Energy efficient hopping with Hill-type muscle properties on segmented legs

The intrinsic muscular properties of biological muscles are the main source of stabilization during locomotion, and superior biological performance is obtained with low energy costs. Man-made actuators struggle to reach the same energy efficiency seen in biological muscles. Here, we compare muscle properties within a one-dimensional and a two-segmented hopping leg. Different force-length-velocity relations (constant, linear, and Hill) were adopted for these two proposed models, and the stable maximum hopping heights from both cases were used to estimate the cost of hopping. We then performed a fine-grained analysis during landing and takeoff of the best performing cases, and concluded that the force-velocity Hill-type model is, at maximum hopping height, the most efficient for both linear and segmented models. While hopping at the same height the force-velocity Hill-type relation outperformed the linear relation as well. Finally, knee angles between 60 degrees and 90 degrees presented a lower energy expenditure than other morphologies for both Hill-type and constant relations during maximum hopping height. This work compares different muscular properties in terms of energy efficiency within different geometries, and these results can be applied to decrease energy costs of current actuators and robots during locomotion.