  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.
