Encrypted Simultaneous Control of Joint Angle and Stiffness of Antagonistic Pneumatic Artificial Muscle Actuator by Polynomial Approximation

This study proposes an encrypted simultaneous control system for an antagonistic pneumatic artificial muscle (PAM) actuator to develop a cybersecure and flexible actuator. First, a simultaneous control system design is considered for the joint angle and stiffness of a PAM actuator in a model-based design approach, thus facilitating the use of an encrypted control method. The designed controller includes a contraction force model expressed as rational polynomial functions, which makes it difficult to encrypt the controller. To overcome this difficulty, a least absolute shrinkage and selection operator-based polynomial approximation is employed for a rational controller. Then, the resulting polynomial controller is transformed into a matrix-vector product form, which enables the use of a specific homomorphic encryption scheme to develop an encrypted simultaneous control system for the PAM actuator. Finally, this study quantitatively evaluates the tracking control performance of the original, approximated, and encrypted controllers. The experimental results show that the proposed encrypted controller achieves simultaneous tracking of the joint angle and stiffness with a tracking error of less than 3.7%.