Combining Energy-Shaping Control of Dynamical Systems with Data-Driven Approaches

Machine learning approaches to the problem of control design are flexible, but they demand large databases and computation time for training. Part of this central challenge is due to treating the environment as a black box, ignoring the useful geometric or algebraic structures of the control system. In this work, we propose an efficient data-driven procedure that leverages the known dynamics and techniques from nonlinear control theory in order to design swing-up controllers for underactuated robotic systems. We embed a neural network into the equations of motion of the robotic manipulator through its control input. This control function is determined by the appropriate gradients of a neural network, acting as an energy-like (Lyapunov) function. We encode the swing-up task through the use of transverse coordinates and goal sets; which provides a concise target for the neural network and drastically accelerates the rate of learning. We demonstrate the efficacy and robustness of the algorithm with numerical simulations and experiments on hardware.