  We propose a Gaussian variational inference framework for the motion planning
problem. In this framework, motion planning is formulated as an optimization
over the distribution of the trajectories to approximate the desired trajectory
distribution by a tractable Gaussian distribution. Equivalently, the proposed
framework can be viewed as a standard motion planning with an entropy
regularization. Thus, the solution obtained is a transition from an optimal
deterministic solution to a stochastic one, and the proposed framework can
recover the deterministic solution by controlling the level of stochasticity.
To solve this optimization, we adopt the natural gradient descent scheme. The
sparsity structure of the proposed formulation induced by factorized objective
functions is further leveraged to improve the scalability of the algorithm. We
evaluate our method on several robot systems in simulated environments, and
show that it achieves collision avoidance with smooth trajectories, and
meanwhile brings robustness to the deterministic baseline results, especially
in challenging environments and tasks.
