Robust Adaptive Backstepping in Tracking Control for Wheeled Inverted Pendulum

Abstract

The previous papers (Olfati-Saber PhD. thesis, 2001) [1], (Khac Duc Do, Gerald Journal of Intelligent and Robotic Systems 60(3), 2010) [2] (Wei et al. Automatica, 841–850 1995) [3] applied feedback linearization or global change coordinates to separate system model into rotate and straight movement, leading to difficulty in control design for uncertain parameter systems. Additionally, paper (Culi et al. Nonlinear control of a swinging pendulum. Automatica 31(6), 1995, 851–862) [4] presenting robust adaptive law ignored time-varying inertia matrix to design control Lyapunov function (CLF) easily, leading to wrong theoretical proof. In this paper, we propose a new adaptive law and a new controller to control WIP system, in that the error tracking of heading angle and position is bounded and tilt angle converges to the small arbitrary ball of origin and tracking position, which is not be ensured (Culi et al. Nonlinear control of a swinging pendulum. Automatica 31(6), 1995, 851–862) [4] (Li et al. Automatica 2010, 1346–1353) [5]. Moreover, time-varying inertia matrix is considered to choose a proper CLF via backstepping technique. The simulation results are implemented to demonstrate the performances of the proposed adaptive law and controller.