Reaction Mass Pendulum (RMP): An explicit model for centroidal angular momentum of humanoid robots

A number of conceptually simple but behavior-rich "inverted pendulum" humanoid models have greatly enhanced the understanding and analytical insight of humanoid dynamics. However, these models do not incorporate the robot\´s angular momentum properties, a critical component of its dynamics. We introduce the reaction mass pendulum (RMP) model, a 3D generalization of the better-known reaction wheel pendulum. The RMP model augments the existing models by compactly capturing the robot\´s centroidal momenta through its composite rigid body (CRB) inertia. This model provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws. In this paper we show how a humanoid robot of general geometry and dynamics can be mapped into its equivalent RMP model. A movement is subsequently mapped to the time evolution of the RMP. We also show how an "inertia shaping" control law can be designed based on the RMP.