  This paper presents a novel control approach for autonomous systems operating
under uncertainty. We combine Model Predictive Path Integral (MPPI) control
with Covariance Steering (CS) theory to obtain a robust controller for general
nonlinear systems. The proposed Covariance-Controlled Model Predictive Path
Integral (CC-MPPI) controller addresses the performance degradation observed in
some MPPI implementations owing to unexpected disturbances and uncertainties.
Namely, in cases where the environment changes too fast or the simulated
dynamics during the MPPI rollouts do not capture the noise and uncertainty in
the actual dynamics, the baseline MPPI implementation may lead to divergence.
The proposed CC-MPPI controller avoids divergence by controlling the dispersion
of the rollout trajectories at the end of the prediction horizon. Furthermore,
the CC-MPPI has adjustable trajectory sampling distributions that can be
changed according to the environment to achieve efficient sampling. Numerical
examples using a ground vehicle navigating in challenging environments
demonstrate the proposed approach.
