Adaptive tracking control for omnidirectional mobile robots with full-state constraints and input saturation

The omnidirectional mobile robot (OMR), which is different from the two-wheeled differential drive mobile robots, can achieve three-degree-of-freedom motion in a plane with no non-holonomic constraint. Therefore, this type of robot has been widely used in many fields owing to its superior maneuverability and controllability. In practical applications, the trajectory tracking problem of the OMRs is a key issue that requires an urgent solution. The challenges with respect to the tracking performance can be categorized into the following: first, the parameter uncertainty of the OMR model and external disturbances affect the accuracy of the control. Second, on account of the limited workspace and the security requirements, the positions, attitudes, and speeds of the OMRs are subject to state constraints during the tracking process. Finally, the limited capability of the actuators can lead to input saturation, which will further degrade the tracking performance or even result in failure to track the desired trajectory. Thus, this study investigates the trajectory-tracking control problem of the OMRs with full-state constraints and input saturation. The kinematics and dynamics for a class of three-wheeled omnidirectional mobile robots were presented with the model uncertainties and external disturbance. Moreover, the barrier Lyapunov method was applied to handle the state constraints using the backstepping technique so that none of the state variables violated the restrictions. Meanwhile, adaptive control laws were designed to deal with the parameter uncertainties and unknown bounded disturbance. Moreover, an anti-windup compensator was adopted to ensure the input torque of the robot met the input constraints. The Lyapunov theory was used to prove that all the signals in the closed-loop system were uniformly bounded when the control parameters were selected suitably. Finally, using numerical simulations, the proposed robust adaptive controller was compared with other controllers, and the results verify the effectiveness and robustness of the proposed method.