Modeling and simulation of stepladder walking

Modeling and control of underactuated mechanical systems—where the number of degrees of freedom exceeds the number of actuators—pose per- sistent challenges, particularly in bipedal locomotion. This study explores a conceptually related system: a stepladder with a decorator/operator, which resembles a compass-gait biped with an upper body but exhibits distinct lo- comotion behavior. Unlike typical bipedal robots, the stepladder preserves leg order during walking, maintaining a fixed leading-trailing relationship with- out leg crossing. The system is driven both by the time-dependent harmonic motion of the upper body and by impulsive forces that cause a velocity drop in the front leg in the direction of locomotion. Inspired by the simplicity and dynamic richness of passive dynamic walk- ing, our approach offers insights into fundamental locomotion principles through a theoretical framework for a hybrid mechanical system characterized by both continuous and discrete dynamics. Building on our earlier theoretical work, this paper focuses on three main objectives: (i) identifying individual gait phases using real-world video recordings, (ii) reducing the original 5-link 3D model to a 3-link 2D version while preserving key dynamic features, and (iii) conducting a numerical analysis of stable walking behavior using a novel cobweb diagram representation.