This study discusses a circular trajectory tracking function through a proposed pneumatic artificial muscle (PAM)-actuated robot manipulator. First, a dynamic model between a robot arm and a PAM cylinder is introduced. Then the parameters thereof are identified through a genetic algorithm (GA). Finally, PID is used along with a high-order sliding-mode feedback controller to perform circular trajectory tracking. As the experimental results show, the parameters of sampling time and moment of inertia are set to accomplish the trajectory tracking task in this study. In addition, the maximum error between the objective locus and the following locus was 11.3035 mm when applying theta-axis control to the circular trajectory of the robot arm with zero load or lower load. In an experiment of controller comparison, the results demonstrate that a high-order sliding-mode feedback controller is more robust in resisting external interference and the uncertainty of modeling, making the robot arm have good performance when tracking.

This study aims to develop a lower limb robotic exoskeleton with the use of artificial neural networks for the purpose of rehabilitation. First, the PID control with iterative learning controller is used to test the proposed lower limb robotic exoskeleton robot (LLRER). Although the hip part using the flat brushless DC motors actuation has good tracking results, the knee part using the pneumatic actuated muscle (PAM) actuation cannot perform very well. Second, to compensate this nonlinearity of PAM actuation, the artificial neural network (ANN) feedforward control based on the inverse model trained in advance are used to compensate the nonlinearity of the PAM. Third, a particle swarm optimization (PSO) is used to optimize the PID parameters based on the ANN-feedforward architecture. The developed controller can complete the tracking of one gait cycle within 3.6 s for the knee joint. Among the three controllers, the controller of the ANN-feedforward with PID control (PSO tuned) performs the best, even when the LLRER is worn by the user and the tracking performance is still very good. The average Mean Absolute Error (MAE) of the left knee joint is 1.658 degrees and the average MAE of the right knee joint is 1.392 degrees. In the rehabilitation tests, the controller of ANN-feedforward with PID control is found to be suitable and its versatility for different walking gaits is verified during human tests. The establishment of its inverse model does not need to use complex mathematical formulas and parameters for modeling. Moreover, this study introduces the PSO to search for the optimal parameters of the PID. The architecture diagram and the control signal given by the ANN compensation with the PID control can reduce the error very well.