Before revision:  We show that this increase in energy cost for turning has behavioral implications, specifically explaining a variety of human : to save energy, we predict that humans should walk slower in smaller circles, slow down when path curvature increases when traveling along more complex curves, turn in placearound a particular optimal angular speed, and avoid sharp turns but use smooth gentle turns while navigating around obstacles or while needing to turnwhile walking . We then tested these behavioral predictions against additional behavioral experiments we performed and existing movement data from previous studies, finding that human behavior in these experiments are consistent with minimizing, at least approximately , the energy cost of locomotion subject to the relevant task constraints .
After revision:  We then used this metabolic cost to mathematically predict energy-optimal movement patterns for five tasks of varying complexity: walking in circles, turning in place, walking through an angled corridor, walking freely from point to point while having to turn, and walking through doors while maneuvering around obstacles. In these tasks, humans moved at speeds and paths approximately predicted by energy optima. Thus, we provide a unified theoretical account that predicts diverse curvilinear locomotor phenomena .