal rods and polymerbased soft rods. To consider dissipative forces in the validation process, distributed estimation filters are proposed. The experimental and numerical tests also illustrate the algorithm's performance on a magnetically-actuated soft continuum manipulator. The model demonstrates good agreement with dynamic experiments in estimating the tip position of a Polydimethylsiloxane (PDMS) rod. The experimental results show an average absolute error and maximum error in tip position estimation of 0.13 mm and 0.58 mm, respectively, for a manipulator length of 60.55 mm.

A Recurrent Neural-Network-Based Real-Time Dynamic Model for Soft Continuum Manipulators

“…The obtained data can thus be transferred to train the algorithms to be implemented in real-world scenarios. In this section and for the presented examples, required data for the training of the proposed RNN-based model are acquired through simulations of the algorithm presented in Tariverdi et al (2020) , Sec. 2).…”

“…Consider a continuum manipulator with large deflections described by dynamic equations of motion [as presented in Tariverdi et al (2020) and Demoures et al (2015)] in the PDEs form as…”

“…Consider a continuum manipulator with large deflections described by dynamic equations of motion [as presented in Tariverdi et al (2020) and Demoures et al (2015) ] in the PDEs form as where ( ρ and A are the manipulator constant mass density and its cross-section area), is the manipulator’s angular velocity, is the manipulator’s inertia matrix, is the position of the manipulator’s line of centroids in its workspace, denotes the orientation of moving cross-sections at point ϕ. Also, and are the stresses and momenta along the manipulator, represents conservative forces (e.g.…”

“…On the other hand, dynamical modeling approaches [e.g. Wen et al (2012) , Jung et al (2014) , Hyatt et al (2019) , Sadati et al (2019) , Till et al (2019) , Tariverdi et al (2020) ], contain dynamics of the manipulators and also take into account time-varying responses of manipulators, including high-frequency modes. However, the dynamic models mostly rely on traditional methods, such as finite elements and finite differences (i.e., quantitative and numerical methods), making the algorithms computationally expensive for real-time applications.…”

Geometric Recursive Dynamic Modelling and Simulation of Soft Robotic Systems

“…However, it suffers a compromise in accuracy under highly dynamic conditions and is sensitive to the discretization used [82]. Various solution methods have been proposed on Cosserat rods using FDM with experimental validation [83,[99][100][101][102]. Multiple considerations need to be made implementing FDM on PDEs and they are discussed below.…”