Multi-agent systems can be extremely efficient when working concurrently and collaboratively, e.g., for transportation, maintenance, search and rescue. Coordination of such teams often involves two aspects: (i) selecting appropriate sub-teams for different tasks; (ii) designing collaborative control strategies to execute these tasks. The former aspect can be combinatorial w.r.t. the team size, while the latter requires optimization over joint state-spaces under geometric and dynamic constraints. Existing work often tackles one aspect by assuming the other is given, while ignoring their close dependency. This work formulates such problems as combinatorial-hybrid optimizations (CHO), where both the discrete modes of collaboration and the continuous control parameters are optimized simultaneously and iteratively. The proposed framework consists of two interleaved layers: the dynamic formation of task coalitions and the hybrid optimization of collaborative behaviors. Overall feasibility and costs of different coalitions performing various tasks are approximated at different granularities to improve the computational efficiency. At last, a Nash-stable strategy for both task assignment and execution is derived with provable guarantee on the feasibility and quality. Two non-trivial applications of collaborative transportation and dynamic capture are studied against several baselines.

翻译：多智能体系统在并行与协作执行任务（如运输、维护、搜救）时展现出极高效率。此类团队的协调通常涉及两个层面：（i）为不同任务选择合适子团队；（ii）设计协作控制策略以执行这些任务。前者面临团队规模的组合性问题，后者则需在几何与动态约束下对联合状态空间进行优化。现有研究通常假设另一方已知来处理单一层面问题，而忽略两者间的紧密关联。本文将此类问题建模为组合-混合优化（CHO），同步迭代优化离散协作模式与连续控制参数。所提框架包含两个交织层：任务联盟的动态形成与协作行为的混合优化。通过多粒度近似评估不同联盟执行各类任务的可行性及代价，以提升计算效率。最终推导出具有可行性及质量可证明保障的任务分配与执行纳什稳定策略。在协作运输与动态捕获两个非平凡应用中，与多个基线方法进行了对比研究。