We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on the task performance, and incorporate the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer programming approach, which gives optimal solutions for small instances of the problem but is computationally expensive. We also develop a greedy heuristic algorithm as a baseline. Our modeling and solution approaches result in task plans that leverage task precedence relationships and robot coordination and cooperation to achieve high mission performance, even in large missions with many agents.

翻译：我们提出了一种新的多机器人任务规划与分配问题形式化方法，该方法融合了：(a) 任务间的优先关系；(b) 允许通过多机器人协作提升效率的协调机制；以及(c) 针对单个机器人无法独立完成的任务，通过构建机器人联盟实现的合作机制。在该形式化中，任务及其相互关系由任务图进行描述。我们在任务图的节点与边上定义了一组奖励函数，这些函数量化了机器人联盟规模对任务执行效果的影响，同时融入了前置任务执行效果对依赖任务的传导效应。该问题的最优求解具有NP难度特性。然而，基于任务图形式化方法，我们能够利用最小成本网络流技术高效获取近似解。此外，我们探索了混合整数规划方法——该方法虽然计算代价较高，但可为小规模问题实例提供最优解，还开发了贪心启发式算法作为基准方案。通过建模与求解手段，即使面对包含大量智能体的大型任务场景，系统仍能生成充分利用任务优先关系、机器人协调与合作机制的高性能任务规划方案。