  Many robotic tasks, such as human-robot interactions or the handling of
fragile objects, require tight control and limitation of appearing forces and
moments alongside sensible motion control to achieve safe yet high-performance
operation. We propose a learning-supported model predictive force and motion
control scheme that provides stochastic safety guarantees while adapting to
changing situations. Gaussian processes are used to learn the uncertain
relations that map the robot's states to the forces and moments. The model
predictive controller uses these Gaussian process models to achieve precise
motion and force control under stochastic constraint satisfaction. As the
uncertainty only occurs in the static model parts -- the output equations -- a
computationally efficient stochastic MPC formulation is used. Analysis of
recursive feasibility of the optimal control problem and convergence of the
closed loop system for the static uncertainty case are given. Chance constraint
formulation and back-offs are constructed based on the variance of the Gaussian
process to guarantee safe operation. The approach is illustrated on a
lightweight robot in simulations and experiments.
