Major challenges of controlling human–robot collaboration (HRC)-oriented modular robot manipulators (MRMs) include the estimation of human motion intention while cooperating with a robot and performance optimization. This article proposes a cooperative game-based approximate optimal control method of MRMs for HRC tasks. A harmonic drive compliance model-based human motion intention estimation method is developed using robot position measurements only, which forms the basis of the MRM dynamic model. Based on the cooperative differential game strategy, the optimal control problem of HRC-oriented MRM systems is transformed into a cooperative game problem of multiple subsystems. By taking advantage of the adaptive dynamic programming (ADP) algorithm, a joint cost function identifier is developed via the critic neural networks, which is implemented for solving the parametric Hamilton–Jacobi–Bellman (HJB) equation and Pareto optimal solutions. The trajectory tracking error under the HRC task of the closed-loop MRM system is proved to be ultimately uniformly bounded (UUB) by the Lyapunov theory. Finally, experiment results are presented, which reveal the advantage of the proposed method.

Due to the limited computing and processing ability of modular robot manipulator (MRM) components, such as sensors and controllers, event-triggered mechanisms are considered a crucial communication paradigm shift in resource constrained applications. Dynamic event-triggered mechanism is developing into a new technology by reason of its higher resource utilization efficiency and more flexible system design requirements than traditional event-triggered. Therefore, an optimal control scheme of multiplayer nonzero-sum game based on dynamic event-triggered is developed for MRM systems with uncertain disturbances. First, dynamic model of the MRM is established according to joint torque feedback technique and model uncertainty is estimated by data-driven-based neural network identifier. In the framework of differential game, the tracking control problem of MRM system is transformed into the optimal control problem for multiplayer nonzero-sum game with the control input of each joint module as the player. Then, the static event-triggered control problem of MRM system is studied based on adaptive dynamic programming algorithm. On this basis, the internal dynamic variable describing the previous state of the system is introduced, and the characteristics of dynamic trigger rule and its relationship with static rule are revealed theoretically. By designing an exponential attenuation signal, the minimum sampling interval of the system is always positive, so that Zeno behavior is excluded. Lyapunov theory proves that the system is asymptotically stable and the experimental results verify the validity of the proposed method.

A Stackelberg-Pareto differential game-based approximate optimal interaction control approach is proposed for user-led modular robot manipulator (MRM) systems modeled by joint torque feedback (JTF) technique. The major objective of optimal control with physical human-robot interaction (pHRI) is evolved into approximating Stackelberg-Pareto equilibrium by adopting cooperative differential game in MRM and Stackelberg differential game between the human and robot. Learning from adaptive dynamic programming (ADP), the approximate optimal interaction control strategy with pHRI is developed by critic neural network (NN) for solving the coupled Hamilton-Jacobian (HJ) and HJ-Bellman (HJB) equations. The position tracking error under pHRI task is ultimately uniformly bounded (UUB) by the concept of Lyapunov theorem. Two distinction experiments demonstrate the superiority of proposed control approach.

Taking advantage of high-performance intelligent robots to solve the coordination control problem such as assembly, handling, and installation, transportation is gradually becoming a kind of frontier subject with great scientific research value in the field of robotics. However, due to possible conflicts and inconsistencies between the manipulator and the operating object, it is challenging to design the optimal coordination control scheme between human and robot. This article presents an event-triggered mixed nonzero-sum game optimal control method, which considers both nonzero-sum game and cooperative game cases, for modular robotic manipulator (MRM) systems performing coordinated operation tasks. First, the joint torque feedback technique and joint task assignment method are employed to establish the dynamic model of MRM subsystem, and then, the global state-space description is deduced. For the unknown information containing interconnected dynamic coupling (IDC) terms and friction modeling errors, an adaptive neural network (NN) identifier is established by utilizing the measured input–output data of each joint module. The adaptive updating law guarantees that the NN weight error finally converged to a minimum neighborhood of zero. To ensure the optimality of system overall performance, the corresponding value functions reflecting the interconnectedness among each joint subsystem and manipulated object are constructed. Based on the idea of differential game, the coordination control problem of MRM system is transformed into a mixed nonzero-sum game problem among each joint module and the operated object. Next, by constructing a single critic NN with learning structure, the optimal value function is approximated to solve the event-based Hamiltonian equations, and then, the optimal control strategy of each player is obtained. Finally, the Lyapunov theory is used to analyze system stability, and the effectiveness of the presented method is reinforced by experimental results.