CN115675942A - Tracking control method, apparatus, and medium considering input saturation and motion constraint - Google Patents
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Abstract
The embodiment of the invention discloses a tracking control method, a device and a medium considering input saturation and motion constraint, wherein the method comprises the following steps: constructing a desired translation for a desired distance between the serving spacecraft and the target spacecraft; constructing a desired attitude of a serving spacecraft for a line-of-sight angular pointing constraint between the serving spacecraft and a target spacecraft; aiming at task requirements in an on-orbit service process, translation and rotation constraint conditions are constructed; constructing an MPC controller aiming at the relative position with the aim of minimizing fuel and tracking error based on the expected translation and the translation constraint condition; acquiring an expected angular speed through an MPC angular speed planning module based on the expected attitude and the rotation constraint condition of the service spacecraft; and designing a self-adaptive anti-saturation sliding mode controller according to the expected angular velocity, and processing the problem of control moment saturation through an anti-saturation auxiliary system to obtain an attitude controller for pointing tracking.
Description
Technical Field
The embodiment of the invention relates to a spacecraft control technology, in particular to a tracking control method, a device and a medium considering input saturation and motion constraint.
Background
As the number of space vehicles increases, more and more space vehicles are sent into the space to perform specific tasks, however, some failed and even uncontrolled non-cooperative target space vehicles pose threats to other on-orbit normally-operated space vehicles, and therefore, the service space vehicles need to approach such non-cooperative target space vehicles and perform on-orbit maintenance or clearing on the non-cooperative target space vehicles. Based on this, the service spacecraft can quickly approach the non-cooperative target and perform a specific tracking and pointing task aiming at the non-cooperative target, which is the key to complete the space tasks such as on-orbit maintenance or cleaning of the non-cooperative target spacecraft.
Relative pose coupling is often involved for quickly approaching and performing specific track-and-point tasks for non-cooperative targets. In a conventional scheme, a potential function method is usually adopted to process the pose tracking problem under motion constraint, namely, a motion forbidden region is described by a repulsive potential function, an expected region is described by an attractive potential function, and finally, an attractive potential field and a repulsive potential field are superposed to obtain virtual resultant force to act on a spacecraft so as to complete a target task under motion constraint; however, the potential function has common disadvantages that it is easy to fall into a local minimum value, and that the constraint may be violated in the case of input saturation, so that the system cannot obtain an ideal large control torque to meet the constraint requirement in the case of limited actual actuator. In addition, under the framework of attitude and orbit integrated modeling, when the model prediction control method is used for processing pose coupling dynamics with high nonlinearity degree, complex linearization problems and large calculation consumption need to be faced, and under the motion constraint, the calculation amount is huge, so that a large amount of calculation consumption is generated, and great challenge is provided for the calculation capacity of the spaceborne computer.
Disclosure of Invention
In view of the above, embodiments of the present invention are directed to a tracking control method, apparatus, and medium considering input saturation and motion constraints; the situation of falling into a local minimum value can be avoided, the requirement on the output capability of an execution mechanism is not high, the problem of safety approach in an in-orbit service task can be well solved, and the attitude dynamic angular speed of the service spacecraft is optimal in real time under the constraint of fuel and error; in addition, the purpose of reducing the calculation amount is achieved through the dimension reduction optimization problem, and the calculation consumption is reduced.
The technical scheme of the embodiment of the invention is realized as follows:
in a first aspect, an embodiment of the present invention provides a tracking control method considering input saturation and motion constraint, where the method includes:
constructing an expected translation for an expected distance between a serving spacecraft and a target spacecraft;
constructing a desired attitude of a serving spacecraft for a line-of-sight angular pointing constraint between the serving spacecraft and a target spacecraft;
constructing constraint conditions of translation and rotation aiming at task requirements in an on-orbit service process;
constructing a Model Predictive Control (MPC) controller aiming at the relative position by taking minimized fuel and tracking error as targets based on the constraint conditions of the expected translation and the translation;
acquiring an expected angular speed through an MPC angular speed planning module based on the expected attitude and the rotation constraint condition of the service spacecraft;
and designing a self-adaptive anti-saturation sliding mode controller according to the expected angular speed, and processing the control moment saturation problem through an anti-saturation auxiliary system to obtain an attitude controller for pointing tracking.
In a second aspect, an embodiment of the present invention provides a tracking control apparatus considering input saturation and motion constraints, where the apparatus includes: a first build portion, a second build portion, a third build portion, a first design portion, an acquisition portion, and a second design portion, wherein,
the first build portion configured to build a desired translation for a desired distance between a serving spacecraft and a target spacecraft;
the second building portion configured to build the desired attitude of the serving spacecraft for a line of sight angular pointing constraint between the serving spacecraft and a target spacecraft;
the third construction part is configured to construct constraint conditions of translation and rotation aiming at task requirements in an on-orbit service process;
the first design part is configured to construct a Model Predictive Control (MPC) controller aiming at relative position with the aim of minimizing fuel and tracking error based on the constraint conditions of the expected translation and the translation;
the acquisition part is configured to acquire an expected angular velocity through an MPC angular velocity planning module based on an expected attitude and a rotation constraint condition of the service spacecraft;
the second design part is configured to design an adaptive anti-saturation sliding mode controller according to the expected angular speed, and process a control moment saturation problem through an anti-saturation auxiliary system to obtain a posture controller for pointing tracking.
