We propose an abstraction-refinement-based algorithm for the problem of verifying the safety of a camera-based autonomous system in a synthetic 3D-scene, based on the notion of interval images. An interval image is an abstract data structure that represents a set of images in a 3D-scene. We give a computer graphics style rendering algorithm to efficiently compute interval images from a given region. Our proposed abstraction-refinement algorithm leverages recent abstract interpretation tools for neural networks. We have implemented and evaluated the proposed technique on complex 3D-scenes, demonstrating its effectiveness and scalability in comparison with earlier techniques.

In this article, we consider the problem of checking approximate conformance of closed-loop systems with the same plant but different neural network (NN) controllers. First, we introduce a notion of approximate conformance on NNs, which allows us to quantify semantically the deviations in closed-loop system behaviors with different NN controllers. Next, we consider the problem of computationally checking this notion of approximate conformance on two NNs. We reduce this problem to that of reachability analysis on a combined NN, thereby, enabling the use of existing NN verification tools for conformance checking. Our experimental results on an autonomous rocket landing system demonstrate the feasibility of checking approximate conformance on different NNs trained for the same dynamics, as well as the practical semantic closeness exhibited by the corresponding closed-loop systems.

We consider the problem of verifying the safety of the trajectories of a camera-based autonomous vehicle in a given 3-D-scene. We give a procedure to verify that all trajectories starting from a given initial region reach a specified target region safely without colliding with obstacles on the way. We also give a prioritization-based falsification procedure that collects unsafe trajectories. Both our procedures are based on the key notion of image-invariant regions, which are regions within which the captured images are identical. We evaluate our methods on a model of an autonomous road-following drone in a variety of 3-D-scenes; our experimental results demonstrate the feasibility and benefits of our approach for both safety analysis and falsification.