Control of an Inverted Pendulum by Learning Swing-up Trajectory

A new algorithm is proposed for learning the swing-up trajectory of an inverted pendulum. In this algorithm input trajectories of the actuator to drive an inverted pendulum are iteratively improved to optimize the performance index which evaluates the feasibile swing-up trajectory to stabilize the pendulum. Input trajectories are described by B-spline curves and their control points are improved by Complex Methed, one of the nonlinear optimization techniques. This algorithm is effective in generating trajectories of real dynamical systems, since the Complex Method needs no gradient of the performance index. The proposed algorithm is applied to obtain a trajectory of direct-drive motor to control an inverted pendulum. The number of iteration times to learn is not so large and the obtained trajectory is satisfactory for stabilizing the pendulum.