RESEARCH ON MULTISTABILITY OF GAITS IN THE PASSIVE WALKING ROBOT WITH ROUND FEET

Current research on passive walking gaits mainly reveals the effects of parameter changes on their stability, while there are fewer studies on the multistability of gaits. The multistability of gaits is not only a source of walking pattern diversity but also a key factor in triggering sudden gait changes. Although the existence of coexisting gaits has received attention, systematic studies on the mechanisms of their generation, evolution, and disappearance have still not been carried out. To this end, this paper takes a round-footed passive walking robot as the research object, applies the cell mapping and point mapping algorithms to explore several high-periodic gaits coexisting with period-one gaits, plots the three-dimensional basin of attraction of the coexisting gaits, and carries out a detailed comparative analysis of the walking characteristics of these gaits. In addition, the Poincaré-Newton-Floquet (PNF) algorithm is improved based on the jump matrix method to solve the unstable orbits and their corresponding Floquet multipliers of the passive walking system and the bifurcation and crisis phenomena in the gait evolution are further revealed by combining with the basin of attraction. The results show that the higher the period of the coexisting gaits, the faster their average gait speeds, but the worse their gait stability; all these coexisting gaits are generated by the fold bifurcation of the limit cycle and lead to chaos by the period-doubling cascade path, eventually disappearing with the unstable orbitals by collisions on the boundary of the basins of attraction. This paper contributes to the understanding of the multistability of passive walking gaits and provides a basis for optimal robot design and stability control.