  Soft slender robots have attracted more and more research attentions in these
years due to their continuity and compliance natures. However, mechanics
modeling for soft robots interacting with environment is still an academic
challenge because of the non-linearity of deformation and the non-smooth
property of the contacts. In this work, starting from a piece-wise local strain
field assumption, we propose a nonlinear dynamic model for soft robot via
Cosserat rod theory using Newtonian mechanics which handles the frictional
contact with environment and transfer them into the nonlinear complementary
constraint (NCP) formulation. Moreover, we smooth both the contact and friction
constraints in order to convert the inequality equations of NCP to the smooth
equality equations. The proposed model allows us to compute the dynamic
deformation and frictional contact force under common optimization framework in
real time when the soft slender robot interacts with other rigid or soft
bodies. In the end, the corresponding experiments are carried out which valid
our proposed dynamic model.
