Research On Spacecraft Relative Position And Attitude Coupled Control On The Basis Of Second-order Sliding Mode Algorithm

Autonomous on-orbit servicing technology has received widespread attention for some of the most extraordinary successes in space exploration. In terms of cost effeciency, there are potential saving benefits for on-orbit servicing to impaired satellites. So it is significant for on-orbit repair, assemblage and promotion when the target spacecraft is already running in space orbit. The ability to automatically perform rendezvous and docking operation is required for spacecraft in future on-orbit servicing mission with even a free tumbling and out-of-control target spacecraft being involved. As a result, the control algorithm for autonomous rendezvous and docking to an out-of-control target is one of the key technologies. The relative position and attitude coupled control algorithms are mainly studily in this article. They are used to automatically manipulate the rendezvous and docking process with a free tumbling target spacecraft. The coupled controllers between two docking ports are further discussed based on second-order sliding model algorithm. The robustness for model uncertainties and limited disturbance, finite time convergence, and the effectiveness of chattering alleviation and attenuation are analyzed and validated. The main contents are as follows:The relative motion relationships between docking ports on two spacecraft are analyzed. Then, three available docking methords are summarized for different ports at two spacecraft. On this basis, a relative position and attitude coupled dynamic model is established for two docking ports. It is proposed by considering the coupled effect of relative rotation on relative translation. Descriptions of the coupled effect are analyzed as follows: external disturbance torque on spacecraft induces dynamic coupling effect; relative attitude quaternion, relative attitude angular velocity and absolute attitude angular velocity of service spacecraft induce kinematical coupled effect. By mathematical simulation, the coupled effects of relative rotation on relative translation are validated by all kinds of coupled factors in the open-loop relative motion model without control operation. The MATLAB and Satellite Tool Kit(STK) interface program are adapted to build an animation scenario design for vividly describing the whole rendezvous and docking control process. It can prove feasibility, security and reliability of the analyzed three docking methods between different pairs of ports at two spacecraft.In order to improve control features of standard twisting sliding model algorithm, a modified twisting controller with second-order sliding surface is designed. The finite time convergence properties of the motified twisting controller is analyzed by Lyapunov stability theory. Further more, a method for calculating the upper bound of convergence time is obtained. The control characteristics of the proposed modified twisting controller with second-order sliding mode plane are verified by mathematical simulation. For solving the problem that the second-order sliding mode alogrithm has poor poor robustness to restrain perturbations very far away from the origin, two modified twisting cotrollers with different forms of sliding surface are proposed. A new Lyapunov function is chosen to prove its property of finite time convergence and the upper bound for the time convergence is received. Numerical simulations are performed to test their robustnesses for dealing with bounded disturbance far away from the origin. The sums of absulte impulse values by control force and moment of force in steady state are calculated to checkout their chattering alleviation efficacy.By utilizing feature of super twisting(ST) control algorithm, a relative position and attitude coupled ST controller is designed for docking ports at two spacecraft, which is the only exception without calculting time derivation of the sliding mode variable. Its finite time convergence characteristic is analyzed on the basis of Lyapunov stability theory. Moreover, the upper bound of convergence time is calculated. Numerical simulations are performed to verify the issues of stability, convergence property and its robustness to uncertainties and bounded perturbations far away from origin. Homoplastically, the ST alogrithm is combined with linear control method to intensify the robustness for dealing with perturbations far away from origin. New Lyapunov function is chosen to approve that the modified super twisting controller can also converge to the equilibrium point in finite time, and the upper bound of convergence time is calculated. The contrast simulation is established to validate its robustness for different forms of bounded perturbations and uncertainties. Moreover, cumulative sums of absulte impulse vaules by steady control force and moment of force are used to test its chattering alleviation and attenuation effect in the actuating mechanism.In order to further improve the robustness of second-order sliding mode controller for dealing with bounded perturbations very far away from the origin, adaptive algorithm is used to dynamically calculate the gain matrix of controller. By considering the two situations: bounded perturbation with known upper bound and limited disturbance with unknown upper bound, two adaptive super twisting controllers are proposed, denoted by AST1 and AST2 respectively, with both parameter uncertainties and relative navigation errors. Lyapunov stability theory is adopted to ensure the convergence in finite time of all trajectoies of system to zero. At the same time, the upper bound of convergence time is calculated. Numerical simulations are performed to verify the robustness to limited different bounded disturbance and parameter uncertainties. Simultaneously, their efficacy to reduce the chattering effect in the actuating mechanism is proved by calculating the cumulative sums of abslute impulse values resulted from control force and moment of force in steady state. By comparing the two adaptive sliding mode controllers, AST2 controller has more extensive adaptability and it has stronger robustness to bounded disturbance very far away from the origin under the condition of the same control parameters.