Leveraging Distributional Bias For Reactive Collision Avoidance under Uncertainty: A Kernel Embedding Approach

Anish Gupta, Arun Kumar Singh, K. Krishna

Abstract:

Many commodity sensors that measure the robot
and dynamic obstacle’s state have non-Gaussian noise char-
acteristics. 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 distri-
bution 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 approx-
imated methods of reactive collision avoidance.