  In this work, we propose a search-based planning method to compute
dynamically feasible trajectories for a quadrotor flying in an
obstacle-cluttered environment. Our approach searches for smooth, minimum-time
trajectories by exploring the map using a set of short-duration motion
primitives. The primitives are generated by solving an optimal control problem
and induce a finite lattice discretization on the state space which can be
explored using a graph-search algorithm. The proposed approach is able to
generate resolution-complete (i.e., optimal in the discretized space), safe,
dynamically feasibility trajectories efficiently by exploiting the explicit
solution of a Linear Quadratic Minimum Time problem. It does not assume a
hovering initial condition and, hence, is suitable for fast online re-planning
while the robot is moving. Quadrotor navigation with online re-planning is
demonstrated using the proposed approach in simulation and physical experiments
and comparisons with trajectory generation based on state-of-art quadratic
programming are presented.