In a third aspect, an embodiment of the present invention provides a computing device, where the computing device includes: a communication interface, a memory and a processor; the various components are coupled together by a bus system; wherein,
the communication interface is used for receiving and sending signals in the process of receiving and sending information with other external network elements;
the memory for storing a computer program operable on the processor;
the processor is configured to execute the steps of the tracking control method according to the first aspect, which takes into account input saturation and motion constraints, when running the computer program.
In a fourth aspect, an embodiment of the present invention provides a computer storage medium, where a tracking control program considering input saturation and motion constraint is stored, and when being executed by at least one processor, the tracking control program considering input saturation and motion constraint realizes the steps of the tracking control method considering input saturation and motion constraint according to the first aspect.
The embodiment of the invention provides a tracking control method, a device and a medium considering input saturation and motion constraint; firstly, designing a model predictive controller for relative position approach, wherein the model predictive controller can not only complete relative position control under constraint, but also provide a predicted state sequence for the expected attitude design method provided by the text; then a double-layer controller for attitude pointing tracking is designed, namely a model prediction control part for optimal angular velocity planning and an adaptive sliding mode controller for angular velocity tracking, compared with a model which simultaneously disperses and linearizes attitude dynamics and kinematics as an optimization model, the optimal expected angular velocity is obtained, and simultaneously, the dimensionality of an optimization problem can be reduced so as to further improve the calculation efficiency; in addition, in order to reduce the requirement of larger moment brought by larger error in the early period, an anti-saturation system is introduced. Since the desired angular velocity is already optimal, the controller has a lower demand on the output capacity of the actuator, in addition to the action of the auxiliary system. Compared with a potential function method, the method can not only ensure that the service spacecraft completes the approaching and pointing tracking tasks at suboptimal speed, but also ensure that the control input meets the requirements of engineering application.
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Fig. 1 is a schematic flowchart of a tracking control method considering input saturation and motion constraint according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of the relative positions of a serving spacecraft and a target spacecraft provided in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of orientation constraints provided by an embodiment of the present invention;
fig. 4 is a schematic flowchart of an embodiment of a tracking control method considering input saturation and motion constraint according to an embodiment of the present invention;
FIG. 5 (a) is a schematic diagram of relative position tracking error of a simulation experiment;
FIG. 5 (b) is a diagram illustrating the tracking error of the relative velocity in the simulation experiment;
FIG. 6 (a) is a diagram illustrating a relative position shift trajectory in a simulation experiment;
FIG. 6 (b) is a schematic diagram of the optical axis attitude trajectory of a simulation experiment;
FIG. 7 is a schematic diagram of control torque of a simulation experiment;
FIG. 8 is a schematic diagram of a tracking control device in accordance with an embodiment of the present invention, in which input saturation and motion constraints are taken into account;
fig. 9 is a schematic diagram of a specific hardware structure of a computing device according to an embodiment of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
Referring to fig. 1, a tracking control method considering input saturation and motion constraint according to an embodiment of the present invention is shown, where the method may include:
s101: constructing a desired translation for a desired distance between the serving spacecraft and the target spacecraft;
s102: constructing a desired attitude of a serving spacecraft for a line of sight angular pointing constraint between the serving spacecraft and a target spacecraft;
s103: aiming at task requirements in an on-orbit service process, translation and rotation constraint conditions are constructed;
s104: constructing a Model Predictive Control (MPC) controller aiming at the relative position by taking minimized fuel and tracking error as targets based on the constraint conditions of the expected translation and the translation;
s105: acquiring an expected angular speed through an MPC angular speed planning module based on the expected attitude and the rotation constraint condition of the service spacecraft;
s106: and designing a self-adaptive anti-saturation sliding mode controller according to the expected angular speed, and processing the control moment saturation problem through an anti-saturation auxiliary system to obtain an attitude controller for pointing tracking.
For the technical scheme shown in fig. 1, a model predictive controller for relative position approach is designed first, which not only can complete relative position control under constraint, but also can provide a predicted state sequence for the expected attitude design method proposed herein; then, a double-layer controller for attitude pointing tracking is designed, namely a model prediction control part for optimal angular velocity planning and an adaptive sliding mode controller for angular velocity tracking, compared with the mode that attitude dynamics and kinematics are dispersed and linearized simultaneously to serve as an optimization model, the optimal expected angular velocity is obtained, and meanwhile, the dimensionality of an optimization problem can be reduced to further improve the calculation efficiency; in addition, in order to reduce the requirement of larger moment brought by larger error in the early period, an anti-saturation system is introduced. Since the desired angular velocity is already optimal, the controller has a lower demand on the output capacity of the actuator, in addition to the effect of the auxiliary system. Compared with a potential function method, the method can not only ensure that the service spacecraft completes approaching and pointing tracking tasks at suboptimal speed, but also ensure that control input meets the requirements of engineering application.
