Title: Learning Sampling Distribution and Safety Filter for Autonomous Driving with VQ-VAE and Differentiable Optimization

Abstract: Sampling trajectories from a distribution followed by ranking them based on a specified cost function is a common approach in autonomous driving. Typically, the sampling distribution is hand-crafted (e.g a Gaussian, or a grid). Recently, there have been efforts towards learning the sampling distribution through generative models such as Conditional Variational Autoencoder (CVAE). However, these approaches fail to capture the multi-modality of the driving behaviour due to the Gaussian latent prior of the CVAE. Thus, in this paper, we re-imagine the distribution learning through vector quantized variational autoencoder (VQ-VAE), whose discrete latent-space is well equipped to capture multi-modal sampling distribution. The VQ-VAE is trained with demonstration data of optimal trajectories. We further propose a differentiable optimization based safety filter to minimally correct the VQVAE sampled trajectories to ensure collision avoidance. We use backpropagation through the optimization layers in a self-supervised learning set-up to learn good initialization and optimal parameters of the safety filter. We perform extensive comparisons with state-of-the-art CVAE-based baseline in dense and aggressive traffic scenarios and show a reduction of up to 12 times in collision-rate while being competitive in driving speeds.