Control of a wheeled robot in presence of sliding of wheels using adaptive backstepping method

There exist satisfactory results in the analysis of the motion control of the vehicles with the assumption of nonslip (pure rolling) condition of robot wheeles, But unfortunately in practice due to the presence of uncertainties such as sliding of wheels especially in agriculture applications where working conditions are rough the results and the quality of the control performance of the system are affected. The ideal control of wheeled systems is performed with the assumption of the existence of nonholonomic non-slip constraints, while in the real system these constraints are violated due to the presence of slippages. In this paper the problem of trajectory tracking control of wheeled vehicles in the presence of sliding is addressed. To take sliding effects into account, sliding models are introduced into the kinematic model. In other words, these effects are added as unknown parameters to the ideal kinematic model. For taking into account the sliding effects their mathematical models are introduced in system kinematic model. In another word these effects as an unknown parameters are added to the system ideal kinematics. An integrating parameter adaptation technique and backstepping control algorithm has been utilized in order to control the system. The backstepping control law is designed to track the reference trajectories and make the robot asymptotically stable around the reference trajectories. Finally, the obtained results are presented for tracking reference trajectories and comparison results shows the efficiency of using the estimation of slips in control of the system.