Adaptive torque estimation-based nonlinear H\(\infty \) control of modular robot manipulators with uncertain environments

Modular robot manipulators (MRMs) based on harmonic drive (HD) transmissions perform various target tasks in unknown environments, and the main challenge is to overcome the uncertain noise and controller errors of systems generated by device vibrations while facing with unknown external disturbance. To address these challenges, a variational Bayesian (VB)-based extended Kalman filter (VBEKF) is developed as part of the MRM dynamic model to mitigate bias in torque estimation resulting from external interference within HD model joints. Furthermore, leveraging a two-player zero-sum game strategy, a robust adaptive dynamic programming (ADP) method based on single critic neural network (NN) is formulated to solve the Hamilton–Jacobi–Isaacs (HJI) equation in H \(\infty \) $\infty$ control problem, ultimately yielding an approximate optimal solution for H \(\infty \) $\infty$ control. The Lyapunov theory guarantees that the trajectory tracking error of a closed-loop MRM system remains ultimately uniformly bounded (UUB), even in the presence of unknown environmental disturbances. Ultimately, the experiment results are given to illustrate the advantages and effectiveness of the proposed method. The experimental results show that the proposed method reduces the control torque error by \(\sim \) $\sim$ 20 \(\%\) $\%$ compared with the existing control methods.