  In this work we present a whole-body Nonlinear Model Predictive Control
approach for Rigid Body Systems subject to contacts. We use a full dynamic
system model which also includes explicit contact dynamics. Therefore, contact
locations, sequences and timings are not prespecified but optimized by the
solver. Yet, thorough numerical and software engineering allows for running the
nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a
time horizon of half a second. This outperforms the state of the art by at
least one order of magnitude. Hardware experiments in form of periodic and
non-periodic tasks are applied to two quadrupeds with different actuation
systems. The obtained results underline the performance, transferability and
robustness of the approach.