For the technical solution shown in fig. 1, in some possible implementations, the constructing the desired translation for the desired distance between the serving spacecraft and the target spacecraft includes:
setting the expected motion parameters of the service spacecraft in the body coordinate system of the target spacecraft as follows:
wherein ρ d Representing the expected position of the service spacecraft, wherein t is a left superscript representing a body coordinate system of the target spacecraft; l. the d Representing a desired distance between the serving spacecraft and the target spacecraft;
transferring the expected motion parameters of the service spacecraft in the target spacecraft body coordinate system to an LVLH coordinate system, and obtaining the expected motion parameters of the service spacecraft in the LVLH coordinate system as follows:
the expected position of the service spacecraft in the LVLH coordinate system is as follows:
the expected speed of the service spacecraft in the LVLH coordinate system is as follows:
the expected acceleration of the service spacecraft in the LVLH coordinate system is as follows:
wherein,
representing a coordinate system Ox consisting of the body of the target spacecraft t y t z t To the earth's center inertial coordinate system Ox I y I z I The transition matrix of (a);
representing an inertial frame Ox by the centre of the earth I y I z I (hereinafter may be simply referred to as an inertial system) to the LVLH coordinate system; omega tL Representing the angular velocity, ω, of the target spacecraft relative to the LVLH coordinate system tL ＝ω tI -ω LI ，ω tI Representing the target spacecraft relative to the earth's center inertial frame Ox I y I z I Angular velocity of (a) ([ omega ]) LI Representing a serving spacecraft orbit angular velocity; i is a left superscript representing the centroid inertial coordinate system Ox I y I z I (ii) a L is a left superscript representing an LVLH coordinate system;
correspondingly, the construction of the constraint conditions of the translation aiming at the task requirements in the in-orbit service process comprises the following steps:
respectively designing a speed constraint condition and a control input saturation constraint condition aiming at the expected relative position model; wherein the speed constraint condition is:
represents the maximum value of the relative linear velocity under the LVLH coordinate system; the control input saturation constraint conditions are as follows:
u denotes a control input variable.
For the above implementation, it should be noted that, as shown in fig. 2, the Target spacecraft is set on the near-circular orbit, and the relative motion between the serving spacecraft (Service space) and the Target spacecraft (Target space) is described as follows by using the C-W equation:
wherein F = [ F = x ,F y ,F z ] T Representing the control acceleration of the serving spacecraft; x L ＝[x,y,z] T Representing the relative position of the serving spacecraft and the space target under LVLH regime.
Representing the orbital angular velocity of the spatial target; μ =3.98 × 10 14 m 3 /s 2 Is the constant of the earth's gravity; r is t ＝||r t And | | represents the norm of the spatial target radial.
The above C-W equation description is rewritten as a state equation:
wherein,
in the form of a state vector, the state vector,
in order to control the input of the electronic device,
n is the orbital angular velocity of the spatial target.
Discretizing the state equation by taking delta T as sampling time to obtain a discrete state equation of X (k + 1) = A d X(k)+B d F (k), wherein X (k) and F (k) represent state quantities and control inputs of the k-th step after the discretization,
and
are respectively A d ＝e AΔT ，
For the desired relative position model of the serving spacecraft,
p is aligned in LVLH coordinate system d Derived to obtain
The expected speed under the LVLH coordinate system can be obtained by unfolding the linear motor under the LVLH coordinate system; the desired speed is continuously derived
And then can obtain
The desired acceleration in the LVLH coordinate system can be obtained by unfolding the device in the LVLH coordinate system.
For the constraint condition of the translation in the implementation manner, the constraint condition can be constructed according to task requirements or current application scenes, firstly, for the ultra-short distance operation, if some emergency occurs in the process, the specified convergence track needs to be changed in a short time, and the speed constraint should be considered to improve the fault tolerance rate and ensure timely collision avoidance. Thus, the speed constraint can be expressed as:
wherein v is max Is the maximum value of the relative linear velocity in the LVLH coordinate system.
Secondly, in a practical spacecraft system, if the capabilities of the actuators do not meet the ideal inputs required by the control laws, this will lead to problems of input saturation of the actuators. The saturation of the control input employed for the control input in the above equation of state can be described by a linear inequality constraint as
Based on the foregoing implementation and the description thereof, in some examples, the constructing a model predictive control MPC controller for a relative position with the goal of minimizing fuel and tracking error based on the constraints of the desired translation and the translation includes:
setting a prediction time domain to N p Control time domain as N c Serializing the state variables and control inputs in the discrete state equation of the service spacecraft to obtain a state variable sequence X s (k) And a control input sequence F s (k) As follows:
according to the state variable sequence X s (k) And a control input sequence F s (k) Rewriting the discrete state equation of the service spacecraft to X s (k)＝A s X(k)+B s F s (k) (ii) a Wherein,
with the objective of minimizing the relative position tracking error and the control input, the design index function is:
wherein Q is Ii And R Ii Respectively representing positively determined states and control weight matrices, Q Ii The last element in the list is a terminal weight matrix P I ,P I Obtained by solving the discrete time Riccati (Riccati) equation, p d Representing a desired sequence of states;
and converting and expressing the relative position constraint condition into a constraint condition on a control input, and combining the final index function to obtain an MPC controller aiming at the relative position as follows:
wherein,
and
are each v max And D is an augmented matrix of elements.
