A unified energy-optimality criterion predicts human navigation paths and speeds

Abstract

Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality criterion that predicts disparate non-straight-line walking phenomena, with straight-line walking as a special case. We first characterized the metabolic cost of turning, deriving the cost landscape as a function of turning radius and rate. We then generalized this cost landscape to arbitrarily complex trajectories, allowing the velocity direction to deviate from body orientation (holonomic walking). We used this generalized optimality criterion to mathematically predict movement patterns in multiple contexts of varying complexity: walking on prescribed paths, turning in place, navigating an angled corridor, navigating freely with end-point constraints, walking through doors, and navigating around obstacles. In these tasks, humans moved at speeds and paths predicted by our optimality criterion, slowing down to turn and never using sharp turns. We show that the shortest path between two points is, counterintuitively, often not energy-optimal, and, indeed, humans do not use the shortest path in such cases. Thus, we have obtained a unified theoretical account that predicts human walking paths and speeds in diverse contexts. Our model focuses on walking in healthy adults; future work could generalize this model to other human populations, other animals, and other locomotor tasks.

Humans optimally anticipate and compensate for an uneven step during walking

“…This study highlights a less-appreciated aspect of vision-based path planning. It is clear that humans use vision to plan paths for the body ( Arechavaleta et al, 2008 ; Brown et al, 2021 ), including adjustment of COM height ( Müller et al, 2012 ) and foot placement ( Matthis and Fajen, 2013 ; Patla, 1998 ). After all, it is sensible to predict which paths are feasible and which are less arduous.…”

“…To our knowledge, the present study is the first to use a mechanistic model to predict behavioral, multistep trajectories performed by humans. Perhaps the closest analog is a model based on empirical energetic cost curves that explain the curvilinear paths that humans take to go through doorways ( Brown et al, 2021 ). We suspect that the empirical costs could be predicted mechanistically by a three-dimensional version of our dynamic walking model (e.g., Rebula et al, 2017 ), although that remains to be tested.…”

“…In contrast, anticipatory control actions take place before the body state has been affected, perhaps using vision to predict an upcoming perturbation or obstacle. For example, humans clearly anticipate and plan for the body’s future location, for example to negotiate around obstacles or through doorways ( Arechavaleta et al, 2008 ; Brown et al, 2021 ; Patla, 1998 ). In particular, foot placement and motion are planned, with the help of vision, to avoid or step over upcoming obstacles ( Patla, 1998 ; Patla and Rietdyk, 1993 ), and to land on foot targets ( Drew et al, 2008 ; Matthis and Fajen, 2013 ).…”

“…For locomotion, the criterion of metabolic energy economy determines features such as the preferred step length and step width during steady walking ( Donelan et al, 2001 ; Zarrugh et al, 1974 ), as governed by the pendulum-like dynamics of the legs ( Kuo et al, 2005 ). Energetic costs are also greater on uneven terrain ( Kowalsky et al, 2021 ; Pandolf et al, 1977 ; Voloshina et al, 2013 ) and under transient conditions ( Brown et al, 2021 ). However, it is unknown whether the economy preferences of steady walking apply to uneven terrain as well.…”

The split-belt rimless wheel

“…This work also suggests a broader class of energy harvesting mechanisms, applicable to any robot that does not operate within a single Newtonian reference frame. Finally, a deeper understanding of these mechanisms in robots may help us to better understand human behavioral choices, just as simple models of energy use in single-velocity environments have helped us to understand interesting features of human gait selection (Srinivasan and Ruina, 2006), speed modulation (Long and Srinivasan, 2013), and path planning (Brown et al, 2021).…”