Nash Bargaining Strategy in Autonomous Decision Making for Multi-Ship Collision Avoidance Based on Route Exchange

A novel scheme is proposed for the distributed multi-ship collision avoidance (CA) problem with consideration of the autonomous, dynamic nature of the real circumstance. All the ships in the envisioned scenarios can share their decisions or intentions through route exchange, allowing them to make subsequent decisions based on the route planning in each iteration. By leveraging route exchange, the multi-ship CA problem involves iterations for negotiation, and is regarded as a staged cooperative game under conditions of complete information. The concept of closest spatio-temporal distance (CSTD) is introduced to more accurately assess collision risk between ships. A coordinated CA mechanism is established when a collision risk is identified, which further incorporates considerations including the stand-on/give-way relationships, negotiation rounds, route re-planning calculation, as well as the cost factor for route evaluation. The Nash bargaining solution (NBS) is elaborated to achieve Pareto-optimal CA routes in the scenarios. In the proposed model, while the individual interest of each ship are maximized, the economic fairness and global optimization of the overall system are also maintained. Simulation results indicate that the NBS shows good flexibility and adaptability, and that when all ships comply with route re-planning solution, the proposed scheme can bring out normal solutions within a limited number of re-planning iterations.