  Re-planning in legged locomotion is crucial to track the desired user
velocity while adapting to the terrain and rejecting external disturbances. In
this work, we propose and test in experiments a real-time Nonlinear Model
Predictive Control (NMPC) tailored to a legged robot for achieving dynamic
locomotion on a variety of terrains. We introduce a mobility-based criterion to
define an NMPC cost that enhances the locomotion of quadruped robots while
maximizing leg mobility and improves adaptation to the terrain features. Our
NMPC is based on the real-time iteration scheme that allows us to re-plan
online at $25\,\mathrm{Hz}$ with a prediction horizon of $2$ seconds. We use
the single rigid body dynamic model defined in the center of mass frame in
order to increase the computational efficiency. In simulations, the NMPC is
tested to traverse a set of pallets of different sizes, to walk into a V-shaped
chimney,and to locomote over rough terrain. In real experiments, we demonstrate
the effectiveness of our NMPC with the mobility feature that allowed IIT's
$87\, \mathrm{kg}$ quadruped robot HyQ to achieve an omni-directional walk on
flat terrain, to traverse a static pallet, and to adapt to a repositioned
pallet during a walk.

Robotics;Systems and Control;Systems and Control