Discrete Adaptive Sliding Mode Control of an Omnidirectional Mobile Robot Using Time Delay Control Method

In this paper, a robust discrete control law is presented, using a time delay control method for an omnidirectional mobile robot in the presence of system uncertainties. Although time delay control method has attracted the great attention of researchers due to its structure simplicity, the major part of these research have been performed by the assumption of continuous time delay control and infinitesimal time delay that is in contradict of physical nature of digital devices, as implementation tools of time delay controllers, which have finite and specific sample time. Also, the discretization of continuous-time systems has been usually done by Euler estimation method, which has sufficient accuracy for infinitesimal sample times. So, in this paper, after modeling the robot, considering the dynamics of robot motors, a new method for more accurate discretization of continuous nonlinear systems is presented and, then, a robust discrete control law is designed, using the backstepping technique at the voltage level of the robot motors. In the design of control law, a new adaptive sliding mode method is used to overcome the system uncertainties and stability of the closed-loop system is proved by error convergence to a small neighborhood of zero. The proposed controller is designed in the discrete domain without the necessity of being known the bound of system uncertainties and simulation results represent the desired performance of the controller in trajectory tracking.