Analytical Derivatives for Efficient Mechanical Simulations of Hybrid Soft Rigid Robots

TL;DR

This paper introduces analytical derivatives for the GVS model to enhance the efficiency and accuracy of simulations for hybrid soft-rigid robots, enabling faster computations and better modeling of complex deformations.

Contribution

It develops analytical derivatives of the GVS model's governing equations using recursive algorithms, significantly improving simulation speed and accuracy for hybrid soft-rigid robots.

Findings

Simulation speed improved up to 1000 times

Validated derivatives through comparison with non-analytical methods

Applied to diverse robotic systems demonstrating versatility

Abstract

Algorithms that use derivatives of governing equations have accelerated rigid robot simulations and improved their accuracy, enabling the modeling of complex, real-world capabilities. However, extending these methods to soft and hybrid soft-rigid robots is significantly more challenging due to the complexities in modeling continuous deformations inherent in soft bodies. A considerable number of soft robots and the deformable links of hybrid robots can be effectively modeled as slender rods. The Geometric Variable Strain (GVS) model, which employs the screw theory and the strain parameterization of the Cosserat rod, extends the rod theory to model hybrid soft-rigid robots within the same mathematical framework. Using the Recursive Newton-Euler Algorithm, we developed the analytical derivatives of the governing equations of the GVS model. These derivatives facilitate the implicit integration of dynamics and provide the analytical Jacobian of the statics residue, ensuring fast and accurate computations. We applied these derivatives to the mechanical simulations of six common robotic systems: a soft cable-driven manipulator, a hybrid serial robot, a fin-ray finger, a hybrid parallel robot, a contact scenario, and an underwater hybrid mobile robot. Simulation results demonstrate substantial improvements in computational efficiency, with speed-ups of up to three orders of magnitude. We validate the model by comparing simulations done with and without analytical derivatives. Beyond static and dynamic simulations, the techniques discussed in this paper hold the potential to revolutionize the analysis, control, and optimization of hybrid robotic systems for real-world applications.