Simultaneous planning and executing (SPAE) control for a fourth-order underactuated inverted pendulum with double-layer asynchronous convergence.

The cart-type inverted pendulum is a typical fourth-order underactuated system that has been widely used in diverse industrial applications. This paper presents a new control method to handle the stability problem of a cart-type inverted pendulum. The system is divided into two second-order subsystems: an inner-layer dynamic system of the rod and an outer-layer dynamic system of the cart. Then a simultaneous planning and executing (SPAE) control method based on double-layer polynomial planning is proposed to make the inner-layer and outer-layer systems asynchronously converge in different time intervals. To achieve this asynchronous convergence, the outer-layer system adjusts the cart displacement. Its goal is to provide a smooth reference angle. The inner-layer system should track this angle quickly and precisely. In contrast to existing control approaches, the proposed method does not require parameter optimization or an accurate nonlinear model. Simulated and experimental results have verified that the proposed control method can achieve the double-layer asynchronous convergence in different time intervals, indicating its superiority over other feedback control approaches.