Imitative Planning using Conditional Normalizing Flow

We explore the application of normalizing flows for improving the performance of trajectory planning for autonomous vehicles (AVs). Normalizing flows provide an invertible mapping from a known prior distribution to a potentially complex, multi-modal target distribution and allow for fast sampling with exact PDF inference. By modeling a trajectory planner's cost manifold as an energy function we learn a scene conditioned mapping from the prior to a Boltzmann distribution over the AV control space. This mapping allows for control samples and their associated energy to be generated jointly and in parallel. We propose using neural autoregressive flow (NAF) as part of an end-to-end deep learned system that allows for utilizing sensors, map, and route information to condition the flow mapping. Finally, we demonstrate the effectiveness of our approach on real world datasets over IL and hand constructed trajectory sampling techniques.Comment: Submittted to 4th Conference on Robot Learning (CoRL 2020), Cambridge MA, US

Robust Forecasting for Robotic Control: A Game-Theoretic Approach

Modern robots require accurate forecasts to make optimal decisions in the real world. For example, self-driving cars need an accurate forecast of other agents' future actions to plan safe trajectories. Current methods rely heavily on historical time series to accurately predict the future. However, relying entirely on the observed history is problematic since it could be corrupted by noise, have outliers, or not completely represent all possible outcomes. To solve this problem, we propose a novel framework for generating robust forecasts for robotic control. In order to model real-world factors affecting future forecasts, we introduce the notion of an adversary, which perturbs observed historical time series to increase a robot's ultimate control cost. Specifically, we model this interaction as a zero-sum two-player game between a robot's forecaster and this hypothetical adversary. We show that our proposed game may be solved to a local Nash equilibrium using gradient-based optimization techniques. Furthermore, we show that a forecaster trained with our method performs 30.14% better on out-of-distribution real-world lane change data than baselines

GPSINDy: Data-Driven Discovery of Equations of Motion

In this paper, we consider the problem of discovering dynamical system models from noisy data. The presence of noise is known to be a significant problem for symbolic regression algorithms. We combine Gaussian process regression, a nonparametric learning method, with SINDy, a parametric learning approach, to identify nonlinear dynamical systems from data. The key advantages of our proposed approach are its simplicity coupled with the fact that it demonstrates improved robustness properties with noisy data over SINDy. We demonstrate our proposed approach on a Lotka-Volterra model and a unicycle dynamic model in simulation and on an NVIDIA JetRacer system using hardware data. We demonstrate improved performance over SINDy for discovering the system dynamics and predicting future trajectories.Comment: Submitted to ICRA 202