Dynamic formation optimisation for energy saving of a fleet of unmanned surface vehicles based on robust optimisation over time strategy

This paper presents a dynamic formation optimisation strategy that focuses on constructing an energy-saving formation for a fleet of unmanned surface vehicles (USVs) by considering two optimisation objectives: minimum energy consumption and minimum switching cost. The dynamic formation optimisation strategy based on robust optimisation over time (ROOT) is used to determine the energy-saving formation with the optimal position layout. The formation switching cost is first proposed to define the energy consumption cost of switching from the original position to the new position. Dynamic environments are established using the modified moving peak benchmark (mMPB) to simulate the movement of waves. A new swarm intelligence algorithm for solving ROOT is designed using an adaptive gradient training predictor and a solver embedded the dingo optimisation algorithm. The ROOT results are compared with the tank test results, which confirms that the dynamic formation optimisation strategy has a high credibility. The energy-saving formation optimised by dynamic formation optimisation based on ROOT not only ensures the minimum energy consumption, but also ensures the minimum switching cost. The survival time of the spacing configuration is prolonged, indicating that the acquired energy-saving formation can be consistently utilized over an extended period without necessitating positional adjustments. This mitigates the escalating energy consumption resulting from frequent formation switching when a fleet encounters dynamic marine conditions.