For the above example, it should be noted that the above example mainly aims to solve the problem of safe approach of the service spacecraft to the rollover target spacecraft when the MPC is used for approaching and maintaining the fault target spacecraft. Under the consideration of thrust constraint and speed constraint, the problem of fuel optimal path tracking MPC, namely the MPC controller mentioned above, is proposed, and the problem can be solved by using the current conventional Quadratic Programming (QP) algorithm.
For the technical solution shown in fig. 1, in some possible implementations, the constructing the desired attitude of the serving spacecraft for the line-of-sight angular orientation constraint between the serving spacecraft and the target spacecraft includes:
relative position of the serving spacecraft to a space target
From Hill coordinate system to geocentric inertial coordinate system
Wherein,
a coordinate transformation matrix representing the Hill coordinate system to the geocentric inertial coordinate system;
expressing the vector of the optical axis direction of the service spacecraft in a geocentric inertial coordinate system:
wherein,
the system is a coordinate transformation matrix from a spacecraft body coordinate system to a geocentric inertial coordinate system;
defining the Euler axis during an attitude maneuver as
Wherein,
representing angle of sight, as vector
And the vector y of the optical axis direction I When the two-way valve is superposed, the two-way valve,
according to the Euler axial angle definition, the attitude deviation of the spacecraft body attitude and the attitude deviation when the expected pointing direction is reached is obtained by quaternion definition:
based on the attitude deviation and the definition of the error quaternion, obtaining an expected attitude as: q. q.s d ＝[q d0 ,-q dv ] T ；
Setting the mathematical description of the attitude constraint condition of the service spacecraft to avoid the bright celestial body appearing in the field of view of the sensor of the service spacecraft
Wherein, y I Representing the optical axis direction vector, S, of said service spacecraft I Representing the direction vector of the bright celestial body,
representing the included angle between the vector of the optical axis direction and the direction of the bright celestial body;
and performing coordinate conversion on the vector of the optical axis direction of the service spacecraft to obtain the following formula:
wherein, (.) × Antisymmetric matrix representing vectoring
Correspondingly, aiming at the task requirement in the in-orbit service process, the constraint condition of rotation is constructed, and the constraint condition comprises the following steps:
obtaining the attitude constraint conditions of the service spacecraft based on the mathematical description of the attitude constraint conditions and the coordinate conversion of the optical axis direction vector, wherein the attitude constraint conditions comprise:
q T k c q≤0
wherein,
y b representing the serving spacecraft body architecture y-axis.
For the above implementation, the unit quaternion may be expressed as
Wherein n is x 、n y And n z Representing the three perpendicular components of the euler axis, respectively, and theta represents the angle of rotation about that axis. The definition of the error quaternion is
The states of the translational motion and the attitude motion of the target spacecraft can be set by the measurement of the service spacecraft, and the target is in an uncontrolled state. Therefore, the attitude dynamics model of the fault target spacecraft which moves freely in the orbit is
Wherein,
a target spacecraft attitude quaternion;
is the moment of inertia of the target spacecraft;
the angular velocity of the target spacecraft relative to the inertial coordinate system under the target spacecraft body coordinate system.
Accordingly, the attitude dynamics model of the serving spacecraft is
Wherein,
serving spacecraft attitude quaternions;
to express in-service spacecraft body coordinate system Ox s y s z s Angular velocity of the serving spacecraft relative to the inertial coordinate system;
to serve the rotational inertia of the spacecraft;
to serve the control moment of the spacecraft.
Based on the attitude dynamics model, the attitude control target of the embodiment of the invention is to point the observation device to the target spacecraft, so that the attitude control target is irrelevant to the relative attitude of the service spacecraft and the target spacecraft, that is, the expected attitude of the embodiment of the invention can be converted from the line-of-sight angular pointing constraint, and the expected attitude design does not need to design the expected angular velocity or even the expected angular acceleration.
In addition, it is important for constraints to avoid bright celestial bodies appearing in the field of view of sensors serving spacecraft during maneuvering, which is important for protecting sensitive elements. As shown in FIG. 3, an additional attitude constraint exclusion zone will be considered to avoid damage to the sensor, that is, the constraint target is the optical axis direction vector y I And the direction S of bright celestial body I Angle therebetween
And if the threshold value is larger than a certain threshold value, the sensor is considered to be in a safe working range. It should be noted that the above-mentioned attitude constraint condition is in the form of a standard quadratic form and it is also a convex quadratic form constraint.
