Space flights have been useful in scientific investigations and will continue to expand our knowledge about the universe. Future Advances in space exploration demands new approaches to meet the mission requirements. Spacecraft formation flying is one of the most promising technology that gained a lot of attention in recent years. Using multiple small inexpensive spacecraft in a formation flight has several advantages in terms of performance, robustness and financial benefits compared to a single large spacecraft. It enables us to do several tasks that are difficult or impossible to achieve using only the conventional space-based operations. The suitability of spacecraft formation comes at the expense of increased difficulties and introduces
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The relative coupled dynamics were separately modeled using different math tools as two components, the translational part and the rotational part, which then, combined together for control law synthesis. A more elegant and integrated approach to describe the rigid body transformation in three-dimensional space (3-D) is based on dual quaternions. Dual quaternions are an extension of traditional real quaternions and can be obtained by using the dual number theory which introduced by Clifford [6]. It has been shown that among many mathematical methods such as quaternion/vector pairs, homogeneous transformation matrices and Lie algebra, the dual quaternions provide the most compact and computationally efficient way to describe the six-DOF coupling motion of rigid bodies in 3-D space [7]. The authors in [8] employed dual quaternions representation to derive the coupled dynamics of relative motion in spacecraft formation. Based on the proposed model, a finite-time sliding mode controller is developed which ensures the finite-time convergence of tracking errors. They also present a finite-time adaptive sliding model controller with adaptation laws to account for model uncertainties and external disturbances which drive the relative motion to a desired trajectory [9]. An advantage of this technique is that the prior information of the upper bound of the system uncertainties …show more content…
Unlike the previous models, the proposed formulation excludes complicated expressions in system dynamics which leads to simplicity and compactness of the model. Moreover, based on the presented model, an adaptive fault-tolerant nonsingular terminal sliding mode controller is presented. The proposed controller not only has the capacity to tackle the problems of saturation and failure in actuator together, it overcomes the issue of singularity which associated in previously finite-time controllers such as [15]. Also, With the online adaptive estimation laws, there are no requirements on prior information about the bounds of uncertainties and faults in actuators. Using Lyapunov’s direct approach, the finite-time stability of the closed-loop system in both the reaching phase and the sliding phase is guaranteed. Numerical simulations indicate that when dealing with external disturbances, uncertain mass and inertia matrix, actuator faults and control input saturation concurrently, the proposed control technique has better performance compared with previous controllers presented in
The relative coupled dynamics were separately modeled using different math tools as two components, the translational part and the rotational part, which then, combined together for control law synthesis. A more elegant and integrated approach to describe the rigid body transformation in three-dimensional space (3-D) is based on dual quaternions. Dual quaternions are an extension of traditional real quaternions and can be obtained by using the dual number theory which introduced by Clifford [6]. It has been shown that among many mathematical methods such as quaternion/vector pairs, homogeneous transformation matrices and Lie algebra, the dual quaternions provide the most compact and computationally efficient way to describe the six-DOF coupling motion of rigid bodies in 3-D space [7]. The authors in [8] employed dual quaternions representation to derive the coupled dynamics of relative motion in spacecraft formation. Based on the proposed model, a finite-time sliding mode controller is developed which ensures the finite-time convergence of tracking errors. They also present a finite-time adaptive sliding model controller with adaptation laws to account for model uncertainties and external disturbances which drive the relative motion to a desired trajectory [9]. An advantage of this technique is that the prior information of the upper bound of the system uncertainties …show more content…
Unlike the previous models, the proposed formulation excludes complicated expressions in system dynamics which leads to simplicity and compactness of the model. Moreover, based on the presented model, an adaptive fault-tolerant nonsingular terminal sliding mode controller is presented. The proposed controller not only has the capacity to tackle the problems of saturation and failure in actuator together, it overcomes the issue of singularity which associated in previously finite-time controllers such as [15]. Also, With the online adaptive estimation laws, there are no requirements on prior information about the bounds of uncertainties and faults in actuators. Using Lyapunov’s direct approach, the finite-time stability of the closed-loop system in both the reaching phase and the sliding phase is guaranteed. Numerical simulations indicate that when dealing with external disturbances, uncertain mass and inertia matrix, actuator faults and control input saturation concurrently, the proposed control technique has better performance compared with previous controllers presented in