  The theoretical unification of Nonlinear Model Predictive Control (NMPC) with
Control Lyapunov Functions (CLFs) provides a framework for achieving optimal
control performance while ensuring stability guarantees. In this paper we
present the first real-time realization of a unified NMPC and CLF controller on
a robotic system with limited computational resources. These limitations
motivate a set of approaches for efficiently incorporating CLF stability
constraints into a general NMPC formulation. We evaluate the performance of the
proposed methods compared to baseline CLF and NMPC controllers with a robotic
Segway platform both in simulation and on hardware. The addition of a
prediction horizon provides a performance advantage over CLF based controllers,
which operate optimally point-wise in time. Moreover, the explicitly imposed
stability constraints remove the need for difficult cost function and parameter
tuning required by NMPC. Therefore the unified controller improves the
performance of each isolated controller and simplifies the overall design
process.
