Modeling of magnetic cilia carpet robots using discrete differential geometry formulation

Abstract

Cilia broadly exist in a wide range of living systems. The metachronal waves generated by arrays of beating cilia are essential for realizing complex biological functions, such as locomotion and transportation, which have inspired the design in advanced engineering systems, e.g., programmable cilia-inspired soft robots. However, due to lack of efficient dynamic modeling and numerical explorations on such complex active systems, design and control of cilia-inspired soft robots usually involve empirical approaches or highly time-consuming numerical simulations. Here, we report a numerical framework based on the discrete differential geometry (DDG) for the dynamic analysis of bio-inspired cilia carpet robots powered by external magnetic field. The active cilia is modeled as discrete magneto-elastic rods (DMER) and the carpet by discrete elastic plate (DEP) method, which are geometrically rigorous frameworks for the nonlinear mechanics of flexible structures. The clamped-type connection between slender cilia and thin carpet is achieved by introducing a special coupling element between rod segments and triangular carpet surfaces. The intersection-free contact and frictional interaction between soft robots and rigid ground is captured based on incremental potential energy theory and lagged dissipative principle, respectively, and, therefore, the constrained elastodynamic system equations can be solved implicitly through a variational approach. Two types of typical dynamic locomotion – crawling and rolling – are considered to demonstrate the effectiveness and robustness of our numerical method. The results show that the locomotion efficiency of the robot depends on the structural design. We also demonstrate that the crawling pathways (e.g., turning) can be programmed via selective actuation. This computationally efficient dynamic framework can not only provide insights on fundamental understanding of the biophysics of microorganisms, but also provide guidelines on the optimal design of cilia-inspired soft robots for biomedical applications.