Formal Verification of Neural Network Controlled Autonomous Systems

In this paper, we consider the problem of formally verifying the safety of an autonomous robot equipped with a Neural Network (NN) controller that processes LiDAR images to produce control actions. Given a workspace that is characterized by a set of polytopic obstacles, our objective is to compute the set of safe initial conditions such that a robot trajectory starting from these initial conditions is guaranteed to avoid the obstacles. Our approach is to construct a finite state abstraction of the system and use standard reachability analysis over the finite state abstraction to compute the set of the safe initial states. The first technical problem in computing the finite state abstraction is to mathematically model the imaging function that maps the robot position to the LiDAR image. To that end, we introduce the notion of imaging-adapted sets as partitions of the workspace in which the imaging function is guaranteed to be affine. We develop a polynomial-time algorithm to partition the workspace into imaging-adapted sets along with computing the corresponding affine imaging functions. Given this workspace partitioning, a discrete-time linear dynamics of the robot, and a pre-trained NN controller with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge is to analyze the behavior of the neural network. To that end, we utilize a Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible segments of different ReLUs. SMC solvers then use a Boolean satisfiability solver and a convex programming solver and decompose the problem into smaller subproblems. To accelerate this process, we develop a pre-processing algorithm that could rapidly prune the space feasible ReLU segments. Finally, we demonstrate the efficiency of the proposed algorithms using numerical simulations with increasing complexity of the neural network controller

DeepPicar: A Low-cost Deep Neural Network-based Autonomous Car

We present DeepPicar, a low-cost deep neural network based autonomous car platform. DeepPicar is a small scale replication of a real self-driving car called DAVE-2 by NVIDIA. DAVE-2 uses a deep convolutional neural network (CNN), which takes images from a front-facing camera as input and produces car steering angles as output. DeepPicar uses the same network architecture---9 layers, 27 million connections and 250K parameters---and can drive itself in real-time using a web camera and a Raspberry Pi 3 quad-core platform. Using DeepPicar, we analyze the Pi 3's computing capabilities to support end-to-end deep learning based real-time control of autonomous vehicles. We also systematically compare other contemporary embedded computing platforms using the DeepPicar's CNN-based real-time control workload. We find that all tested platforms, including the Pi 3, are capable of supporting the CNN-based real-time control, from 20 Hz up to 100 Hz, depending on hardware platform. However, we find that shared resource contention remains an important issue that must be considered in applying CNN models on shared memory based embedded computing platforms; we observe up to 11.6X execution time increase in the CNN based control loop due to shared resource contention. To protect the CNN workload, we also evaluate state-of-the-art cache partitioning and memory bandwidth throttling techniques on the Pi 3. We find that cache partitioning is ineffective, while memory bandwidth throttling is an effective solution.Comment: To be published as a conference paper at RTCSA 201