Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

Abstract

This paper investigates the control of Back-and-Forth motion to fetch object and Lower-Raise-Head motion to avoid obstacle of the wheeled inverted pendulum system with an input delay. In controlling the Back-and-Forth motion, the linear optimal control theory is used because the tilt angle of the pendulum is forced to be small enough by minimizing a quadratic performance criterion with large weight of tilt angle error, and the controller is represented by using predictor-based feedback. In controlling the Lower-Raise-Head motion, linearized models do not work due to the strong nonlinearity caused by big tilt angle for avoiding obstacle. Without considering yaw movement, the wheeled inverted pendulum system is decoupled, the subsystem governing the state of the tilt angle is transformed into a simple linear system by using feedback linearization. With a properly chosen trajectory tracking target, the control of Lower-Raise-Head motion is solved on the basis of optimal trajectory tracking control for linear subsystems with an input delay. Numerical simulations illustrate the effectiveness of the proposed approaches.