  Modern robotic systems are endowed with superior mobility and mechanical
skills that make them suited to be employed in real-world scenarios, where
interactions with heavy objects and precise manipulation capabilities are
required. For instance, legged robots with high payload capacity can be used in
disaster scenarios to remove dangerous material or carry injured people. It is
thus essential to develop planning algorithms that can enable complex robots to
perform motion and manipulation tasks accurately. In addition, online
adaptation mechanisms with respect to new, unknown environments are needed. In
this work, we impose that the optimal state-input trajectories generated by
Model Predictive Control (MPC) satisfy the Lyapunov function criterion derived
in adaptive control for robotic systems. As a result, we combine the stability
guarantees provided by Control Lyapunov Functions (CLFs) and the optimality
offered by MPC in a unified adaptive framework, yielding an improved
performance during the robot's interaction with unknown objects. We validate
the proposed approach in simulation and hardware tests on a quadrupedal robot
carrying un-modeled payloads and pulling heavy boxes.
