A Novel Robust Control Method Combining DNN-Based NMPC Approximation and PI Control: Application to Exoskeleton Squat Movements

Nonlinear Model Predictive Control (NMPC) is a precise controller, but its heavy computational load often prevents application in robotic systems. Some studies have attempted to approximate NMPC using deep neural networks (NMPC-DNN). However, in the presence of unexpected disturbances or when operating conditions differ from training data, this approach lacks robustness, leading to large tracking errors. To address this issue, for the first time, the NMPC-DNN output is combined with a PI controller (Hybrid NMPC-DNN-PI). The proposed controller is validated by applying it to an exoskeleton robot during squat movement, which has a complex dynamic model and has received limited attention regarding robust nonlinear control design. A human-robot dynamic model with three active joints (ankle, knee, hip) is developed, and more than 5.3 million training samples are used to train the DNN. The results show that, under unseen conditions for the DNN, the tracking error in Hybrid NMPC-DNN-PI is significantly lower compared to NMPC-DNN. Moreover, human joint torques are greatly reduced with the use of the exoskeleton, with RMS values for the studied case reduced by 30.9%, 41.8%, and 29.7% at the ankle, knee, and hip, respectively. In addition, the computational cost of Hybrid NMPC-DNN-PI is 99.93% lower than that of NMPC.