Dynamic modeling, analysis, and comparative study of a quadruped with bio-inspired robotic tails

Looking to nature, animals frequently utilize tails to work alongside or in place of their legs to maneuver, stabilize, and/or propel to achieve highly agile motions. Although the single-link robotic tail shows its dynamical superiority and practical effectiveness in mobile platform maneuvering, most tails observed in nature have multi-link structures. Therefore, to investigate this novel tail structure, bio-inspired and biomimetic multi-link robotic tails were proposed and implemented. However, due to the lack of a whole-body dynamic model, previous research focused on investigating the tail subsystem independently without considering the mobile platform's motions, which introduces deficiencies on both analysis and control. To bridge this theoretical gap, this paper presents a unified dynamics model that incorporates both the quadruped and the tail subsystems as a complete coupled dynamic system. Classical multibody dynamics formulation based on the principle of virtual work is utilized to derive the dynamic model. Based on the new whole-body dynamic model, three typical tail structures, including a single-link pendulum tail, a multi-link rigid tail, and a multi-link flexible tail are evaluated. The results indicate that by using a center of mass-based benchmark, the multi-link tail structure is dynamically equivalent to the single-link tail structure for bending motion. However, for rolling motions, the multi-link structure illustrates noticeable dynamical benefits compared to a single-link structure due to its higher inertia. In addition, a multi-link flexible structure shows significant oscillations and uncontrollable dynamic behaviors due to its under-actuation feature, which may limit its usage for highly dynamic applications.