Optimal coordination control of multiple modular robot manipulators based on bilayer Nash games

Abstract This paper proposes an optimal coordination control method based on bilayer Nash games for multiple modular robot manipulators (MRMs) collaborative handling task. The overall dynamic model describing the coupling between a single MRM and the target object is formulated by combining the joint torque feedback technique with the Newton–Euler iterative approach, and the unknown interconnected joint coupling term is identified via a neural network observer. A bilayer Nash games framework is established, transforming the optimal control problem of a multi-MRM system into a Nash-game problem among the subsystems of a single MRM, as well as a Nash-game problem among the multiple MRMs involved in the collaborative handling task. The coupled Hamilton–Jacobi (HJ) equation is solved through an adaptive dynamic programming algorithm, combined with the optimal control strategy based on the bilayer Nash games. Lyapunov theory is employed to prove that the trajectory tracking error of the MRM system is ultimately uniformly bounded, while the global system of multiple MRMs in collaborative handling of the target object is asymptotically stable. Finally, the effectiveness and superiority of the proposed method are validated through experimental results, under the same setup, our controller reduces root mean square (RMS) joint error by 62.5%–66.4% and lowers control torque RMS by 17.0%–24.8% across representative joints, highlighting both accuracy and actuation-efficiency gains.