Elasticity Versus Hyperelasticity Considerations in Quasistatic Modeling of a Soft Finger-Like Robotic Appendage for Real-Time Position and Force Estimation

Abstract

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.

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

“…Discretized VC Kinematics-Discretized versions of Eq. 2 with rotation matrices are discussed in (Takano et al 2017;Shiva et al 2018). Shiva et al used…”

“…The above relation is used for the comparison purpose in our study. A similar representation is discussed in (Shiva et al 2018), Appendix section, arguing that the order of the rotations is not important as long as small enough elements are considered along with the backbone (infinitesimal curvatures/torsion). They showed that using any of the above methods does not affect the accuracy of modeling a short appendage with beam theory, even for large deformations.…”

A review of recent advancements in soft and flexible robots for medical applications

“…This model has behaved in a highly similar fashion to that of their soft manipulator for MIS . Researchers of King's College London have developed a quasistatic approach for 3D modeling and real‐time simulation of the STIFF‐FLOP arm appendage to estimate the contact force and overall posture …”

Stiffness Imaging With a Continuum Appendage: Real-Time Shape and Tip Force Estimation From Base Load Readings

“…Finally, an intermediate step is applied in the numerical integration to account for the braid constraint as r * p = r p 1 − λ 2 cos(γ) 2 / sin(γ) [4], and the material hyper-elastic deformation as r * = r/ √ λ and E * |G * = E|G/λ [21], [22], except for r p , which follows the braid constraint. Here, λ = 1 + v 2 is the local axial stretch along the manipulator backbone.…”

“…The use of a hydraulically actuated STIFF-FLOP module, which is a 3-DOF braided continuum appendage, is proposed for probing and stiffness imaging of a soft silicon tissue phantom, as in Fig. 1-a, with the aim of detecting anomalies in the form of a hard nodules in the soft tissue phantom (section II-C) Hyperelasticity and braiding effects are taken into consideration in an intermediate numerical step as in [21], [22]. The results from multiple probing runs with different actuation pressures provide sufficient information to construct the surface profile and the linear stiffness map of the phantom tissue with good accuracy compared to experimental results, showing the location of the anomalies in the tissue.…”