Online Model Predictive Control of Robot Manipulator With Structured Deep Koopman Model

The model predictive control (MPC) can provide the benefit of optimality (sub-optimality, exactly speaking) and explicitly treat hard constraints in both states and inputs, which makes it an attractive approach in the fields of robotics. However, the performance of this approach heavily depends on the system model and it is computationally intensive, which hinders its application in the real-time control of robotic systems with fast dynamics, such as the robotic manipulators. Data-driven modeling approaches based on the Koopman operator have the potential to remove the barriers to adopting the MPC in robotics, through learning a globally linear model. In this letter, we propose a novel Koopman model—the structured deep Koopman model, which can improve the accuracy of the learned linear model and reduce the number of states in the lifted space, through exploiting the deep Lipschitz neural network and making the lifted dynamics structured. We also prove the rationality of the presented method and provide a new perspective on Koopman operator-based models, which brings the local and global linearization methods under the same umbrella. The effectiveness of the presented method has been verified by simulations and a real-world robotic experiment.