A Stable Model Reference Adaptive Controller Developed for a Prosthetic Hand Wrist (I)

Abstract

Advanced control algorithms are essential for enhancing the functionality of prosthetic hands, enabling them to operate in diverse conditions. This paper presents a Model Reference Adaptive Controller (MRAC) developed for a tendondriven soft continuum wrist, integrated into the ‘PRISMA HAND II’ prosthetic hand. The primary objective of our research is to design an adaptive controller that facilitates wrist movements eliminating external disturbances while minimizing computational requirements. To achieve this, kinematic and dynamic models of the wrist are developed based on the Piece-wise Constant Curvature (PCC) hypothesis. The controller consists of a reference model generated using the PCC model, and state errors are evaluated by comparing the responses of the reference model to those of the wrist model. These errors are reduced using the MRAC approach to make the wrist’s behavior closely align with that of the reference model. Stability of the closed-loop system is ensured using the Lyapunov direct method, along with the ‘New Theorem of Stability’, a replacement for Barbalat’s lemma, ensuring that the error between the reference model and the actual system converges to zero and that the adaptive gains stabilize to fixed values.