Planning with global state constraints is an extension of classical planning such that some properties of each state are derived via a set of rules common to all states. This approach is important for the application of planning techniques in manipulating cyber-physical systems, and has been shown to be effective in practice. Urban Traffic Control (UTC) deals with the control and management of traffic in urban regions, and includes the optimisation of traffic signals configuration to minimise traffic congestion and travel delays. In this paper, we briefly introduce how to cast the UTC problem into the formalism of planning with global state constraints, and we perform a preliminary experimental evaluation considering significant scenarios taken from the literature, and a new one based on real-world data. The results show that the approach is feasible, and the quality of generated solutions has been confirmed in simulation using existing symbolic models.

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context.