II. MODEL OF PNEUMATIC ACTUATOR
As mentioned above, the master and the slave manipulators
are identical, thus only one pneumatic robot is presented in
this section. To describe the air flow dynamics in a cylinder,
we assume the following [18].
1) Air is a perfect gas and its kinetic energy is negligible
in the chamber.
2) The pressure and the temperature are homogeneous in
each chamber.
3) The evolution of the gas in each cylinder chamber is
polytropic.
4) The temperature variation in chambers is negligible with
respect to the supply temperature.
5) The mass flow rate leakages are negligible.
6) The supply and exhaust pressures are constant.
A schematic of a 1-DOF pneumatic actuation system is shown
in Fig. 1. The device consists of a pneumatic cylinder, four
solenoid valves, a position sensor, and two pressure sensors.
Each chamber is connected to two solenoid valves. Valves 1
and 4 are connected to the supply pressure, while valves 2
and 3 are connected to the atmosphere pressure. The choice
of four valves rather than two valves allows us to increase
the DOF in the choice of the control vector and the resulting
behavior of the closed-loop system.