  Jumping and hopping locomotion are efficient means of traversing unstructured
rugged terrain with the former being the focus of roboticists. This focus has
led to significant performance and understanding in jumping robots but with
limited practical applications as they require significant time between jumps
to store energy, thus relegating jumping to a secondary role in locomotion.
Hopping locomotion, however, can preserve and transfer energy to subsequent
hops without long energy storage periods. Therefore, hopping has the potential
to be far more energy efficient and agile than jumping. However, to date, only
a single untethered hopping robot exists with limited payload and hopping
heights (< 1 meter). This is due to the added design and control complexity
inherent in the requirements to input energy during dynamic locomotion and
control the orientation of the system throughout the hopping cycle, resulting
in low energy input and control torques; a redevelopment from basic principles
is necessary to advance the capabilities of hopping robots. Here we report
hopping robot design principles for efficient and robust systems with high
energy input and control torques that are validated through analytical,
simulation, and experimental results. The resulting robot (MultiMo-MHR) can hop
nearly 4 meters (> 6 times the current state-of-the-art); and is only limited
by the impact mechanics and not energy input. The results also directly
contradict a recent work that concluded hopping with aerodynamic energy input
would be less efficient than flight for hops greater than 0.4 meters.
