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Many commodity sensors that measure the robot and dynamic obstacle's statehave non-Gaussian noise characteristics. Yet, many current approaches treat theunderlying-uncertainty in motion and perception as Gaussian, primarily toensure computational tractability. On the other hand, existing planners workingwith non-Gaussian uncertainty do not shed light on leveraging distributionalcharacteristics of motion and perception noise, such as bias for efficientcollision avoidance.  This paper fills this gap by interpreting reactive collision avoidance as adistribution matching problem between the collision constraint violations andDirac Delta distribution. To ensure fast reactivity in the planner, we embedeach distribution in Reproducing Kernel Hilbert Space and reformulate thedistribution matching as minimizing the Maximum Mean Discrepancy (MMD) betweenthe two distributions. We show that evaluating the MMD for a given controlinput boils down to just matrix-matrix products. We leverage this insight todevelop a simple control sampling approach for reactive collision avoidancewith dynamic and uncertain obstacles.  We advance the state-of-the-art in two respects. First, we conduct anextensive empirical study to show that our planner can infer distributionalbias from sample-level information. Consequently, it uses this insight to guidethe robot to good homotopy. We also highlight how a Gaussian approximation ofthe underlying uncertainty can lose the bias estimate and guide the robot tounfavorable states with a high collision probability. Second, we show tangiblecomparative advantages of the proposed distribution matching approach forcollision avoidance with previous non-parametric and Gaussian approximatedmethods of reactive collision avoidance.

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