Singularity-Avoidance Prescribed Performance Control for Spacecraft Attitude Tracking

The attitude tracking control problem with preassigned performance requirements has earned tremendous interest in recent years, and the prescribed performance control (PPC) scheme is often adopted to tackle this problem. Nevertheless, traditional PPC schemes may suffer singularity problems when the expected state constraint is violated. This may cause a decrease in the control effect or even instability of the system. Motivated by this issue, this article proposes a singularity-avoidance PPC scheme (SAPPC) to deal with these problems, of which the core is a shear-mapping-based error transformation procedure that globally transforms the original error state without singularity. Based on the presented nonsingular error transformation, this article presents a perspective to guarantee the satisfaction of given transient performance requirements by leading the state trajectory converging along a preassigned smooth trajectory called reference performance function (RPF). Based on the concept of the RPF, this article naturally adopts an error-defined-type state constraint, providing a time-varying constraint boundary and alleviating the potential overcontrol problem at the steady state. Furthermore, in order to validate the proposed SAPPC scheme, a simple backstepping controller is developed by employing the predefined-time stability technique and the dynamic surface control technique. Finally, theoretical analysis and numerical simulation results are presented to validate the proposed control scheme's effectiveness and robustness.