Reinforcement learning control of four degree of freedom inverted pendulum

In this paper, a robust linear quadratic regulator (LQR) based Reinforcement learning method is designed for a four degree of freedom inverted pendulum. The considered system contains a four degree of freedom inverted pendulum with a concentrated mass at the tip of it. The bottom of inverted pendulum is moved in x-y plane in x and y directions. For tracking control of two angles of inverted pendulum, two plane forces are applied in x and y directions at the bottom of pendulum. The governing equations of the system are derived using the Lagrange method and then a robust linear quadratic regulator (LQR) based Reinforcement learning controller is designed. The inverted pendulum is learned for a range of different angles, different lengths and different masses. The parametric uncertainties are defined as various lengths and masses of inverted pendulum and the disturbances are defined as impact and continuous forces which are applied on the inverted pendulum. After learning, the controller can learn online the system for any arbitrary angle, length, mass or disturbance which are not learned in the defined range. Numerical results show that the good performance of the reinforcement learning controller for the inverted pendulum in the presence of structural and parametric uncertainties, impact and continuous disturbances and sensor noises.