A framework for dynamic modeling of legged modular miniature robots with soft backbones

In this work, the dynamics of ”n” legged modular miniature robots with a soft body is modeled. The dynamic formulation is obtained using Newton–Euler formulation that depends on the contact parameters and the feet closed-chain kinematic analysis. The dynamic model determines the locomotion parameters of each module as an individual system as well as the dynamics of the whole robot in a 3D space; i.e., the robot is modeled as one system, and modules are considered to be sets of flexible links connected within this system. Kinematic constraints among these modules are obtained by considering the type of backbone integrated into the modular robot. Various types of backbones are used that are classified into three groups: rigid, only torsional, and soft. The model is verified using SMoLBot, an origami-inspired miniature robot made of multiple modules and soft/rigid backbones. Additional to the dynamic model, the effect of different sets of design parameters on the locomotion of the legged soft-bodied modular miniature robots is studied. Analyses comparing the velocity of SMoLBot with a different number of modules and various types of backbones are presented using the proposed dynamic model. Our results show the existence of an optimum backbone torsional stiffness for legged miniature modular robots and an optimum number of legs for a given backbone stiffness that maximizes the robot’s velocity. In this research, presented results and locomotion study show that the robot’s design should be iteratively improved based on specific optimum goals for exclusively defined task to satisfy the operational needs.