A Non-iterative Spatio-temporal Multi-task Assignments based Collision-free Trajectories for Music Playing Robots

This paper addresses the music-playing robot problem, which is a benchmark problem for the spatio-temporal multi-task assignment problem. In the music-playing robot problem, an algorithm needs to compute the trajectories for a dynamically-sized team of robots who will play musical notes by traveling through the specific locations associated with musical notes at their respective specific times. A two-step dynamic resource allocation based on a spatio-temporal multi-task assignment problem (DREAM) has been implemented to assign robots to play a musical tune. The algorithm computes the number of robots required to play the music in the first step. In the second step, optimal assignments are computed for the updated team of robots, which minimizes the total distance traveled by the team. Even for individual feasible trajectories, the multi-robot execution may fail if robots encounter a collision. As some time will be utilized for this conflict resolution, robots may not be able to reach the desired location on time. This paper analyses and proves that if robots are operating in a convex region, the solution of the DREAM approach provides collision-free trajectories. The working of the DREAM approach is illustrated using high-fidelity simulations in a Gazebo operated using ROS2. The result clearly shows that the DREAM approach computes the required number of robots and assigns multiple tasks to robots in at most two steps. A simulation of the robots playing the ‘happy birthday’ is available at https://youtu.be/XToicNm-CO8.