Dynamic Model of a Compliant Quadruped Trunk Under Large Deflections

Abstract Recent trends in robots mechanical design include the use of compliant mechanical parts for different purposes. Here, we consider the trunk of a quadruped. Many of such mechanical parts can be modelled as flexible beams. However, classic cantilever dynamics analysis considers small bending angles of the flexible parts. When the bending is large, the resonant frequency of the beam changes as a result of mechanical deformation. Therefore, the classical cantilever beam formulation cannot be used for dynamic modelling, which is key for the development of suitable control strategies. In this work, a dynamic that takes into account the changes resulting from the large deflections of the beam is formulated. In addition, the effects on the dynamics are studied when an extra mass is connected to a rigid bar at the free end of the beam. As a result, our mathematical formulation is applicable to quadruped robotic structures composed of both rigid and flexible components, allowing the development of a control system capable of achieving energetically efficient galloping by tuning to the quasi-resonant frequency of the system. Experimental results carried out using a physical prototype representing the trunk-hind legs of a quadrupedal robot confirm the precision of the proposed model.