where c is the valve duty ratio. The required vertical jumping speed
is determined by combining the two constraints. Once this is
known, the corresponding duty ratio needed for the solenoid valve
to cause the pneumatic cylinder rod to exert the desired force on
the ground can be determined from the pneumatic pressure, mass of the cylinder rod, and mass of the robot body. By utilizing the impact
principle between two bodies, the vertical jumping speed v0y
can be expressed by