Abstract—Twisting, second order sliding mode control is presented to accommodate the thruster faults in the nonlinear MIMO picosatellite formation flying system with unknown time-varying disturbances. Robustness and stability of the proposed scheme is proved using twisting algorithm and its capability for formation keeping demonstrated against periodic thruster faults and external disturbances through simulations. Keywords— Fault tolerant control; second order sliding mode control; twisting algorithm; satellite formation flying I. INTRODUCTION pacecraft formation flying (SFF) is defined as a cluster of small spacecrafts for the distribution of a large spacecraft which any of the spacecraft dynamic states are coupled through a common control law [1]. The multiple smaller satellite formation has several benefits including low consumption of fuel for launch operation, increased aperture size, easier satellite design and upgrade, lower cost, higher flexibility, redundancy and reliability. Satellite formation flying has been recently utilized in many space and geosciences [2]-[4]. In the satellite formation flying accurate control of the follower relative to the leader as reliably as possible, is necessary [6]-[11]. Most of the reported SFF control approaches are based on the linearized spacecraft motion dynamics, viz., Clohessy–Wiltshire equations [5]. The rendezvous problem of spacecrafts (leader/follower) using traditional linear control techniques to regulate relative positions was reported as the initial work on SFF [6]. Since Clohessy–Wiltshire equations neglect the influence of nonlinear and perturbation terms on the relative motion dynamics, control designs based on its equations could yield acceptable performance only for specific operating conditions. Wong et al. [7] considered an adaptive tracking controller. Yeh et al. [8] introduced robust sliding mode control to the SFF problems. More recently, Liu et al. [9], [10] respectively developed conventional and terminal sliding mode control for the SFF based on the nonlinear model with bounded uncertainties. Moreover, Shtessel et al. [11] improved sliding mode control of the SFF by using continuous control law base on high order sliding modes. But in that investigation, robust controller designs are based on linearized model in which linearization residuals are treated as unknown disturbances. In this work, we propose a second order sliding mode control law based on nonlinear dynamics instead of CW. In the last two decades, Fault Detection and Isolation (FDI) problem has been studied extensively [12]-[13]. Saif et al. [14] proposed a robust fault detection and diagnosis scheme for a multiple satellite formation flying system using second order sliding mode observers and wavelet networks. More recently, Khorasani et al. [16]-[17] proposed several innovative fault accommodation methodologies for the SFF in deep space. Control of systems with component failures known as fault tolerant control [15] is a challenging problem and is addressed in this study for the SFF. The proposed fault tolerant control for the SFF is based on the second order sliding mode control which has not been studied in the existing literature. II. SATELLITE FORMATION FLYING SYSTEM MODEL In the nonlinear SFF system model describing the position dynamics of follower satellite relative to a leader satellite used here, the leader satellite is moving in a circular orbit and the satellites are modeled as point masses and therefore the rotational dynamics of the satellites are not taken into account . In Fig.1. Let  1 ={, , } be the inertial coordinate system attached to the center of the earth in origin. () ∈ℝ 3 is the position vector from the origin of the inertial coordinate frame to the leader satellite. Moreover, according to Fig.1, the Fig.1. Schematic representation of the SFF system satellite with the   -axis pointing along the direction of vector (), the   -axis pointing along the orbital angular momentum of the leader satellite, and   -axis being mutually Fault Tolerant Control of Satellite Formation Flying Using Second Order Sliding Mode Control M. Saif 1 , B. Ebrahimi 2 , M. Vali 3 1 School of Engineering Science, Simon Fraser University, Vancouver, BC Canada 2 Aerospace Research Institute, Ministry of Science, Research, and Technology, Tehran, Iran 3 School of Mechanical Engineering, Kashan University, Kashan, Iran S 978-1-4577-0653-0/11/$26.00 ©2011 IEEE 2015