Multi-robot planning and coordination in uncertain environments is a fundamental computational challenge, since the belief space increases exponentially with the number of robots. In this paper, we address the problem of planning in uncertain environments with a heterogeneous robot team comprised of fast scout vehicles for information gathering and more risk-averse carrier robots from which the scout vehicles are deployed. To overcome the computational challenges associated with multi-robot motion planning in the presence of environmental uncertainty, we represent the environment and operational scenario using a topological graph, where the edge weight distributions vary with the state of the robot team on the graph. While this belief space representation still scales exponentially with the number of robots, we formulate a computationally efficient mixed-integer program which is capable of generating optimal multi-robot plans in seconds. We evaluate our approach in a representative scenario where the robot team must move through an environment while minimizing detection by observers in positions that are uncertain to the robot team. We demonstrate that our approach is sufficiently computationally tractable for real-time re-planning in changing environments, can improve performance in the presence of imperfect information, and can be adjusted to accommodate different risk profiles.

翻译：不确定环境下的多机器人规划与协调是一个基础性的计算难题，因为置信空间随机器人数量呈指数级增长。本文研究在不确定环境中，由用于信息收集的快速侦察车辆和部署侦察车辆的风险规避型运载机器人组成的异构机器人团队的规划问题。为克服存在环境不确定性时多机器人运动规划相关的计算挑战，我们使用拓扑图表示环境和操作场景，其中边权分布随机器人团队在图上状态的变化而变化。尽管这种置信空间表示仍随机器人数量呈指数级扩展，但我们构建了一个计算高效的混合整数规划模型，能够在数秒内生成最优的多机器人规划方案。我们在一个代表性场景中评估了所提方法，该场景要求机器人团队在环境中移动，同时最小化被位置对机器人团队不确定的观察者发现的概率。我们证明，该方法具有足够的计算可处理性，适用于变化环境中的实时重规划，能够在信息不完善的情况下提升性能，并可调整以适应不同的风险偏好。