Real-Time Learning of Non-Gaussian Uncertainty Models for Autonomous Racing

Performance and robustness targets have been considered for controller design for decades. However, robust controllers usually suffer from performance limitations due to conservative uncertainty assumptions made a priori to system operation. The increased number of systems (e.g. autonomous vehicles) which require high-performance operation in safety- critical environments is motivating research in novel design methods. Recently, machine learning methods have emerged as a promising way to reduce conservatism, based on data gathered during system operation. We propose a combination of a recursive least squares estimator with a recursive quantile estimator to identify feature-dependent upper and lower uncertainty bounds. We give conditions under which the estimator converges to a robust invariant set, such that the resulting bounds cover a target proportion of the samples up to small error. In contrast to widely applied Gaussian process regression or Bayesian linear regression approaches, we do not imply any assumptions about the probability distribution of the samples. We demonstrate that the estimated bounds achieve the desired data coverage in contrast to state-of-the-art approaches on academic examples, as well as a motion control example for an autonomous race car. Furthermore, the approach exhibits very low computational requirements and is therefore suitable for application on embedded systems.