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

Research in interactive scene analysis

Cooperative (man-machine) scene analysis techniques were developed whereby humans can provide a computer with guidance when completely automated processing is infeasible. An interactive approach promises significant near-term payoffs in analyzing various types of high volume satellite imagery, as well as vehicle-based imagery used in robot planetary exploration. This report summarizes the work accomplished over the duration of the project and describes in detail three major accomplishments: (1) the interactive design of texture classifiers; (2) a new approach for integrating the segmentation and interpretation phases of scene analysis; and (3) the application of interactive scene analysis techniques to cartography

Technical Report: Distribution Temporal Logic: Combining Correctness with Quality of Estimation

We present a new temporal logic called Distribution Temporal Logic (DTL) defined over predicates of belief states and hidden states of partially observable systems. DTL can express properties involving uncertainty and likelihood that cannot be described by existing logics. A co-safe formulation of DTL is defined and algorithmic procedures are given for monitoring executions of a partially observable Markov decision process with respect to such formulae. A simulation case study of a rescue robotics application outlines our approach.Comment: More expanded version of "Distribution Temporal Logic: Combining Correctness with Quality of Estimation" to appear in IEEE CDC 201

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio

A mixed-signal fuzzy controller and its application to soft start of DC motors

Presents a mixed-signal fuzzy controller chip and its application to control of DC motors. The controller is based on a multiplexed architecture presented by the authors (1998), where building blocks are also described. We focus here on showing experimental results from an example implementation of this architecture as well as on illustrating its performance in an application that has been proposed and developed. The presented chip implements 64 rules, much more than the reported pure analog monolithic fuzzy controllers, while preserving most of their advantages. Specifically, the measured input-output delay is around 500 ns for a power consumption of 16 mW and the chip area (without pads) is 2.65 mm/sup 2/. In the presented application, sensed motor speed and current are the controller input, while it determines the proper duty cycle to a PWM control circuit for the DC-DC converter that powers the motor drive. Experimental results of this application are also presented.Comisión Interministerial de Ciencia y Tecnología TIC99-082

Proportional sampling strategy: A compendium and some insights

There have been numerous studies on the effectiveness of partition and random testing. In particular, the proportional sampling (PS) strategy has been proved, under certain conditions, to be the only form of partition testing that outperforms random testing regardless of where the failure-causing inputs are. This paper provides an integrated synthesis and overview of our recent studies on the PS strategy and its related work. Through this synthesis, we offer a perspective that properly interprets the results obtained so far, and present some of the interesting issues involved and new insights obtained during the course of this research. © 2001 Elsevier Science Inc. All rights reserved.postprin