For the foregoing implementation, in some examples, the obtaining, by the MPC angular velocity planning module, the desired angular velocity based on the desired attitude and rotation constraints of the serving spacecraft includes:
sampling and discretizing an attitude kinematics equation described by a quaternion by utilizing a forward Euler method to obtain an original discrete state equation related to the attitude as follows:
q(k+1)＝A t q(k)+B t U(k+1)
wherein, A t ＝E 4 ，B t ＝T s E 4 ，T s Representing the sampling interval, U (k + 1) = B (q (k)) ω (k + 1) represents the input to a discrete equation of state for attitude, including the angular velocity driving the attitude motion;
setting a prediction time domain to be equal to a control time domain, and enabling the predicted state sequence q in the original discrete state equation related to the attitude s And control input sequence U s Represented by:
q s (k)＝(q T (k+1|k),q T (k+2|k),......,q T (k+N p |k)) T
U s (k)＝(U T (k+1|k),U T (k+1|k),......,U T (k+N p |k)) T
prediction-based state sequences q s And control input sequence U s The original discrete state equation about the attitude is sorted into q s (k)＝A s q(k)+B s U s (k) Wherein
the construction of the optimization controller is as follows:
wherein q is e Representing the error quaternion, q ed ＝[1,0,0,0] T ，Q IIIi 、R IIIi Representing a positive definite weight matrix;
introducing an auxiliary variable A according to the constructed optimization controller and the discrete state equation after the arrangement of the attitude v ＝P d A s q(k)-q ed (k) The final MPC controller obtained was:
s.t.q(t+k|t)＝A t q(k|t)+B t U(t+k|t),k＝1,...,N pc -1
q T (t+k|t)K i q(t+k|t)≤λ i ,i＝1,...,n
wherein,
input amplitude, P, representing an original discrete equation of state with respect to attitude d Representing expected attitude information of a prediction time domain, and resolving according to predicted relative position information;
the first control input obtained after the final MPC controller is optimized acts on the discrete state equation after the arrangement of the attitude, and the attitude maneuver angular speed which is optimal in real time under the objective function of the minimum error and fuel is obtained
It should be noted that the above example does not cause the attitude to violate the taboo constraint by linearizing the quaternion attitude kinematics, and on the contrary, the planned maneuvering angular velocity is more conservative due to the error caused by the linearization, so the sensor in the pointing tracking process is further away from the attitude forbidden zone.
For the above example, preferably, the designing an adaptive anti-saturation sliding-mode controller according to the desired angular velocity and processing the control torque saturation problem through an anti-saturation auxiliary system to obtain an attitude controller for pointing tracking includes:
based on the output saturation of the actuating mechanism, the attitude dynamics equation of the service spacecraft is rewritten as follows:
wherein,
u d which represents the overall uncertainty of the system and,
introducing an integral term of an angular velocity tracking error, and designing a nonsingular integral terminal sliding mode surface as follows:
wherein, ω is e ＝ω s -ω d Indicating the error angular velocity, s q ＞s p > 0 is a positive number to be designed,
is a positive definite diagonal matrix;
based on avoiding the actuator saturation, the anti-saturation auxiliary system is designed as follows:
wherein Δ u = sat (u) c )-u c Is an input of the auxiliary system, u c Is a control law to be designed; eta is the state of the auxiliary system, k η ,k η2 ,k η3 ,γ η ,ε η Are parameters of the auxiliary system to be designed and are all normal values;
based on the bounded nature of the external disturbance, the integrated uncertainty δ is expressed as:
||δ||≤b 0 +b 1 ||ω s ||+b 2 ||ω s || 2 ≤bL
wherein, b 0 ＝(h 0 +h 3 )，b 1 ＝h 1 ，b 2 ＝h 2 ，b＝max{b 0 ,b 1 ,b 2 ,b 3 }，L＝1+||ω s ||+||ω s || 2 ，h i (i = 0.. 3) represents an uncertainty parameter upper bound;
the design adaptive update law is as follows:
wherein,
is an estimate of b, ξ 1 And xi 2 Is a normal value;
and is
Is at a normal value
Based on an attitude dynamics equation of a service spacecraft, a nonsingular integral terminal sliding mode surface, an anti-saturation auxiliary system and comprehensive uncertainty of the system, an attitude controller for pointing tracking is designed as follows:
wherein,
to expect angular acceleration, k 1 、k 2 And α is a normal number.
Based on the above example, it should be noted that, first, the nonsingular integral terminal sliding mode surface is continuous and nonsingular;
second, for anti-saturation assist systems, conventional anti-saturation assist systems are typically designed to include only-k η η+k η2 Two terms of delta u, examples of the invention introduce
Aiming at proving that the finite time of the state quantity eta of the auxiliary system converges to zero; introducing (eta/| eta | | non-phosphor powder 2 )(|s T BΔu|+k η2 Δu T Δ u/2) is to counteract the relevant term in order to facilitate controller stability certification; due to the addition of the introduction items, in order to avoid singularity caused by over-small eta, the auxiliary system is designed into a segmented form.
Finally, for the comprehensive uncertainty δ, the external dry disturbance acting on the spacecraft
Is bounded, and can be viewed as the model uncertainty of the disturbance term
Is also bounded and can be written as follows:
wherein h is i (i = 0.., 3) is an unknown normal number.
With reference to the foregoing technical solutions, in some possible implementations, the method further includes:
controlling the relative position of the service spacecraft by the control quantity output by the MPC controller aiming at the relative position through a C-W equation;
and controlling the attitude dynamics equation by using the control quantity output by the pointing tracking attitude controller.
Based on the foregoing technical solution and the implementation and example thereof, in the specific implementation process of the tracking control method considering input saturation and motion constraint provided in the embodiment of the present invention, as shown in fig. 4, the MPC controller is used to control the relative positions of the serving spacecraft and the target spacecraft by using the ghost position guidance law and the C-W equation related to the desired relative position; after the expected angular speed is output through an MPC controller of angular speed planning according to the expected attitude and the attitude kinematics, the attitude of the pointing tracking is controlled through an adaptive sliding mode controller and an anti-saturation auxiliary system, so that a control scheme of approaching and pointing tracking is realized.
