Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise

TL;DR

This paper introduces a novel planning method for autonomous systems that provides probabilistic safety guarantees without relying on explicit noise distribution models, using scenario-based bounds and interval Markov decision processes.

Contribution

It develops a noise-agnostic planning approach that uses scenario approach and iMDPs to ensure safety in autonomous control under unknown noise distributions.

Findings

Method provides safety guarantees with finite noise samples.

Scalable to large state spaces with millions of transitions.

Applicable to realistic autonomous system benchmarks.

Abstract

Controllers for autonomous systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modelled as process noise, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel planning method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP, and compute a controller for which these guarantees carry over to the autonomous system. Realistic benchmarks show the practical applicability of our method, even when the iMDP has millions of states or transitions.