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

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.

Filter-Based Abstractions with Correctness Guarantees for Planning under Uncertainty

We study planning problems for continuous control systems with uncertainty caused by measurement and process noise. The goal is to find an optimal plan that guarantees that the system reaches a desired goal state within finite time. Measurement noise causes limited observability of system states, and process noise causes uncertainty in the outcome of a given plan. These factors render the problem undecidable in general. Our key contribution is a novel abstraction scheme that employs Kalman filtering as a state estimator to obtain a finite-state model, which we formalize as a Markov decision process (MDP). For this MDP, we employ state-of-the-art model checking techniques to efficiently compute plans that maximize the probability of reaching goal states. Moreover, we account for numerical imprecision in computing the abstraction by extending the MDP with intervals of probabilities as a more robust model. We show the correctness of the abstraction and provide several optimizations that aim to balance the quality of the plan and the scalability of the approach. We demonstrate that our method can handle systems that result in MDPs with thousands of states and millions of transitions.