Open directions for extending and validating guideline-based posetal motion planning
Extend guideline-based posetal motion planning by developing a receding-horizon scheme with conservative belief updates from observations, constructing real-time-capable solvers that exploit COLREGS game structure, establishing conditions under which COLREGS games are potential games, characterizing the dependence of audit outcomes on action-space discretization, designing a mechanism for social-metric-based equilibrium selection in the presence of lawful defectors, and evaluating the framework in other partially ordered regulatory domains such as autonomous driving and airborne collision avoidance.
References
Several directions remain open. First, we would like to extend our framework into a receding-horizon scheme, in which agents repeatedly re-solve the game as the encounter evolves and refine their beliefs about the preferences of the others based on observed behavior. The main difficulty is to update the beliefs from observations while keeping them conservative, since the technical result only holds for conservative beliefs. Second, deploying such a scheme on real vessels requires real-time capable solvers. While exhaustive enumeration of the joint action space provides exact references, its cost grows exponentially with the number of agents. Specialized planners for COLREGS encounters that exploit the structure of the game, such as the pairwise symmetric collision metrics, could substantially reduce this cost. Establishing conditions under which the COLREGS game is a potential game would, in addition, guarantee the convergence of distributed IBR, which we have so far observed empirically. Third, the auditability results are relative to the finite action lattice, so that a violation classified as unsatisfiable may become satisfiable under a richer action space. Characterizing how the audit outcome depens on the discretization would strengthen the legal interpretation of such certificates. Fourth, a defector whose action is still a legal best response can steer the equilibrium selection without violating the law, which calls for a mechanism-design perspective on the social metric. Finally, applying our framework to other domains in which regulators specify only partial priorities, like autonomous driving or airborne collision avoidance, would further test its generality. In both domains, interaction rules are also stated pairwise, so the lifting of pairwise rules to many agents would apply directly.