  As robotic systems continue to address emerging issues in areas such as
logistics, mobility, manufacturing, and disaster response, it is increasingly
important to rapidly generate safe and energy-efficient trajectories. In this
article, we present a new approach to plan energy-optimal trajectories through
cluttered environments containing polygonal obstacles. In particular, we
develop a method to quickly generate optimal trajectories for a
double-integrator system, and we show that optimal path planning reduces to an
integer program. To find an efficient solution, we present a distance-informed
prefix search to efficiently generate optimal trajectories for a large class of
environments. We demonstrate that our approach, while matching the performance
of RRT* and Probabilistic Road Maps in terms of path length, outperforms both
in terms of energy cost and computational time by up to an order of magnitude.
We also demonstrate that our approach yields implementable trajectories in an
experiment with a Crazyflie quadrotor.
