Model-free tracking control of regular and chaotic trajectories with machine learning

Nonlinear tracking control is fundamental to robotics with a variety of civil and defense applications, the aim of which is to design a control law such that the output of the closed-loop system tracks a given reference signal. In traditional control engineering, designing tracking control requires complete knowledge of the system model and equations. While a problem of great current interest, developing model-free tracking control to track any desired trajectory, regular or chaotic, has remained to be a significant challenge. Here, by exploiting machine learning, we articulate a completely model-free framework to control a two-arm robotic manipulator, where the control objective is to track both simple and complicated trajectories, e.g., periodic and chaotic trajectories, as desired by using only partially observed states. In particular, we employ reservoir computing, a class of recurrent neural networks, as the controller and conduct the training via uniform noise as the control input, through which the reservoir-computing controller learns a mapping between the state error and a suitable control signal. In the testing phase, given the current and desired states, the reservoir controller generates the control signal that enables the robotic manipulator to track any desired trajectories, regular or chaotic. We demonstrate the robustness of our machine-learning based tracking control against measurement noise, disturbances, and uncertainties.