Further Analysis of the Passive Dynamics of the Compass Biped Walker and Control of Chaos via Two Trajectory Tracking Approaches

This work consists in analyzing and controlling the walk of the compass-type bipedal walker in order to stabilize its passive dynamic gait. The dynamic walking of the compass-gait walker is modeled by an impulsive hybrid nonlinear system. This impulsive hybrid nature is considered very complex as it can generate unwanted phenomena such as chaos and bifurcations. We show first by means of bifurcation diagrams and by varying the slope angle of the walking surface and also the length of the lower leg segment that the passive dynamic walking exhibits successive period-doubling bifurcations leading to chaos. Furthermore, in order to control chaos and hence obtain one-periodic walking behavior, we propose two control approaches based on tracking a desired trajectory. The first method consists in tracking the one-periodic passive dynamic walking generated by the compass model itself. The second control method lies in following a planned trajectory using the 4th-order Spline function. An optimization method is also achieved to design the parameters of the desired trajectory. Some features of the period-1 passive gait are used in the design of such Spline trajectory. Finally, we show some simulation results revealing the efficiency of the two proposed control methods in the control of the chaotic passive gait of the compass-gait walker. Moreover, we demonstrate the stabilization of the bipedal locomotion of the compass biped walker on different slopes: descending and ascending inclined planes and walking on a level ground. A comparison with the OGY-based control method is also performed to further show the superiority of these two control approaches.

Experimental verification of the characteristic behaviors in passive dynamic walking

It is well known that passive dynamic walking shows chaotic behavior owing to changes in the environment. In addition, when the environment changes continuously during walking, passive dynamic walking shows “adaptive behaviors” in which the stride angle changes itself in an attempt to keep walking. These behaviors are very interesting and useful for the legged robot design. However, the studies on passive dynamic walking are preceded only by numerical simulations. For this reason, it is very important to confirm, by actual experiments, whether these characteristic behaviors appear. In this paper, we verify the existence of these behaviors by several actual experiments.