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.

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Much modern engineering design work uses S -N curves and empirical applications thereof. In industry, currently popular methods for predicting fatigue life under complex loading use ad hoc cycle counting algorithms along with Miner's rule, in spite of its known weaknesses. Many ad hoc alternatives to Miner's rule have been proposed, each with limited experimental justification. Of these, Manson's double linear damage rule (DLDR) is widely considered to be good. In this paper, we bring a new perspective to empirical, as opposed to mechanistic, fatigue damage evolution models. It is first assumed, with reasonable justification, that there is a scalar, abstract, damage variable f, whose evolution under cyclic loading satisfies _ fZ af m , where a and m are unknown functions of load parameters. One main contribution of the paper lies in deducing what the functions a and m must be in order to obtain consistency with fatigue data in handbooks. A small correction to this basic power law model is then developed. The final explicit model initially has 10 unknown fitted parameters, but these are brought down to three unknowns; the accompanying discussion is the other main contribution of the paper. Finally, comparison with Manson's and other data suggests that, with two fitted parameters, our model works as well as the DLDR and much better than Miner's rule. For other parameter choices, our model reduces to Miner's rule. We conclude with speculation about ways in which the model might be extended beyond the scope of the DLDR.

Walking humans display great versatility when achieving task goals, like avoiding obstacles or walking alongside others, but the relevance of this to fall avoidance remains unknown. We recently demonstrated a functional connection between the motor regulation needed to achieve task goals (e.g., maintaining walking speed) and a simple walker’s ability to reject large disturbances. Here, for the same model, we identify the viability kernel—the largest state-space region where the walker can step forever via at least one sequence of push-off inputs per state. We further find that only a few basins of attraction of the speed-regulated walker’s steady-state gaits can fully cover the viability kernel. This highlights a potentially important role of task-level motor regulation in fall avoidance. Therefore, we posit an adaptive hierarchical control/regulation strategy that switches between different task-level regulators to avoid falls. Our task switching controller only requires a target value of the regulated observable—a “task switch”—at every walking step, each chosen from a small, predetermined collection. Because humans have typically already learned to perform such goal-directed tasks during nominal walking conditions, this suggests that the “information cost” of biologically implementing such controllers for the nervous system, including cognitive demands in humans, could be quite low.

Humans display great versatility when performing goal-directed tasks while walking. However, the extent to which such versatility helps with fall avoidance remains unclear. We recently demonstrated a functional connection between the motor regulation needed to achieve task goals (e.g. maintaining walking speed) and a simple walker's ability to reject large disturbances. Here, for the same model, we identify the viability kernel---the state space region in which the walker can step forever via at least one sequence of push-off inputs per state. We further find that only a few basins of attraction of the speed-regulated walker's steady-state gaits can fully cover the viability kernel. This highlights a potentially important role of task-level motor regulation in fall avoidance. Therefore, we posit an adaptive hierarchical control/regulation strategy that switches between different task-level regulators to avoid falls. Our hierarchical task switching controller only requires a target value of the regulated observable---a 'task switch'---at each walking step, each chosen from a small, predetermined collection. Because humans have typically already learned to perform such tasks during nominal walking conditions, this suggests that the 'information cost' of biologically implementing such controllers for the nervous system, including cognitive demands in humans, could be relatively low.