Tip position estimation of a 3-DOF soft mechanism using artificial muscles with optical fibers

McKibben-type pneumatic artificial muscles (PAMs) are lightweight and flexible soft actuators with a high power-to-weight ratio, and have been widely applied to rehabilitation devices, power-assist systems, and soft robotic mechanisms. By integrating sensing functions into PAMs, their usability and controllability can be enhanced, enabling the development of more practical and advanced soft mechanisms. We previously proposed a smart artificial muscle (SAM) by integrating an optical fiber into the braided sleeve of a McKibben-type PAM, which enables displacement estimation by measuring optical bending loss. The SAM is compatible with conventional PAM fabrication processes; however, the sensor output exhibits strong nonlinearity and time dependency. In this study, an LSTM-based state estimation framework is extended from a single SAM to a three-degree-of-freedom soft mechanism composed of multiple SAMs, where strong nonlinear coupling and mutual interference arise among actuators. In the proposed framework, the LSTM model jointly processes time-series data of multi-channel optical sensor outputs and applied pressures of the three SAMs, along with past estimated states as inputs. This structure enables the model to capture nonlinear coupling, hysteresis, and time-dependent behavior, allowing estimation of the tip position of the soft mechanism. Experimental results demonstrate that the proposed method accurately captures complex nonlinear dynamics and mutual mechanical interference among multiple SAMs, achieving accurate tip position estimation. These results indicate that SAMs with integrated sensing and actuation capabilities, combined with machine-learning-based estimation, provide an effective approach for state estimation of multi-DOF soft robotic mechanisms.