In practical applications, the unpredictable movement of obstacles and the imprecise state observation of robots introduce significant uncertainties for the swarm of robots, especially in cluster environments. However, existing methods are difficult to realize safe navigation, considering uncertainties, complex environmental structures, and robot swarms. This paper introduces an extended state model predictive control planner with a safe probability field to address the multi-robot navigation problem in complex, dynamic, and uncertain environments. Initially, the safe probability field offers an innovative approach to model the uncertainty of external dynamic obstacles, combining it with an unconstrained optimization method to generate safe trajectories for multi-robot online. Subsequently, the extended state model predictive controller can accurately track these generated trajectories while considering the robots' inherent model constraints and state uncertainty, thus ensuring the practical feasibility of the planned trajectories. Simulation experiments show a success rate four times higher than that of state-of-the-art algorithms. Physical experiments demonstrate the method's ability to operate in real-time, enabling safe navigation for multi-robot in uncertain environments.

翻译：在实际应用中，障碍物的不可预测运动与机器人状态观测的不精确性，尤其在集群环境中，为机器人群体引入了显著的不确定性。然而，现有方法难以在同时考虑不确定性、复杂环境结构以及机器人集群的情况下实现安全导航。本文提出了一种结合安全概率场的扩展状态模型预测控制规划器，以解决复杂、动态且不确定环境中的多机器人导航问题。首先，安全概率场提供了一种创新的方法来对外部动态障碍物的不确定性进行建模，并将其与无约束优化方法相结合，在线为多机器人生成安全轨迹。随后，扩展状态模型预测控制器能够精确跟踪这些生成的轨迹，同时考虑机器人固有的模型约束与状态不确定性，从而确保规划轨迹的实际可行性。仿真实验表明，其成功率比现有先进算法高出四倍。物理实验验证了该方法能够实时运行，实现多机器人在不确定环境中的安全导航。