Soft robotics technology has the potential for a wide range of applications; however, their implementation is hindered by the lack of accurate mathematical models and control methods. For example, a method to control multiple pneumatic inflatable actuators in turn by a passive mechanism has been proposed in a literature, but no mathematical model was presented to develop control laws for the system. This study proposes a mathematical model for the inflation characteristics of sequential soft actuators, and theoretical control law for passive sequential control of the inflation of multiple actuators by using flow resistors. The model is constructed from the physical requirements of the actuators based on fluid dynamics and thermodynamics. The study shows that the pressure change characteristics can be derived from the differential equations even for complex parallel and series circuits. The model mathematically represents the physical principle by which the actuators' inflation order depends on the relationship between changes in the input pressure and internal pressure with time. Experiments with real circuits of simple and complex layouts are presented. The actuators are inflated in sequence from a single air pressure source, and the mathematical model was able to describe the pressure and flow rate change characteristics at each point in the circuit.
