  We propose a Model Predictive Control (MPC) method for collision-free
navigation that uses amortized variational inference to approximate the
distribution of optimal control sequences by training a normalizing flow
conditioned on the start, goal and environment. This representation allows us
to learn a distribution that accounts for both the dynamics of the robot and
complex obstacle geometries. We can then sample from this distribution to
produce control sequences which are likely to be both goal-directed and
collision-free as part of our proposed FlowMPPI sampling-based MPC method.
However, when deploying this method, the robot may encounter an
out-of-distribution (OOD) environment, i.e. one which is radically different
from those used in training. In such cases, the learned flow cannot be trusted
to produce low-cost control sequences. To generalize our method to OOD
environments we also present an approach that performs projection on the
representation of the environment as part of the MPC process. This projection
changes the environment representation to be more in-distribution while also
optimizing trajectory quality in the true environment. Our simulation results
on a 2D double-integrator and a 3D 12DoF underactuated quadrotor suggest that
FlowMPPI with projection outperforms state-of-the-art MPC baselines on both
in-distribution and OOD environments, including OOD environments generated from
real-world data.
