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— Understanding Zeno phenomena plays an important role in understanding hybrid systems. A natural—and intriguing—question to ask is: what happens after a Zeno point? Inspired by the construction of [9], we propose a method for extending Zeno executions past a Zeno point for a class of hybrid systems: Lagrangian hybrid systems. We argue that after the Zeno(More)
— This paper presents a control law that results in stable walking for a three-dimensional bipedal robot with a hip. To obtain this control law, we utilize techniques from geometric reduction, and specifically a variant of Routhian reduction termed functional Routhian reduction, to effectively decouple the dynamics of the three-dimensional biped into its(More)
—In this paper we present a hierarchical framework that enables motion planning for asymptotically stable 3D bipedal walking in the same way that planning is already possible for ZMP walking. This framework is based on the construction of asymptotically stable gait primitives for a class of hybrid dynamical systems with impacts. Each primitive corresponds(More)
— In this paper we develop a feedback control law that results in stable walking gaits on flat ground for a three-dimensional bipedal robotic walker given stable walking gaits for a two-dimensional bipedal robotic walker. This is achieved by combining disparate techniques that have been employed in the bipedal robotic community: controlled symmetries,(More)
— This paper presents a hybrid mechanical model for the Gibbot, a robot that dynamically locomotes along a vertical wall in a manner analogous to gibbons swinging between branches in the forest canopy. We focus on one particular gait, continuous-contact brachiation, which always has one handhold in contact with the wall. We use zero-cost, unstable solutions(More)
This paper develops the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We prove a geometric property of general serial-chain robots termed recursive cyclicity, identifying the inherent robot symmetries that we exploit with the Subrobot Theorem. This shows that any(More)
Recent powered (or robotic) prosthetic legs independently control different joints and time periods of the gait cycle, resulting in control parameters and switching rules that can be difficult to tune by clinicians. This challenge might be addressed by a unifying control model used by recent bipedal robots, in which virtual constraints define joint patterns(More)
This brief presents a novel control strategy for a powered prosthetic ankle based on a biomimetic virtual constraint. We first derive a kinematic constraint for the "effective shape" of the human ankle-foot complex during locomotion. This shape characterizes ankle motion as a function of the Center of Pressure (COP)-the point on the foot sole where the(More)
Human locomotion is a rhythmic task in which patterns of muscle activity are modulated by state-dependent feedback to accommodate perturbations. Two popular theories have been proposed for the underlying embodiment of phase in the human pattern generator: a time-dependent internal representation or a time-invariant feedback representation (i.e., reflex(More)
— This paper presents a novel control strategy for a powered knee-ankle prosthesis based on biomimetic virtual constraints. We begin by deriving kinematic constraints for the " effective shape " of the human leg during locomotion. This shape characterizes ankle and knee motion as a function of the Center of Pressure (COP)—the point on the foot sole where(More)