A Graph-Based Approach to Generate Energy-Optimal Robot Trajectories in Polynomial Environments

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.