  Model predictive control (MPC) schemes have a proven track record for
delivering aggressive and robust performance in many challenging control tasks,
coping with nonlinear system dynamics, constraints, and observational noise.
Despite their success, these methods often rely on simple control
distributions, which can limit their performance in highly uncertain and
complex environments. MPC frameworks must be able to accommodate changing
distributions over system parameters, based on the most recent measurements. In
this paper, we devise an implicit variational inference algorithm able to
estimate distributions over model parameters and control inputs on-the-fly. The
method incorporates Stein Variational gradient descent to approximate the
target distributions as a collection of particles, and performs updates based
on a Bayesian formulation. This enables the approximation of complex
multi-modal posterior distributions, typically occurring in challenging and
realistic robot navigation tasks. We demonstrate our approach on both simulated
and real-world experiments requiring real-time execution in the face of
dynamically changing environments.
