Kinematic and dynamic analogies between planar biped robots and the reaction mass pendulum (RMP) model

In order to simplify dynamic analysis, humanoid robots are often abstracted with various versions of the inverted pendulum model. However, most of these models do not explicitly characterize the robotpsilas rotational inertia, a critical component of its dynamics, and especially of its balance. To remedy this, we have earlier introduced the reaction mass pendulum (RMP), an extension of the inverted pendulum, which models the rotational inertia and angular momentum of a robot through its centroidal composite rigid body (CCRB) inertia. However, we presented only the kinematic mapping between a robot and its corresponding RMP. Focussing in-depth on planar mechanisms, here we derive the dynamic equations of the RMP and explicitly compute the parameters that it must possess in order to establish equivalence with planar compass gait robot. In particular, we show that, a) an angular momentum equality between the robot and RMP does not necessarily guarantee kinetic energy equality, and b) a cyclic robot gait may not result in a cyclic RMP movement. The work raises the broader question of how quantitatively similar the simpler models of humanoid robot must be in order for them to be of practical use.