Energy and time trade-offs explain everyday human reaching movements

Humans perform reaching movements with stereotypically smooth trajectories, attributed to neural optimality principles. Previous models focus on maximizing objectives like accuracy to explain smooth reaching under the speed-accuracy tradeoff, but none explain individuality. In everyday tasks such as reaching for a cup or pen, individuals self-select their own relaxed and idiosyncratic speeds that prioritize neither speed nor accuracy and appear to defy purely objective optimality. Here we propose an Energy-Time trade-off that better predicts the smoothness, speed, and individuality of everyday reaching. Energy refers to metabolic energy expenditure, and Time represents a weighted cost adjustable for individual and contextual factors. The balance between the two predicts human speed trajectories, durations, and peak speeds more accurately than prior models. Individuals move differently because they value time individualistically yet consistently. For example, one’s time valuation may be inferred from a single reach, and then applied to predict reaches of any distance by the same individual. Instructions to reach “faster” or “slower” also yield individualistic yet identifiable time valuations sufficient to predict other movements within each context. In fact, all movements across individuals and contexts align with a universal set of Energy-Time predictions. Energy economy objectively favors smoothness and slowness, whereas the time cost captures one’s individualistic preference to spend energy to save time.