Robert D. Gregg

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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)
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 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)
The development of powered lower-limb prostheses has the potential to significantly improve amputees' quality of life. By applying advanced control schemes, such as hybrid zero dynamics (HZD), to prostheses, more intelligent prostheses could be designed. Originally developed to control bipedal robots, HZD-based control specifies the motion of the actuated(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)
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)
In this paper, we present a hierarchical framework that enables motion planning for asymptotically stable 3-D bipedal walking in the same way that planning is already possible for zero moment point walking. This framework is based on the construction of asymptotically stable gait primitives for a class of hybrid dynamical systems with impacts. Each(More)
The ankle contributes the majority of mechanical power during walking and is a frequently studied joint in biomechanics. Specifically, researchers have extensively investigated the torque-angle relationship for the ankle during dynamic tasks, such as walking and running. The slope of this relationship has been termed the "quasi-stiffness." However, over(More)
This paper presents the design and experimental implementation of a novel feedback control strategy that regulates effective shape on a powered transfemoral prosthesis. The human effective shape is the effective geometry to which the biological leg conforms - through movement of ground reaction forces and leg joints - during the stance period of gait.(More)