This paper extends the use of virtual constraints and hybrid zero dynamics (HZD), a successful control strategy for pointfoot bipeds, to the design of controllers for planar curved foot bipeds. Although the rolling contact constraint at the foot-ground interface increases complexity somewhat, the measure of local stability remains a function of configuration only, and a closed-form solution still determines the existence of a periodic orbit. The formulation is validated in experiment using the planar five-link biped ERNIE. While gaits designed for point feet yielded stable walking when ERNIE was equipped with curved feet, errors in both desired speed and joint tracking were significantly larger than for gaits designed for the correct radius curved feet. Thus, HZD-based control of this biped is shown to be robust to some modeling error in the foot radius, but at the same time, to require consideration of foot radius to achieve predictably reliable walking gaits. Additionally, under HZD-based control, this biped walked with lower specific energetic cost of transport and joint tracking errors for matched curved foot gait design and hardware compared to matched point-foot gait design and hardware.
This paper presents the development of the planar bipedal robot ERNIE as well as numerical and experimental studies of the influence of parallel knee joint compliance on the energetic efficiency of walking in ERNIE. ERNIE has 5 links-a torso, two femurs and two tibias-and is configured to walk on a treadmill so that it can walk indefinitely in a confined space. Springs can be attached across the knee joints in parallel with the knee actuators. The hybrid zero dynamics framework serves as the basis for control of ERNIE's walking. In the investigation of the effects of compliance on the energetic efficiency of walking, four cases were studied: one without springs and three with springs of different stiffnesses and preloads. It was found that for low-speed walking, the addition of soft springs may be used to increase Electronic supplementary material The online version of this article (http://dx.energetic efficiency, while stiffer springs decrease the energetic efficiency. For high-speed walking, the addition of either soft or stiff springs increases the energetic efficiency of walking, while stiffer springs improve the energetic efficiency more than do softer springs.
In this paper, a new intelligent control approach for high-speed quadruped bounding and galloping gaits is presented. The controller is capable of learning the leg touchdown angles and leg thrusts required to track the desired running height and velocity of a quadruped in only one stride. Training of the controller is accomplished not with a mathematical model, but with simple rules based on a heuristic knowledge of the quadruped mechanics. The result is a controller that produces better velocity and height tracking characteristics than a Raibert-based controller and is robust to modeling errors. Additionally, by making use of the natural dynamics of the system, gait characteristics comparable to biological quadrupeds result. The status of a legged machine being constructed for demonstration of the control approach and further study of the characteristics of galloping is also presented.
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