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

Abstract

In the field of robotics, the accurate modeling of uncertainty in the robot’s motion and perception is crucial for effective collision avoidance. Many commodity sensors exhibit nonGaussian noise characteristics, yet existing approaches often assume Gaussian uncertainty to ensure computational tractability. This thesis addresses the gap between non-Gaussian uncertainty and collision avoidance by developing a framework that leverages the distributional characteristics of motion and perception noise. We propose a novel approach that interprets reactive collision avoidance as a distribution matching problem between collision constraint violations and the Dirac Delta distribution. To ensure fast reactivity, we embed each distribution in a Reproducing Kernel Hilbert Space and reformulate the distribution matching as the minimization of the Maximum Mean Discrepancy (MMD). By exploiting the insight that evaluating the MMD reduces to matrix-matrix products, we develop a simple control sampling approach for reactive collision avoidance with dynamic and uncertain obstacles. Furthermore, this thesis advances the state-of-the-art in two key aspects. Firstly, we conduct an extensive empirical study to demonstrate that our planner can effectively infer distributional bias from sample-level information. This insight enables the planner to guide the robot towards good homotopy, utilizing the distributional characteristics of motion and perception noise. In contrast, we highlight how a Gaussian approximation of uncertainty can lead to loss of bias estimation and guide the robot towards unfavorable states with high collision probabilities. Secondly, we compare our proposed distribution matching approach with previous non-parametric and Gaussian approximated methods of reactive collision avoidance. Through tangible comparative advantages, we showcase the superior performance of the distribution matching approach. In summary, this thesis presents a comprehensive framework that addresses the challenge of non-Gaussian uncertainty in collision avoidance. By leveraging the distributional characteristics of motion and perception noise, our approach provides a more accurate and effective method for reactive collision avoidance with dynamic and uncertain obstacles. The empirical study and comparative evaluations demonstrate the advantages of the proposed distribution matching approach over previous methods. This research contributes to advancing the understanding and applicability of collision avoidance strategies, particularly in the context of non-holonomic motion and non-Gaussian uncertainty.