In order to illustrate the technical effect of the foregoing technical solution, the embodiment of the present invention is illustrated by a specific simulation experiment, and for the approaching task, the tracking errors of the relative position and the relative velocity are respectively shown in fig. 5 (a) and (b), and it can be seen that both converge in about 30s, and the relative velocity does not exceed a defined amplitude. For the optical axis posture trajectory, as shown in fig. 6 (a) and 6 (b), the relative position transition trajectory and the optical axis posture trajectory have a large angle error with the expected direction in the earlier stage of the optical axis direction, the expected trajectory in the middle stage directly passes through the conical strong light irradiation area, the actual direction bypasses the posture forbidden area, and then the expected direction is tracked again. For the control torque shown in fig. 7, saturation occurs due to a large initial error; due to the fact that the posture forbidden zone needs to be avoided in about 200s, the control moment fluctuates, and the amplitude constraint is always met at other times.
Compared with the conventional potential function method, the method provided by the embodiment of the invention does not need to avoid the problem of minimum value, has low requirement on the output capability of the executing mechanism under the motion constraint, can well solve the problem of safety approach in the on-orbit service task, and ensures that the attitude maneuvering angular speed of the service spacecraft is optimal in real time under the fuel and error constraints. Compared with the mode that the attitude dynamics model is directly adopted for model prediction control, the method can achieve the purpose of reducing the calculated amount of the dimension reduction optimization problem. For the attitude control part, the attitude control part also has certain superiority in processing the attitude limitation problem.
Based on the same inventive concept of the foregoing technical solution, referring to fig. 8, it shows a tracking control apparatus 80 considering input saturation and motion constraint according to an embodiment of the present invention, where the apparatus 80 includes: first build portion 801, second build portion 802, third build portion 803, first design portion 804, acquisition portion 805, and second design portion 806, wherein,
the first building portion 801 configured to build a desired translation for a desired distance between a serving spacecraft and a target spacecraft;
the second building portion 802 configured to build the serving spacecraft desired attitude for a line of sight angular pointing constraint between the serving spacecraft and the target spacecraft;
the third constructing portion 803 is configured to construct constraint conditions of translation and rotation for task requirements in an on-orbit service process;
the first design part 804 is configured to construct a model predictive control MPC controller for a relative position with the goal of minimizing fuel and tracking error based on the constraint conditions of the expected translation and the translation;
the obtaining part 805 is configured to obtain a desired angular velocity through an MPC angular velocity planning module based on a desired attitude and a rotation constraint condition of the serving spacecraft;
the second design part 806 is configured to design an adaptive anti-saturation sliding mode controller according to the desired angular velocity and to handle the control moment saturation problem by an anti-saturation assistance system to obtain a pose controller for point tracking.
It should be noted that, for specific implementation of the configured functions of each "part" in the above apparatus, reference may be made to the implementation manner and example of the corresponding step in the tracking control method considering input saturation and motion constraint shown in fig. 1, and details are not described here again.
It is to be understood that, in this embodiment, "part" may be part of a circuit, part of a processor, part of a program or software, or the like, and may also be a unit, and may also be a module or a non-modular.
In addition, each component in this embodiment may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware or a form of a software functional module.
Based on the understanding that the technical solution of the present embodiment essentially or a part contributing to the prior art, or all or part of the technical solution may be embodied in the form of a software product stored in a storage medium, and include several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) or a processor (processor) to execute all or part of the steps of the method of the present embodiment. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Therefore, the present embodiment provides a computer storage medium, where a tracking control program considering input saturation and motion constraint is stored, and when the tracking control program considering input saturation and motion constraint is executed by at least one processor, the tracking control program considering input saturation and motion constraint implements the steps of the tracking control method considering input saturation and motion constraint in the above technical solution.
Referring to fig. 9, which shows a specific hardware structure of a computing device 90 capable of implementing the tracking control apparatus 80 considering input saturation and motion constraints, the computing device 90 may be a wireless device, a mobile or cellular phone (including a so-called smart phone), a Personal Digital Assistant (PDA), a video game console (including a video display, a mobile video game apparatus, and a mobile video conference unit), a laptop computer, a desktop computer, a television set-top box, a tablet computing apparatus, an e-book reader, a fixed or mobile media player, and the like. The computing device 90 includes: a communication interface 901, a memory 902, and a processor 903; the various components are coupled together by a bus system 904. It is understood that the bus system 904 is used to enable communications among the components. The bus system 904 includes a power bus, a control bus, and a status signal bus in addition to a data bus. But for clarity of illustration the various buses are labeled as bus system 904 in figure 9. Wherein,
the communication interface 901 is configured to receive and send signals in the process of receiving and sending information with other external network elements;
the memory 902 is used for storing computer programs capable of running on the processor 903;
the processor 903 is configured to execute the steps of the tracking control method considering input saturation and motion constraint in the above technical solution when the computer program is run.
It is to be understood that the memory 902 in embodiments of the present invention may be either volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory. The non-volatile Memory may be a Read-Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an Electrically Erasable PROM (EEPROM), or a flash Memory. Volatile Memory can be Random Access Memory (RAM), which acts as external cache Memory. By way of illustration and not limitation, many forms of RAM are available, such as Static random access memory (Static RAM, SRAM), dynamic Random Access Memory (DRAM), synchronous Dynamic random access memory (Synchronous DRAM, SDRAM), double Data Rate Synchronous Dynamic random access memory (ddr Data Rate SDRAM, ddr SDRAM), enhanced Synchronous SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory 902 of the systems and methods described herein is intended to comprise, without being limited to, these and any other suitable types of memory.
