Quantifying balance capabilities using momentum gain

The ability of a legged system to balance depends on both the control strategy used and the system's physical design. To quantify a system's inherent balance capabilities, we define momentum gains for general 2D and 3D models. We provide two methods for calculating these gains, and relate both velocity and momentum gains to the centroidal momentum of a system, a commonly used measure of aggregate system behavior. Finally, we compare velocity and momentum gains as criteria for the design of simple balancing systems using a parameterized optimization framework.