Modeling and Mixed-Integer Nonlinear MPC of Positive-Negative Pressure Pneumatic Systems

Positive-negative pressure regulation is critical to soft robotic actuators, enabling large motion ranges and versatile actuation modes. However, it remains challenging due to complex nonlinearities, oscillations, and direction-dependent, piecewise dynamics introduced by affordable pneumatic valves and the bidirectional architecture. We present a model-based control framework that couples a physics-grounded switched nonlinear plant model (inflation/deflation modes) with a mixed-integer nonlinear model predictive controller (MI-NMPC). The controller co-optimizes mode scheduling and PWM inputs to realize accurate reference tracking while enforcing input constraints and penalizing energy consumption and excessive switching. To make discrete mode decisions tractable, we employ a Combinatorial Integral Approximation that relaxes binary mode variables to continuous surrogates within the valve-scheduling layer. With parameters identified from the physical system, simulations with step and sinusoidal references validate the proposed MI-NMPC, showing a consistently favorable trade-off among accuracy, control effort, and switching, and outperforming conventional PID and NMPC with heuristic mode selection.