And the processor 903 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by instructions in the form of hardware integrated logic circuits or software in the processor 903. The Processor 903 may be a general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, or discrete hardware components. The various methods, steps and logic blocks disclosed in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules may be located in ram, flash, rom, prom, or eprom, registers, etc. as is well known in the art. The storage medium is located in the memory 902, and the processor 903 reads information in the memory 902 and performs the steps of the above method in combination with hardware thereof.
It is to be understood that the embodiments described herein may be implemented in hardware, software, firmware, middleware, microcode, or any combination thereof. For a hardware implementation, the Processing units may be implemented within one or more Application Specific Integrated Circuits (ASICs), digital Signal Processors (DSPs), digital Signal Processing Devices (DSPDs), programmable Logic Devices (PLDs), field Programmable Gate Arrays (FPGAs), general purpose processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described herein, or a combination thereof.
For a software implementation, the techniques described herein may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes may be stored in a memory and executed by a processor. The memory may be implemented within the processor or external to the processor.
It should be understood that the above exemplary technical solutions of the tracking control device 80 and the computing device 90 considering the input saturation and the motion constraint belong to the same concept as the above technical solution of the tracking control method considering the input saturation and the motion constraint, and therefore, the above detailed descriptions of the technical solutions of the tracking control device 80 and the computing device 90 considering the input saturation and the motion constraint can be referred to the above technical solution of the tracking control method considering the input saturation and the motion constraint, which is not described in detail. The embodiment of the present invention will not be described in detail.
It should be noted that: the technical schemes described in the embodiments of the present invention can be combined arbitrarily without conflict.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. A tracking control method that takes into account input saturation and motion constraints, the method comprising:
constructing an expected translation for an expected distance between a serving spacecraft and a target spacecraft;
constructing a desired attitude of a serving spacecraft for a line of sight angular pointing constraint between the serving spacecraft and a target spacecraft;
constructing constraint conditions of translation and rotation aiming at task requirements in an on-orbit service process;
constructing a Model Predictive Control (MPC) controller aiming at the relative position by taking minimized fuel and tracking error as targets based on the constraint conditions of the expected translation and the translation;
acquiring an expected angular speed through an MPC angular speed planning module based on the expected attitude and the rotation constraint condition of the service spacecraft;
and designing a self-adaptive anti-saturation sliding mode controller according to the expected angular velocity, and processing the problem of control moment saturation through an anti-saturation auxiliary system to obtain an attitude controller for pointing tracking.
2. The method of claim 1, wherein constructing the desired translation for the desired distance between the serving spacecraft and the target spacecraft comprises:
setting the hovering position of the service spacecraft in the target spacecraft body coordinate system as follows:
ρ d ＝ t [0 l d 0] T
wherein ρ d Representing the expected position of the service spacecraft, wherein t is a left superscript representing a body coordinate system of the target spacecraft; l d Representing a desired distance between the serving spacecraft and the target spacecraft;
transferring the expected position parameters of the service spacecraft in the target spacecraft body coordinate system to an LVLH coordinate system, and obtaining the expected motion parameters of the service spacecraft in the LVLH coordinate system as follows:
the expected positions of the service spacecraft in the LVLH coordinate system are as follows:
the expected velocity of the service spacecraft in the LVLH coordinate system is as follows:
the expected acceleration of the service spacecraft in the LVLH coordinate system is as follows:
wherein,
representing a coordinate system Ox consisting of the body of the target spacecraft t y t z t To the earth's center inertial coordinate system Ox I y I z I The transition matrix of (2);
representing an inertial system Ox by the centre of the earth I y I z I (hereinafter may be simply referred to as an inertial system) to the LVLH coordinate system; omega tL Representing the angular velocity, ω, of the target spacecraft relative to the LVLH coordinate system tL ＝ω tI -ω LI ，ω tI Representing the target spacecraft relative to the earth's center inertial frame Ox I y I z I Angular velocity of (a) ([ omega ]) LI Representing a serving spacecraft orbit angular velocity; i is a left superscript representation of the geocentric inertial coordinate system Ox I y I z I (ii) a L is a left superscript which represents an LVLH coordinate system;
correspondingly, the construction of the constraint conditions of the translation aiming at the task requirements in the in-orbit service process comprises the following steps:
respectively designing a speed constraint condition and a control input saturation constraint condition aiming at the translational motion of the service spacecraft; wherein the speed constraint condition is:
the maximum value of the relative linear velocity under the LVLH coordinate system is represented; the control input saturation constraint conditions are as follows:
f denotes the control input variable.
