  Planning in hybrid systems with both discrete and continuous control
variables is important for dealing with real-world applications such as
extra-planetary exploration and multi-vehicle transportation systems.
Meanwhile, generating high-quality solutions given certain hybrid planning
specifications is crucial to building high-performance hybrid systems. However,
since hybrid planning is challenging in general, most methods use greedy search
that is guided by various heuristics, which is neither complete nor optimal and
often falls into blind search towards an infinite-action plan. In this paper,
we present a hybrid automaton planning formalism and propose an optimal
approach that encodes this planning problem as a Mixed Integer Linear Program
(MILP) by fixing the action number of automaton runs. We also show an extension
of our approach for reasoning over temporally concurrent goals. By leveraging
an efficient MILP optimizer, our method is able to generate provably optimal
solutions for complex mixed discrete-continuous planning problems within a
reasonable time. We use several case studies to demonstrate the extraordinary
performance of our hybrid planning method and show that it outperforms a
state-of-the-art hybrid planner, Scotty, in both efficiency and solution
qualities.
