پایداری دینامیکی پیاده روی دو پا منفعل بر زمین ناهموار: یک مطالعه شبیه سازی مقدماتی

A simplified 2D passive dynamic model was simulated to walk down on a rough slope surface defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness. Our results show that the passive walker can walk on rough surfaces subject to surface roughness up to approximately 0.1% of its leg length. This indicates that bipedal walkers based on passive dynamics may possess some intrinsic stability to adapt to rough terrains although the maximum roughness they can tolerate is small. Orbital stability method was used to quantify the walking stability before the walker started to fall over. It was found that the average maximum Floquet multiplier increases with surface roughness in a non-linear form. Although the passive walker remained orbitally stable for all the simulation cases, the results suggest that the possibility of the bipedal model moving away from its limit cycle increases with the surface roughness if subjected to additional perturbations. The number of consecutive steps before falling was used to measure the walking stability after the passive walker started to fall over. The results show that the number of steps before falling decreases exponentially with the increase in surface roughness. When the roughness magnitude approached to 0.73% of the walker's leg length, it fell down to the ground as soon as it entered into the uneven terrain. It was also found that shifting the phase angle of the surface profile has apparent affect on the system stability. This is probably because point contact was used to simulate the heel strikes and the resulted variations in system states at heel strikes may have pronounced impact on the passive gaits, which have narrow basins of attraction. These results would provide insight into how the dynamic stability of passive bipedal walkers evolves with increasing surface roughness.

We improved a simplified 2D passive dynamic model to walk down on a slope with rough surfaces defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness. Our results show that the passive walker can walk on rough surfaces subject to roughness perturbations perturbations up to approximately 0.1% of its leg length. This indicates that bipedal robots based on the passive dynamic principle may possess some intrinsic stability to overcome rough terrains although the maximum roughness they can tolerate is small. We used orbital stability to quantify the walking stability of the walker before it falls. It was found that the average maximum Floquet multiplier increases with the surface roughness in a non-linear form. A plateau is reached when it is approaching to the instability margin. Although the passive walker remained orbitally stable for all the simulation cases, the results suggest that the possibility of the model moving away from its periodic stable pattern increases with the surface roughness if subjected to additional perturbations. The number of consecutive steps before falling was used to measure the walking stability after the passive walker started to fall over. The results show that the number of steps before falling decreases exponentially with the increase in surface roughness. When the roughness magnitude approaches to 0.73% of the walker’s leg length, the model can only walk less than 3 steps before falling. Interestingly, we found that shifting the phase angle of the surface wave profile affects the system stability. This indicates that variations in system states at heel strikes due to roughness may have pronounced effect on the passive gaits that possess narrow basin of attraction. Our future work includes the investigation by scrutinizing various ways to increase the basin of attraction of the passive bipedal gait on rough terrains, such as adding upper body, circular arc feet, spring yankle and knee joints or active control mechanisms etc. Additionally, more geometrical features of rough surfaces will be considered, e.g. surface wave frequency changes, stochastic surfaces and three-dimensional surface profile. We are also in the development of 3D physical passive dynamic walkers, based on which we can examine the dynamic stability of realistic passive walkers on irregular surfaces and also compare with the results we obtained from computer simulations. This would help to gain better insight into the fundamental principles underlying bipedal locomotion.