Planning for hybrid systems is important for dealing with real-world applications, and PDDL+ supports this representation of domains with mixed discrete and continuous dynamics. In this paper we present a new approach for planning for hybrid systems, based on encoding the planning problem as a Satisfiability Modulo Theories (SMT) formula. This is the first SMT encoding that can handle the whole set of PDDL+ features (including processes and events), and is implemented in the planner SMTPlan. SMTPlan not only covers the full semantics of PDDL+, but can also deal with non-linear polynomial continuous change without discretization. This allows it to generate plans with non-linear dynamics that are correct-by-construction. The encoding is based on the notion of happenings, and can be applied on domains with nonlinear continuous change. We describe the encoding in detail and provide in-depth examples. We apply this encoding in an iterative deepening planning algorithm. Experimental results show that the approach dramatically outperforms existing work in finding plans for PDDL+ problems. We also present experiments which explore the performance of the proposed approach on temporal planning problems, showing that the scalability of the approach is limited by the size of the discrete search space. We further extend the encoding to include planning with control parameters. The extended encoding allows the definition of actions to include infinite domain parameters, called control parameters. We present experiments on a set of problems with control parameters to demonstrate the positive effect they provide to the approach of planning via SMT.

Temporal logics have been used in autonomous planning to represent and reason about temporal planning problems. However, such techniques have typically been restricted to either (1) representing actions, events, and goals with temporal properties or (2) planning for temporally-extended goals under restrictive assumptions. We introduce Mixed Propositional Metric Temporal Logic (MPMTL) where formulae are built over mixed binary and continuous real variables. We introduce a planner, MTP, that solves MPMTL problems and includes a SAT-solver, model checker for a polynomial fragment of MPMTL, and a forward search algorithm. We extend PDDL 2.1 with MPMTL syntax to create MPDDL and an associated parser. The empirical study shows that MTP outperforms the state-of-the-art PDDL+ planner SMTPlan+ on several domains it performed best on and MTP performs and scales on problem size well for challenging domains with rich temporal properties we create.