This study addresses the critical challenge of simulating pedestrian crowd dynamics in staircase environments, where existing models often neglect three-dimensional geometric constraints and dynamic interactions. We propose a novel dual-layer motion model (DLM) that integrates a hierarchical kinematic-dynamic coupling framework, geometric discretization methods, and crowd interaction mechanisms. The model abstracts pedestrians as a multi-node "dual-foot and single-point" system, distinguishing between an upper-layer centroid motion plane and a lower-layer dual-foot support space. This approach combines spatiotemporal modeling and contact mechanics to address the complexity of stairwell dynamics. The lower layer employs cellular path planning to constrain stepping motions and ensures spatiotemporal consistency of the crowd through a quasi-synchronous state transition mechanism. The upper layer utilizes an ellipse-projection-based separating axis algorithm to detect collision conflicts and quantifies contact effects using collision dynamics. Additionally, a quasi-synchronous state migration mechanism is introduced within a hybrid discrete-continuous time framework to coordinate gait cycles in large-scale multi-agent simulations, resolving temporal asynchrony. Based on the stability control principle of inverted pendulum dynamics, combined with biomechanical regulation capabilities and motion threshold constraints, the perturbation effects of contact forces on pedestrian balance are quantified, enabling individual dynamic stability analysis.
To validate the model, parameterized stairwell scenarios (step height: 0.15 m, tread depth: 0.26 m) were constructed to simulate the motion of heterogeneous pedestrians (mass: 65±5 kg, height: 1.70±0.2 m). Simulation results demonstrate that the model accurately captures dynamic features of pedestrian motion in stairwells: the centroid displacement ratio aligns closely with the theoretical stair slope, and the crowd’s average velocity deviates by less than 6% from empirical data. Dynamic stability analysis reveals the evolution from individual local imbalance to group instability. Further parametric studies indicate that balancing target attraction weight (α) and repulsion weight (β) regulates crowd behavioral cohesion, while increasing the collision restitution coefficient (e) amplifies contact force fluctuations.
In conclusion, the dual-layer model bridges motion planning and dynamic stability in stairwell environments, offering high-fidelity insights into pedestrian safety. The results emphasize the interdependence of geometric constraints, biomechanical adjustments, and density-driven instability. Future research may extend the model to irregular stair geometries and incorporate heterogeneous pedestrian parameters to enhance predictive accuracy for evacuation optimization and architectural safety design.