Disturbance Estimation and Predefined-Time Control Approach to Formation of Multi-Spacecraft Systems

Accurate sensing and control are important for high-performance formation control of spacecraft systems. This paper presents a strategy of disturbance estimation and distributed predefined-time control for the formation of multi-spacecraft systems with uncertainties based on a disturbance observer. The process begins by formulating a kinematics model for the relative motion of spacecraft, with the formation's communication topology represented by a directed graph for the formation system of the spacecraft. A disturbance observer is then developed to estimate the disturbances, and the estimation errors can be convergent in fixed time. Following this, a disturbance-estimation-based sliding mode control is proposed to guarantee the predefined-time convergence of the multi-spacecraft formation system, regardless of initial conditions. It allows each spacecraft to reach its desired position within a set time frame. The results of the analysis of the multi-spacecraft formation system are also provided. Finally, an example simulation of a five-spacecraft formation flying system is provided to demonstrate the presented formation control method.