Legged mechanism design with momentum gains

There are two main goals for any mobile, bipedal system: locomotion and balance. These behaviors both require the biped to effectively move its center of mass (COM). In this work, we define an optimization framework which can be used to design a biped that maximizes its ability to move its COM, without having to define an associated controller or trajectory. We use angular momentum gain in our objective function, a measure of how efficiently a system can move its COM based on its physical properties. As a comparison, we also optimize the model using a cost of transport-based objective function over a set of trajectories and show that it provides similar results. However, the cost of transport calculation requires slow hybrid dynamics equations and hand-designed trajectories, whereas the angular momentum gain calculation requires only the joint space inertia matrix at each configuration of interest.