The Joint Spacecraft Rendezvous In Close Proximity Based On The PD Sliding Surface

Spacecraft rendezvous and docking refers to the technology that tracking spacecraft and target spacecraft rendezvous at the same time and at the same place at the same speed and form a body.It plays a vital role in in-orbit service,capture of failed satellites,maintenance and supply of space station and so on.In complex space missions,the precision requirements of spacecraft rendezvous and docking are gradually improving.When two spacecraft are very close to each other,not only the orbit but also the attitude of the spacecraft should be considered when rendezvous.Based on the close rendezvous of cooperative and non-cooperative target spacecraft,this paper mainly studies the joint control problem of attitude and orbit based on PD sliding mode surface.Geocentric equatorial coordinate system is established,the spacecraft body coordinate system,coordinate system,such as,the relationship between the coordinate system is described by using transformation matrix,introduce the spacecraft orbit root number and the number of classical orbit dynamics equation of the track number was deduced and the relative coordinates of state vector conversion relationship,when the spacecraft orbit earth flight,the flight path close to the circular trajectory,At this time,the denominator of the classical orbital root number equation is zero,which cannot be solved,so the improved equinox orbital dynamics equation is adopted.The relative motion equations between the tracking spacecraft’s centroid and the target spacecraft’s centroid are derived,and the nonlinear relative motion dynamics equations are obtained by simplifying the approximate and equivalent forms.On this basis,the relative orbit dynamics model between the docking ports of the spacecraft is established.The method to describe the attitude of the spacecraft is derived in detail,expounds the MRPs gesture description method,in order to avoid the singular equation in the special Angle,introduced the shadow MRPs as switching,three parameters such as the attitude Angle in three directions,there is no extra parameters,has certain advantages.The non-negligible perturbation force and perturbation moment of spacecraft close rendezvous are modeled,and the perturbation force and perturbation moment of spacecraft are analyzed.The relative motion of spacecraft only under the action of perturbation force and perturbation moment is described in detail through a simulation example,which proves that the perturbation force and perturbation moment are non-negligible.Firstly,the sliding mode control and PID control methods are introduced,and then the PD sliding mode surface control method used in this paper is introduced.The specific framework of the control problem is described,and the nonlinear dynamics equation of the relative motion of the spacecraft is selected.Considering the main factors affecting the spacecraft’s relative motion in short distance,such as the earth’s non-spherical gravitational perturbation and the solar pressure perturbation,the switching function in the form of PD was designed.When the system was in the switching plane,it was in the sliding mode region.The sliding mode stability was analyzed.When the first derivative of Lyapunov function is less than or equal to zero,the sliding mode is asymptotically stable according to Lyapunov stability theory.The asymptotic stability of the control rate is proved by selecting the exponential reaching law and deducing the control rate,and similarly designing the Lyapunov function.The rendezvous is completed when the relative distance,velocity,attitude and angular velocity of the tracking spacecraft approach zero with the nominal trajectory.Due to the abrupt change of the symbol function at zero,the chattering phenomenon of the calculation results is obvious.In order to suppress the chattering,the exponential approaching law is improved and the reaching law of the form of saturated function is designed to effectively weaken the chattering phenomenon.The influence of the control parameter k on the convergence speed is analyzed,and the control parameter k and the convergence time are plotted into a table and curve to facilitate the observation of the law more intuitively.For non-cooperative target spacecraft rendezvous up close,observation coordinate system is established,in the observation system of two spacecrafts orbit and attitude motion model,using the tracking spacecraft observer to the target spacecraft pose rail for data collection,and then design the desired trajectory and expectation,when the target spacecraft to desired trajectory and expectations,The close rendezvous is complete.In the case of non-cooperative target,the feasibility of the improved approach law is verified by a numerical example,and the relationship between the control parameters and the convergence time is shown in a graph.