Design and Validation of Cyber-Physical Systems Through Co-Simulation: The Voronoi Tessellation Use Case

This paper reports on the use of co-simulation techniques to build prototypes of co-operative autonomous robotic cyber-physical systems. Designing such systems involves a mission-specific planner algorithm, a control algorithm to drive an agent performing its task; and the plant model to simulate the agent dynamics. An application aimed at positioning a swarm of unmanned aerial vehicles (drones) in a bounded area, exploiting a Voronoi tessellation algorithm developed in this work, is taken as a case study. The paper shows how co-simulation allows testing the complex system at the design phase using models created with different languages and tools. The paper then reports on how the adopted co-simulation platform enables control parameters calibration, by exploiting design space exploration technology. The INTO-CPS co-simulation platform, compliant with the Functional Mock-up Interface standard to exchange dynamic simulation models using various languages, was used in this work. The different software modules were written in Modelica, C, and Python. In particular, the latter was used to implement an original variant of the Voronoi algorithm to tesselate a convex polygonal region, by means of dummy points added at appropriate positions outside the bounding polygon. A key contribution of this case study is that it demonstrates how an accurate simulation of a cooperative drone swarm requires modeling the physical plant together with the high-level coordination algorithm. The coupling of co-simulation and design space exploration has been demonstrated to support control parameter calibration to optimize energy consumption and convergence time to the target positions of the drone swarm. From a practical point of view, this makes it possible to test the ability of the swarm to self-deploy in space in order to achieve optimal detection coverage and allow unmanned aerial vehicles in a swarm to coordinate with each other.