A Solution to the Synchronization Problem for a Shoal of Fish Robots Via Max-Plus Algebra

Abstract Within the underwater exploration and patrolling domain, a novel approach based on the max-plus algebra framework is presented to model and control the coordinated and synchronized behavior of a shoal of three fish robots. These robots aim to cyclically survey a submerged area with many points of interest (POI) through predefined paths. The work leads to obtaining a max-plus linear system, which represents the behavior of such robots, followed by the formalization of a “System Synchronization Problem (SSP)” for such a system, to check the mission's feasibility in the desired time. The theoretical basis for the SSP is revised, and the results confirm that robots can adhere to the defined model through a control law derived as a solution of the SSP. Consequently, it becomes achievable to synchronize the system with the model. Calculations to find the solution of the SSP are presented and performed using the ScicosLab software. Finally, a numerical example is provided to illustrate the resolution process and the solution of the SSP.