Spatial Functions for Modeling and Analysis of Safety-Critical Systems of Systems

Our work is concerned with the modeling and analysis of safety-critical systems of systems (SoS). They emerge from the arrangement of independent and useful physical systems integrated into a larger system that delivers unique capabilities such as multi-Unmanned Aircraft Systems (UAS) or robotic swarms. Successful collaboration and interaction between component systems in (increasingly) reduced spaces is contingent to precise and accurate perception, interpretation and management of various spatial representations of self and teaming systems. This is needed for effective decision making (the right action at the right time, and in the right place) for keeping safety-critical SoS safe. Thus, we develop and propose space-based interaction functions to model and evaluate the spatial properties and interactions of systems (as agents) within a safety-critical SoS. These mathematical spatial functions define, express and provide means to evaluate physical and communication interactions between pairs of agents and between an agent and all the other agents in the SoS. They are shown to be valuable mechanisms for rigorous, systematic, domain independent analysis of safety-critical SoS and can be implemented by systems of any size or shape. Architecture for the implementation of the functions is described for support of models and simulations of safety-critical SoS across a wide variety of applications including multi-UAS package delivery systems.