Structural Properties and Control of Soft Robots Modeled as Discrete Cosserat Rods

Soft robots featuring approximate finitedimensional reduced-order models (undergoing small deformations) are increasingly becoming paramount in literature and applications. In this paper, we consider the piecewise constant strain (PCS) discrete Cosserat model whose dynamics admit the standard Newton-Euler dynamics for a kinetic model. Contrary to popular convention that soft robots under these modeling assumptions admit similar mechanical characteristics to rigid robots, the schemes employed to arrive at the properties for soft robots under finite deformation show a far dissimilarity to those for rigid robots. We set out to first correct the false premise behind this syllogism: from first principles, we established the structural properties of soft slender robots undergoing finite deformation under a discretized PCS assumption; we then utilized these properties to prove the stability of designed proportional-derivative controllers for manipulating the strain states of a prototypical soft robot under finite deformation. Our newly derived results are illustrated by numerical examples on a single arm of the Octopus robot and demonstrate the efficacy of our designed controller based on the derived kinetic properties. This work rectifies previously disseminated kinetic properties of discrete Cosserat-based soft robot models with greater accuracy in proofs and clarity.