Heuristic Planning for Continuous Systems in Hybrid Temporal Situation Calculus

Given a description of domain and its dynamics, temporal numeric planning attempts to find a sequence of actions that satisfies a given set of constraints for a dynamical system. Current planners operate on grounded transition systems and discretized representations of the domain which lead to poor scalability. Furthermore, given the problem’s difficulty, most modern planners restrict their capabilities to a subset of hybrid domains, e.g. support for only polynomial evolution of numeric state variables and linear action conditions. To address these concerns, we present a lifted planner, NEAT (Non-linEAr Temporal) Planner, that utilizes a logical description of the domain described in Hybrid Temporal Situation Calculus. Furthermore, we develop AMPLEX, an interface to AMPL and several non-linear programming solvers, which allows us handle several non-linear functions. We also present a novel non-linear programming based heuristic to improve scalability. Lastly, we perform a detailed comparison between current state-of-the-art solvers and our planner.