  Many commodity sensors that measure the robot and dynamic obstacle's state
have non-Gaussian noise characteristics. Yet, many current approaches treat the
underlying-uncertainty in motion and perception as Gaussian, primarily to
ensure computational tractability. On the other hand, existing planners working
with non-Gaussian uncertainty do not shed light on leveraging distributional
characteristics of motion and perception noise, such as bias for efficient
collision avoidance.
  This paper fills this gap by interpreting reactive collision avoidance as a
distribution matching problem between the collision constraint violations and
Dirac Delta distribution. To ensure fast reactivity in the planner, we embed
each distribution in Reproducing Kernel Hilbert Space and reformulate the
distribution matching as minimizing the Maximum Mean Discrepancy (MMD) between
the two distributions. We show that evaluating the MMD for a given control
input boils down to just matrix-matrix products. We leverage this insight to
develop a simple control sampling approach for reactive collision avoidance
with dynamic and uncertain obstacles.
  We advance the state-of-the-art in two respects. First, we conduct an
extensive empirical study to show that our planner can infer distributional
bias from sample-level information. Consequently, it uses this insight to guide
the robot to good homotopy. We also highlight how a Gaussian approximation of
the underlying uncertainty can lose the bias estimate and guide the robot to
unfavorable states with a high collision probability. Second, we show tangible
comparative advantages of the proposed distribution matching approach for
collision avoidance with previous non-parametric and Gaussian approximated
methods of reactive collision avoidance.
