Graph-based Motion Planning with Primitives in a Continuous State Space Search

Motion primitives exploit symmetries of nonlinear systems to reduce the complexity of the motion planning problem. A graph search algorithm for motion primitives based on Hybrid
$\mathrm{A}^{*}$
was developed in a previous work; however, each continuous state is associated with discrete grid-cells and the planning is solved by a numerically complex optimization problem after the search is done. We extend this approach by considering directly the continuous states, which is the first pillar on a continuous state space search. The second pillar is adjusting some primitives' durations by an online optimization problem of reduced complexity. Then, our algorithm is able to solve motion planning tasks for leading the vehicle to an exact desired goal state, while respecting computation time constraints. Two numerical examples are given for a single-track vehicle model.