Fixed-Time and Prescribed-Time Image-Based Visual Servoing with Asymmetric Time-Varying Output Constraint

This paper addresses image-based visual servoing with the field-of-view limitation of the camera. A novel control method is proposed with dual constraints based on fixed-time and prescribed-time convergence. With the introduction of a prescribed-time performance function and an asymmetric barrier Lyapunov function, asymmetric time-varying output constraints are achieved. This ensures that the image features remain within the predefined range, thereby addressing the field-of-view constraint problem in visual servoing applications. The combination of the prescribed-time performance function and the fixed-time stability theory ensures that the tracking error converges to a predetermined range within a prescribed time. Furthermore, it can converge to zero in fixed time, thus significantly improving the error convergence rates. The effectiveness and superiority of the method are demonstrated through physical experiments. Moreover, a case study of a contact network component bolt alignment task, aiming at automatically aligning a sleeve to a bolt, is carried out to demonstrate the applicability of the proposed method in practice.