Deep Koopman Operator Based Model Predictive Control for Nonlinear Robotics Systems

Modeling and control of nonlinear robotic systems have been challenging tasks. If a linear approximate embed-ding space for nonlinear dynamical robotic systems can be constructed, well-established techniques in the field of linear systems are expected to be used to deal with this problem. The Koopman theory suggests that a data-driven approach can be used to construct a suitable set of observation functions to map the nonlinear system into an equivalent linear model in the embedding space. We use deep neural networks to construct more adaptive sets of observation functions, treat the control inputs as generalized states, learn the input-Koopman operator of the controlled nonlinear robotic system, and construct the embedded linear state model DKoopman-predictor. The learned linear state model is then used to design the model prediction controller (DKoopman-MPC) to control the original nonlinear robotic system. The proposed approach is easy to implement and is data-driven without the need for a priori knowledge of model dynamics. Our experiments on mobile robot modeling and control show that the proposed method has higher model fidelity than existing local linearization methods, achieving 79.27% error reduction in the prediction task and has good convergence properties in the control task.