LAUSR

As the capabilities of robots and their control systems improve, we see an increasing number of use cases where the simultaneous operation of robots within a space is advantageous. Although trajectories for individual robots can be computed quickly using the existing methods, when robots operate simultaneously and in close proximity, the requirement for collision avoidance introduces a coupling between robot trajectories and makes the trajectory generation problem difficult to solve quickly. In this paper, we propose a parallelizable formulation of such problems and a method for solving them quickly on modern graphics processing units, using momentum-based gradient descent. We demonstrate the proposed framework in simulation using two case studies: a swarm of 200 quadcopters traversing a maze and a fleet of 100 bicycle robots changing their formation. In both the cases, our method requires just seconds to generate feasible, collision-free trajectories for the entire swarm.