Evidence for a Time-Invariant Phase Variable in Human Ankle Control

Abstract

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 mechanisms). In either case the neuromuscular system must update or represent the phase of locomotor patterns based on the system state, which can include measurements of hundreds of variables. However, a much simpler representation of phase has emerged in recent designs for legged robots, which control joint patterns as functions of a single monotonic mechanical variable, termed a phase variable. We propose that human joint patterns may similarly depend on a physical phase variable, specifically the heel-to-toe movement of the Center of Pressure under the foot. We found that when the ankle is unexpectedly rotated to a position it would have encountered later in the step, the Center of Pressure also shifts forward to the corresponding later position, and the remaining portion of the gait pattern ensues. This phase shift suggests that the progression of the stance ankle is controlled by a biomechanical phase variable, motivating future investigations of phase variables in human locomotor control.

Unifying the gait cycle in the control of a powered prosthetic leg

“…The controller is then able to automatically react to disturbances. This would be advantageous for a prosthesis controller because it allows the prosthesis to react to disturbances in a predictable manner that may be similar to the natural human response [8]. …”

Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments With Transfemoral Amputees

“…The significance of effective shape begs the question as to whether human locomotion might employ a phase variable [42], [48]. Phase-based virtual constraints could also be applied to powered exoskeletons (e.g., [11]), motivating future investigation of hybrid zero dynamics for wearable robots.…”

“…Note that the joint patterns look different over the phase variable than over time (Fig. 12c–d) because the COP did not increase linearly with respect to time, i.e., the phase domain in which control law (9) operated was a warped representation of the time domain [42]. …”

Design and characterization of a biologically inspired quasi-passive prosthetic ankle-foot

“…The stiffness of the pneumatic ankle prosthesis (413 kPa) increased by a factor of three, following similar trends to those observed in biological data. Work estimating ankle impedance during walking showed ankle stiffness increasing by a factor of four as the ankle was dorsiflexed and the COP translated anteriorly (COP data obtained from an open dataset [14]). It should be noted that the negative linear trends of pneumatic ankle COP and ankle angle is an artifact of the testing apparatus and protocol.…”