A Unified View of Piecewise Linear Neural Network Verification

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and the theoretical hardness of proving their properties, researchers have been successful in verifying some classes of models by exploiting their piecewise linear structure and taking insights from formal methods such as Satisifiability Modulo Theory. These methods are however still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we make two key contributions. First, we present a unified framework that encompasses previous methods. This analysis results in the identification of new methods that combine the strengths of multiple existing approaches, accomplishing a speedup of two orders of magnitude compared to the previous state of the art. Second, we propose a new data set of benchmarks which includes a collection of previously released testcases. We use the benchmark to provide the first experimental comparison of existing algorithms and identify the factors impacting the hardness of verification problems.Comment: Updated version of "Piecewise Linear Neural Network verification: A comparative study

Réseaux de Neurones pour la Detection de Collisions et Localisation de Contacts des Polyèdres Convexes

Dans ce papier nous avons procéder au développement de l’architecture du Réseau de Neurones de Détection de collisions (DCNN). Ce réseau, dont on a particulièrement revue la conception, nous a permis de résoudre avec une nouvelle approche le problème de détection de collision entre deux polyèdres convexes en un temps fixe (o(1)time). Pour ce faire, nous avons employer deux types de neurones, linéaire et logique à seuil. Par ailleurs, les poids de connexion relatifs aux neurones ainsi que le seuil seront fournis sous forme de réels par le biais de notre système. Cela facilite la mise en oeuvre matériellement réelle des réseaux de neurones proposés.L'identification de ces collisions a été faite dans un premier temps entre un point et un polyèdre. Dans une seconde partie l’étude se fera entre deux polyèdres convexes. Notre but est de déterminer grâce aux fonctions MAXNET et MINNET, en un temps fixe, un point mini-maximum qui, lui, nous permet de statuer sur la présence d’une éventuelle collision

A study of mobile robot motion planning

This thesis studies motion planning for mobile robots in various environments. The basic tools for the research are the configuration space and the visibility graph. A new approach is developed which generates a smoothed minimum time path. The difference between this and the Minimum Time Path at Visibility Node (MTPVN) is that there is more clearance between the robot and the obstacles, and so it is safer. The accessibility graph plays an important role in motion planning for a massless mobile robot in dynamic environments. It can generate a minimum time motion in 0(n2»log(n)) computation time, where n is the number of vertices of all the polygonal obstacles. If the robot is not considered to be massless (that is, it requires time to accelerate), the space time approach becomes a 3D problem which requires exponential time and memory. A new approach is presented here based on the improved accessibility polygon and improved accessibility graph, which generates a minimum time motion for a mobile robot with mass in O((n+k)2»log(n+k)) time, where n is the number of vertices of the obstacles and k is the number of obstacles. Since k is much less than n, so the computation time for this approach is almost the same as the accessibility graph approach. The accessibility graph approach is extended to solve motion planning for robots in three dimensional environments. The three dimensional accessibility graph is constructed based on the concept of the accessibility polyhedron. Based on the properties of minimum time motion, an approach is proposed to search the three dimensional accessibility graph to generate the minimum time motion. Motion planning in binary image representation environment is also studied. Fuzzy logic based digital image processing has been studied. The concept of Fuzzy Principal Index Of Area Coverage (PIOAC) is proposed to recognise and match objects in consecutive images. Experiments show that PIOAC is useful in recognising objects. The visibility graph of a binary image representation environment is very inefficient, so the approach usually used to plan the motion for such an environment is the quadtree approach. In this research, polygonizing an obstacle is proposed. The approaches developed for various environments can be used to solve the motion planning problem without any modification. A simulation system is designed to simulate the approaches

Identifying Single-Input Linear System Dynamics from Reachable Sets

This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the reachable sets are known from partially transparent manufacturer specifications or observations of the collective behavior of adversarial agents, we aim to utilize such sets to determine the unknown system's dynamics. This paper has two contributions. Firstly, we show that the sequence of the system's reachable sets can be used to uniquely determine the system's dynamics for asymmetric input sets under some generic assumptions, regardless of the system's dimensions. We also prove the same property holds up to a sign change for two-dimensional systems where the input set is symmetric around zero. Secondly, we present an algorithm to determine these dynamics. We apply and verify the developed theory and algorithms on an unknown band-pass filter circuit solely provided the unknown system's reachable sets over a finite observation period.Comment: 8 pages, 1 figure, published at the 62nd Conference on Decision and Control (CDC 2023

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.Siirretty Doriast

Advances in Robot Navigation

Robot navigation includes different interrelated activities such as perception - obtaining and interpreting sensory information; exploration - the strategy that guides the robot to select the next direction to go; mapping - the construction of a spatial representation by using the sensory information perceived; localization - the strategy to estimate the robot position within the spatial map; path planning - the strategy to find a path towards a goal location being optimal or not; and path execution, where motor actions are determined and adapted to environmental changes. This book integrates results from the research work of authors all over the world, addressing the abovementioned activities and analyzing the critical implications of dealing with dynamic environments. Different solutions providing adaptive navigation are taken from nature inspiration, and diverse applications are described in the context of an important field of study: social robotics

A Neural Network Based Strategy for Robot Navigation in Dynamic Environments

This thesis studies the problem of robot navigation in the presence of unexpected environmental changes, which include unknown static obstacles and moving objects with unknown trajectories. Throughout this work, neural networks, as a new technique, are used to develop the functional components, which constitute the proposed navigation strategy. The neural network based navigation strategy we propose follows a two-level hierarchy and operates by integrating three network components (planner, navigator and predictor). At the higher level, the planner generates a nominal path from the initial position to the goal among the fixed known obstacles. At the lower level, the navigator incorporates the predictor to refine the coarse path by taking into account unexpected environment changes to achieve on line real-time guidance. During this research, three neural network components were developed. The path planner was developed first by using a three-layer feedforward network to optimize the cost (collision penalty) function of a path. The first version of the navigator - Navigator-1 - was then implemented using a multilayer feedforward network in which steering commands for static obstacle avoidance were generated by directly converting sensor reading through the network. To enable the navigator to handle moving objects with unknown trajectories, on-line motion prediction was introduced. The predictor was developed using an Elman recurrent net. Following that, an enhanced version of the Navigator-1 - Navigator-2 - was developed using a structured network in which three sub-nets were used - two of the sub-nets were used to realise dynamic obstacle avoidance and static obstacle avoidance respectively, and the third sub-net was used to make final steering decision by reconciling the results from those two sub-nets. Finally, the overall navigation strategy was implemented in a simulation system. Simulations showed encouraging results. It demonstrates that the neural network based strategy is capable of achieving adaptive navigation in the presence of unexpected environmental changes