Modeling, optimization, and control of a variable stiffness pneumatic rotary joint with soft-rigid hybrid twisting modules

Soft actuators have seen significant advancements in recent years, driven by their potential for adaptive and safe actuation in various applications. However, soft pneumatic actuators may exhibit undesirable deformation, bringing challenges in kinematic modeling and motion control. To address these issues, this paper systematically investigates a soft-rigid hybrid pneumatic rotary joint that integrates two antagonistic twisting modules in series-one performs clockwise helical motion, and another produces anticlockwise helical motion. Theoretical models for the rotary joint's angular displacement, output torque, and stiffness are revealed and verified through simulation and experiments. Experimental results show that the rotary joint can adjust its angular displacement, output torque and stiffness by changing the pressures of two bellows muscles. Additionally, with a classical PID controller, the rotary joint can follow triangle waves with a frequency of 0.5 Hz with a mean absolute error of 3.35 degrees and resist an external disturbance of 1 Nm. The variable stiffness pneumatic rotary joint contains no electronic components, thereby having the potential for applications in electronics-free robots operating in extreme environments, such as nuclear power stations, and explosive gas platforms.