Task-level regulation enhances global stability of the simplest dynamic walker

Abstract

Much remains unknown about how considerations such as stability and energy minimization shape the way humans walk. While active neuromotor control keeps humans upright, they also need to choose from multiple stepping regulation strategies to achieve one or more task goals, such as maintaining a desired speed or direction. Experiments on human treadmill walking motivate an important question: why do humans prefer one task-level regulation strategy over another—perhaps to enhance their ability to reject large disturbances? Here, we study the relationship between task-level regulation and global stability in a powered compass walker on a treadmill, with added step-to-step speed and position regulators. For treadmill walking, we find that speed regulation greatly enlarges and regularizes the unregulated walker’s stability region, i.e. its basin of attraction, much more than position regulation. Thus, our results suggest a possible explanation for the experimental finding that humans strongly prioritize regulating speed from one stride to the next, even as they walk economically on average. Furthermore, our work suggests a functional connection between task-level motor regulation and global stability—and, thus, perhaps even fall risk.

Viability, task switching, and fall avoidance of the simplest dynamic walker

“…The walker admits families of 'long-period' and 'short-period' gaits 6,19 , which are fixed points (θ * , θ * ; P * ) of the map F F F (equation 2), for a given P * . While the long-and short-period gaits admit distinct step times and contrasting open-loop stability as θ + → 0 20 , their curves 17 intersect at (0, 0) in the original state space (Fig. 2a).…”

“…Therefore, the viable region is also the set within which different motor regulation strategies can be meaningfully compared for their effect on the walker's ability to avoid falls. Taking step-to-step speed regulation as a model task-level motor regulation strategy 9,16,17 , we estimate the speed-regulated walker's basins for several target speeds vis-à-vis the viable region. Not only do the speed-regulated walker's basins occupy large regular regions, but we find that only a small collection of these basins covers nearly the entire viable region itself.…”

Implementation and acceleration of optimal control for systems biology

“…Across the life sciences, we encounter systems over which we wish to exert control. Whether we consider outbreak control in epidemiology [1,2], chemotherapy in oncology [3][4][5], muscle contraction and gait regulation in biomechanics [6][7][8], engineering cellular processes in synthetic biology [9,10], cell population growth in tissue engineering [11,12], or biodiversity and invasive species management in ecology [13][14][15], we face decisions around how a particular intervention should be applied to best achieve desired outcomes. Using mathematical models of such systems, optimal control theory provides insight into these resource allocation decisions.…”

Comparing system identification techniques for identifying human-like walking controllers

“…These studies typically solve the dynamics of the SLIP model, then derive a controller to create a closed system model [17][18][19][20]. Beyond this, work with both the inverted pendulum and SLIP models have shown that different controllers can drastically change important gait properties [14,21]. Thus, it is clear that developing an appropriate controller is critical to producing a desired gait.…”