Finite Time Trajectory Tracking of a Mobile Robot Using Cascaded Terminal Sliding Mode Control Under the Presence of Random Gaussian Disturbance

Abstract

In this paper, dynamic modeling of a differential drive mobile robot (DDMR) using Langrage formulation and terminal sliding mode trajectory tracking control is presented. The proposed controller is a cascaded controller designed to improve the dynamic response of the system, i.e. kinematic and dynamic problems, asymptotical convergence, and chattering problem using terminal sliding mode control (TSMC). The terminal sliding mode control provides faster convergence and higher-precision control than the conventional linear hyperplane sliding control which guarantees the asymptotic stability. This is due to fact that the terminal sliding mode control system guarantees a finite time convergence to the sliding phase. The entire control design consists of an outer loop kinematics control and inner loop speed control system. Here, outer kinematic control system provides an appropriate velocity control input for the inner loop angular velocity control of each wheel. An angular and linear velocity control input is designed in order to make angular and posture error to converge to zero in a finite time based on global fast terminal sliding mode control (GFTSMC). Then, the inner loop GFTSMC of the robot is designed to ensure that the tracking error between the actual and desired angular velocity of each wheels converges to zero in a finite time. Both the inner and outer closed loop controllers achieve path following in a finite time and avoids high frequency switching in the closed loop such that the overall dynamic response of the system is improved using the cascaded control technique and the stability of each controller was checked using lyapunov criteria. Generally, the proposed control system shows the performance and effectiveness of the proposed method compared to conventional SMC, and the simulation results indicate good convergence and robustness of the system for circular trajectories under both model uncertainty and random Gaussian disturbances using GFTSMC.