Model free adaptive control of the under-actuated robot manipulator with the chaotic dynamics.

Development of practical control approaches for the under-actuated chaotic systems such as the robot manipulators are challenging due to the unpredictable character of the chaotic dynamics, and the inevitable real-time application properties like delays, saturations, and uncertainties In this paper, we propose a model free digital adaptive control approach, which considers the time delay of the control signal, actuator saturation, and non-parametric uncertainties, for an under-actuated manipulator. We also develop a chaos control to learn the unbiased and smooth digital control policy inside the chaotic regions of the continuous time under-actuated manipulator. We perform real-time experiments in a dynamic environment with the proposed digital adaptive control. Then we compare the results of the learning and control with and without chaos control. We observe that the proposed model free adaptive control approach can accurately learn both the long-term predictor and unbiased control policy even in the chaotic regions of the under-actuated robot manipulator.