Adaptive fuzzy control of electrically stimulated muscles for arm movements

A modified adaptive Takagi-Sugeno (TS) fuzzy logic controller (FLC) is proposed that allows a simulated elbow-like biomechanical system to accurately track sigmoidal and sinusoidal trajectories in the sagittal plane. The work is a first effort towards the implementation of a system to restore elbow movements in quadriplegics using functional neuromuscular stimulation. The single-joint musculo-skeletal system is composed of a co-contractable pair of electrically stimulated muscles; the muscle model accounts for the increase in fatigue during the tracking exercise. In the proposed controller structure, a reinforcement learning scheme is used to accomplish the parameter tuning, and the parameter projection algorithm guarantees the system stability during the adaptation process. The controller performance is evaluated using computer simulation experiments and compared with the performance achievable when a standard proportional-integrative-derivative (PID) controller is employed for the same application. The modified adaptive TSFLC outperforms the PID controller in all tested situations, with a clear-cut advantage in the case of high-frequency sinusoidal trajectories (angular frequencies spanning the interval 8-12 rad s-1). The standard controller suffers from a dramatic increase in root mean square (RMS) tracking error above the value at 8 rad s-1, e.g. ERMS > or = 0.013, whereas the correlation coefficient between the actual and desired trajectory falls almost to zero, starting from the value rho approximately equal to 0.97 at 8 rad s-1. On the other hand, the adaptive TSFLC yields ERMS < or = 0.015, with rho > or = 0.78, over the whole range of tested angular frequencies.