  In this paper, we propose a novel framework on force-and-moment-based Model
Predictive Control (MPC) for dynamic legged robots. In specific, we present a
formulation of MPC designed for 10 degree-of-freedom (DoF) bipedal robots using
a simplified rigid body dynamics with input forces and moments. This MPC
controller will calculate the optimal inputs applied to the robot, including
3-D forces and 2-D moments at each foot. These desired inputs will then be
generated by mapping these forces and moments to motor torques of 5 actuators
on each leg. We evaluate our proposed control design on physical simulation of
a 10 degree-of-freedom (DoF) bipedal robot. The robot can achieve fast walking
speed up to 1.6 m/s on rough terrain, with accurate velocity tracking. With the
same control framework, our proposed approach can achieve a wide range of
dynamic motions including walking, hopping, and running using the same set of
control parameters.
