SPF-EMPC planner: A real-time motion planner for multi-robot in cluttered environments with dynamic obstacles and uncertainties

Safe and efficient navigation for multi-robot systems in cluttered, dynamic environments remains challenging, primarily due to uncertainties from internal disturbances and dynamic external conditions. While existing methods enable real-time navigation in static or sparse settings, they often fail to respond effectively in environments dense with both static and moving obstacles. To address this limitation, this article proposes a novel safety probability field-based extended state model predictive control (SPF-EMPC) planner. The framework first introduces a safety probability field to model dynamic obstacles and integrates it with an unconstrained optimization approach for online generation of collision-free trajectories. Subsequently, an extended state model predictive controller ensures accurate trajectory tracking by explicitly accounting for robot model constraints and state perturbations, thereby guaranteeing practical feasibility. Both simulations and physical experiments demonstrate that the proposed method reliably prevents inter-robot and robot–obstacle collisions, even under significant motion and control uncertainties.