Numerical Integration and Dynamic Discretization in Heuristic Search
  Planning over Hybrid Domains
  In this paper we look into the problem of planning over hybrid domains, where
change can be both discrete and instantaneous, or continuous over time. In
addition, it is required that each state on the trajectory induced by the
execution of plans complies with a given set of global constraints. We approach
the computation of plans for such domains as the problem of searching over a
deterministic state model. In this model, some of the successor states are
obtained by solving numerically the so-called initial value problem over a set
of ordinary differential equations (ODE) given by the current plan prefix.
These equations hold over time intervals whose duration is determined
dynamically, according to whether zero crossing events take place for a set of
invariant conditions. The resulting planner, FS+, incorporates these features
together with effective heuristic guidance. FS+ does not impose any of the
syntactic restrictions on process effects often found on the existing
literature on Hybrid Planning. A key concept of our approach is that a clear
separation is struck between planning and simulation time steps. The former is
the time allowed to observe the evolution of a given dynamical system before
committing to a future course of action, whilst the later is part of the model
of the environment. FS+ is shown to be a robust planner over a diverse set of
hybrid domains, taken from the existing literature on hybrid planning and
systems.
