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.