Abdelrahman Sayed Sayed

Higher autonomy is an increasingly common goal in the design of transportation systems for the cities of the future. Recently, part of this autonomy in both rail and maritime transport has come from the field of artificial intelligence and machine learning, particularly for perception tasks (detection and recognition of rail signals, other vessels, or other elements in the vehicle environment) using neural networks. Although AI-based approaches have gained significant popularity in many application fields due to their good performance, their unpredictability and lack of formal guarantees regarding their desired behavior present a major issue for the deployment of such safety-critical systems in urban areas. The goal of my PhD thesis is to design new formal methods to analyze and ensure the safety of such AI-based perception modules in autonomous vehicles. More specifically, my PhD topic aims to formally evaluate the safety of a recently introduced class of continuous AI models which is neural ODE.

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability analysis tools adapted to them. We propose a novel interval-based reachability method that leverages continuous-time mixed monotonicity techniques for dynamical systems to compute an over-approximation for the neural ODE reachable sets. By exploiting the geometric structure of full initial sets and their boundaries via the homeomorphism property, our approach ensures efficient bound propagation. By embedding neural ODE dynamics into a mixed monotone system, our interval-based reachability approach, implemented in TIRA with single-step, incremental, and boundary-based approaches, provides sound and computationally efficient over-approximations compared with CORA’s zonotopes and NNV2.0 star set representations, while trading tightness for efficiency. This trade-off makes our method particularly suited for high-dimensional, real-time, and safety-critical applications. Applying mixed monotonicity to neural ODE reachability analysis paves the way for lightweight formal analysis by leveraging the symmetric structure of monotone embeddings and the geometric simplicity of interval boxes, opening new avenues for scalable verification aligned with the symmetry and geometry of neural representations. This novel approach is illustrated on two numerical examples of a spiral system and a fixed-point attractor system modeled as a neural ODE.

A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuousdepth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be seen as the Euler discretization of the neural ODE. These two models are therefore strongly related in a way that the behaviors of either model are considered to be an approximation of the behaviors of the other. In this work, we establish a more formal relationship between these two models by bounding the approximation error between two such related models. The obtained error bound then allows us to use one of the models as a verification proxy for the other, without running the verification tools twice: if the reachable output set expanded by the error bound satisfies a safety property on one of the models, this safety property is then guaranteed to be also satisfied on the other model. This feature is fully reversible, and the initial safety verification can be run indifferently on either of the two models. This novel approach is illustrated on a numerical example of a fixed-point attractor system modeled as a neural ODE.

In this paper we focus on the proof of concept prototype of fully autonomous centralized Multi-Robot System (MRS) consisting of a Hexapod walking robot and a six wheeled mobile robot. Recently, there has been an increasing demand for such systems as they can be involved in several tasks such as collaborative search and rescue, surveillance, monitoring, and disinfecting Field hospitals. To name a few, COVID-19 pandemic showed the weak points in the medical sector around the world, including those in the most advanced nations that had to go through hard decisions due to the lack of medical supplies and personal protective equipment. The developed system was rapidly adjusted due to COVID-19 pandemic to perform additional tasks like disinfection and remote body temperature detection. The developed system abide by ISO 13482 safety requirements for personal care robots, meaning it will be used and deployed in Field hospitals. We implemented the proposed approach in a game setting of a field hospital where the Hexapod is used to scan and draw a map of the Field hospital environment and to draw a path then the six wheeled mobile robot acts as a medical cargo delivery that enters based on the predefined map and path.