In this paper, a non-iterative spatio-temporal multi-task assignment approach is used for playing piano music by a team of robots. This paper considers the piano playing problem, in which an algorithm needs to compute the trajectories for a dynamically sized team of robots who will play the 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 for playing the musical tune. The algorithm computes the required number of robots 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 the 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 has been illustrated with the help of the high fidelity simulations in 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. The simulation of the robots playing music, using computed assignments, is demonstrated in the attached video. video link: \url{https://youtu.be/XToicNm-CO8}

翻译：本文采用非迭代的时空多任务分配方法，实现了机器人团队演奏钢琴音乐的任务。本文考虑了钢琴演奏问题，即算法需要为一组规模动态变化的机器人计算轨迹，使其在各自指定的时间点通过音符对应的特定位置来演奏音乐。基于时空多任务分配问题的动态资源分配（DREAM）已通过两步实现，用于分配机器人演奏音乐曲调：第一步，算法计算演奏音乐所需的机器人数量；第二步，为更新后的机器人团队计算最优分配方案，以最小化机器人团队的总移动距离。即便个体轨迹均可行，若机器人在执行过程中发生碰撞，多机器人任务仍可能失败。由于冲突消解会占用部分时间，机器人可能无法按时到达目标位置。本文分析并证明，若机器人在凸区域内运行，DREAM方法提供的解可实现无碰撞轨迹。通过在高保真仿真环境Gazebo（基于ROS2运行）中验证DREAM方法的工作流程，结果清晰表明：DREAM方法至多两步即可计算出所需机器人数量，并为机器人分配多个任务。使用计算所得分配方案的机器人演奏音乐仿真演示见附件视频。视频链接：\url{https://youtu.be/XToicNm-CO8}