  This paper presents a unified optimization-based path planning approach to
efficiently compute locally optimal solutions to advanced path planning
problems. The approach is motivated by first showing that a lattice-based path
planner can be cast and analyzed as a bilevel optimization problem. This
information is then used to tightly integrate a lattice-based path planner and
numerical optimal control in a novel way. The lattice-based path planner is
applied to the problem in a first step using a discretized search space, where
system dynamics and objective function are chosen to coincide with those used
in a second numerical optimal control step. As a consequence, the lattice
planner provides the numerical optimal control step with a resolution optimal
solution to the problem, which is highly suitable as a warm-start to the second
step. This novel tight combination of a sampling-based path planner and
numerical optimal control makes, in a structured way, benefit of the former
method's ability to solve combinatorial parts of the problem and the latter
method's ability to obtain locally optimal solutions not constrained to a
discretized search space. Compared to previously presented combinations of
sampling-based path planners and optimization, the proposed approach is shown
in several path planning experiments to provide significant improvements in
terms of computation time, numerical reliability, and objective function value.
