Prescribed-Time Fractional Order Control of DWR via Time-Varying Scaling Function

This study focuses on a differential wheeled robot's (DWR) prescribed-time fractional order position control. Firstly, based on the kinematic model of DWR, a distance-related orientation error is designed using the inverse sine function. Based on this, an improved linear velocity constraint function is proposed. Compared with existing methods, while ensuring the correlation between velocity and orientation error, the multibalance point risk caused by large angle errors is avoided. Then, a prescribed-time fractional order position controller based on a time-varying scaling function is proposed to stabilize the kinematic system of DWR in the prescribed time. This controller can stabilize the position control system of the DWR in a prescribed time by adjusting the prescribed-time parameter, avoiding the infinite gain risk in traditional prescribed-time controllers. Finally, through numerical simulation, we verify that the proposed control law can converge the system status of DWR to the bounded interval in the prescribed time.