The paper addresses the problem of energy-efficient control of running legged mechanisms via the case study of the planar one-legged hopper, one of the simplest mechanisms capable of ballistic running gaits. What makes this system particularly interesting is that, endowed with a proper selection of springs, it can be controlled without spending much actuation energy. Giving core to this possibility has already motivated a few studies, but has not yet, to our knowledge, been extensively explored. The present study is another attempt in this direction. The study also unveils new resutls and intriguing questions, among which some could prove to be central to a better understanding of legged locomotion in general, its potentialities and also its limitations.
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