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.

翻译：软体细长机器人因其连续性与柔顺特性，近年来吸引了越来越多的研究关注。然而，由于变形的非线性以及接触的非光滑特性，软体机器人与环境交互的力学建模仍是一项学术挑战。本文从分段局部应变场假设出发，基于牛顿力学框架，采用Cosserat杆理论提出了一种非线性动力学模型。该模型能够处理与环境的摩擦接触，并将其转化为非线性互补约束（NCP）形式。此外，我们对接触约束和摩擦约束进行了光滑化处理，从而将NCP的不等式方程转化为光滑等式方程。所提出的模型能够在软体细长机器人与其他刚体或软体交互时，在通用优化框架下实时计算动态变形与摩擦接触力。最后，通过相应的实验验证了所提动力学模型的有效性。