Hybrid Temporal Situation Calculus

The ability to model continuous change in Reiter's temporal situation calculus action theories has attracted a lot of interest. In this paper, we propose a new development of his approach, which is directly inspired by hybrid systems in control theory. Specifically, while keeping the foundations of Reiter's axiomatization, we propose an elegant extension of his approach by adding a time argument to all fluents that represent continuous change. Thereby, we insure that change can happen not only because of actions, but also due to the passage of time. We present a systematic methodology to derive, from simple premises, a new group of axioms which specify how continuous fluents change over time within a situation. We study regression for our new temporal basic action theories and demonstrate what reasoning problems can be solved. Finally, we formally show that our temporal basic action theories indeed capture hybrid automata

Hybrid Temporal Situation Calculus

We present a hybrid discrete-continuous extension of Reiter’s temporal situation calculus, directly inspired by hybrid systems in control theory. While keeping to the foundations of Reiter’s approach, we extend it by adding a time argument to all fluents that represent continuous change. Thereby, we ensure that change can happen not only because of actions, but also due to the passage of time. We present a systematic methodology to derive, from simple premises, a new group of axioms which specify how continuous fluents change over time within a situation. We study regression for our new hybrid action theories and demonstrate what reasoning problems can be solved. Finally, we show that our hybrid theories indeed capture hybrid automata

Hybrid temporal situation calculus

We extend Reiter's temporal situation calculus by introducing continuous change due to passage of time in addition to discrete change due to actions. We define regression for hybrid action theories and show that hybrid action theories can capture hybrid automata

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.</p