3. The method of claim 2, wherein constructing a Model Predictive Control (MPC) controller for relative position with the goal of minimizing fuel and tracking error based on constraints of the desired translation and translation comprises:
setting a prediction time domain to N p Control time domain as N c Serializing the state variables and control inputs in the discrete state equation of the service spacecraft to obtain a state variable sequence X s (k) And a control input sequence F s (k) As follows:
according to the state variable sequence X s (k) And control input sequence U s (k) Rewriting the discrete state equation of the service spacecraft to X s (k)＝A s X(k)+B s U s (k) (ii) a Wherein,
with the objective of minimizing the relative position tracking error and the control input, the design index function is:
wherein Q Ii And R Ii Respectively representing positive definite states and control weight matrices, Q Ii The last element in the list is a terminal weight matrix P I ,P I Obtained by solving the discrete time Riccati equation of rho d Representing a desired sequence of states;
and converting and expressing the relative position constraint condition into a constraint condition on a control input, and combining the final index function to obtain an MPC controller aiming at the relative position as follows:
wherein,
and
are each v max And D is an augmented matrix of elements.
4. The method of claim 1, wherein said constructing the serving spacecraft desired attitude for a line of sight angular pointing constraint between the serving spacecraft and a target spacecraft comprises:
relative position of the serving spacecraft to a spatial target
From Hill coordinate system to geocentric inertial coordinate system
Wherein,
a coordinate transformation matrix representing a Hill coordinate system to a geocentric inertial coordinate system;
expressing the vector of the service spacecraft in the direction of the optical axis in the geocentric inertial navigationThe system of the sexual coordinate is as follows:
wherein,
the coordinate transformation matrix is from a spacecraft body coordinate system to a geocentric inertial coordinate system;
defining the Euler axis during an attitude maneuver as
Wherein,
representing angle of sight, as vector
And the vector y of the optical axis direction I When the two-dimensional images are overlapped, the two-dimensional images,
according to the Euler axial angle definition, the attitude deviation of the spacecraft body attitude and the attitude deviation when the expected pointing direction is reached is obtained by quaternion definition:
based on the attitude deviation and the definition of the error quaternion, obtaining an expected attitude as: q. q.s d ＝[q d0 ,-q dv ] T ；
Setting the mathematical description of the attitude constraint condition of the service spacecraft to avoid the bright celestial body appearing in the field of view of the sensor of the service spacecraft
Wherein, y I Representing the optical axis direction vector, S, of said service spacecraft I Representing the bright celestial direction vector,
representing the included angle between the vector of the optical axis direction and the direction of the bright celestial body;
and performing coordinate conversion on the optical axis direction vector of the service spacecraft to obtain the following formula:
wherein, (.) × An antisymmetric matrix representing the vector;
correspondingly, aiming at the task requirement in the in-orbit service process, the constraint condition of rotation is constructed, and the constraint condition comprises the following steps:
obtaining the attitude constraint conditions of the service spacecraft based on the mathematical description of the attitude constraint conditions and the coordinate conversion of the optical axis direction vector, wherein the attitude constraint conditions comprise:
q T k c q≤0
wherein,
y b representing the serving spacecraft body system y-axis.
5. The method of claim 4, wherein obtaining the desired angular velocity by the MPC angular velocity planning module based on the desired attitude and rotation constraints of the serving spacecraft comprises:
sampling and discretizing an attitude kinematics equation described by a quaternion by utilizing a forward Euler method to obtain an original discrete state equation related to the attitude as follows:
q(k+1)＝A t q(k)+B t U(k+1)
wherein, A t ＝E 4 ，B t ＝T s E 4 ，T s Representing the sampling interval, U (k + 1) = B (q (k)) ω (k + 1) represents the input to a discrete equation of state for attitude, including the angular velocity driving the attitude motion;
setting a prediction time domain to be equal to a control time domain, and enabling the predicted state sequence q in the original discrete state equation related to the attitude s And control input sequence U s Represented by:
q s (k)＝(q T (k+1|k),q T (k+2|k),......,q T (k+N p |k)) T
U s (k)＝(U T (k+1|k),U T (k+1|k),......,U T (k+N p |k)) T
prediction-based state sequence q s And control input sequence U s The original discrete state equation about the attitude is arranged as q s (k)＝A s q(k)+B s U s (k) Wherein
the construction of the optimization controller is as follows:
wherein q is e Representing the error quaternion, q ed ＝[1,0,0,0] T ，Q IIIi 、R IIIi Representing a positive definite weight matrix;
introducing an auxiliary variable A according to the constructed optimization controller and the discrete state equation after the arrangement of the posture v ＝P d A s q(k)-q ed (k) The final MPC controller was obtained as:
s.t.q(t+k|t)＝A t q(k|t)+B t U(t+k|t),k＝1,...,N pc -1
q T (t+k|t)K i q(t+k|t)≤λ i ,i＝1,...,n
wherein,
input amplitude, P, representing an original discrete equation of state with respect to attitude d Representing expected attitude information of a prediction time domain, and resolving according to predicted relative position information;
the first control input obtained after the final MPC controller is optimized acts on the discrete state equation after the arrangement of the attitude, and the attitude maneuver angular speed which is optimal in real time under the objective function of the minimum error and fuel is obtained
6. The method according to claim 5, wherein the designing an adaptive anti-saturation sliding-mode controller according to the desired angular velocity and processing a control torque saturation problem through an anti-saturation assist system to obtain an attitude controller for point tracking comprises:
based on the output saturation of the actuating mechanism, the attitude dynamics equation of the service spacecraft is rewritten as follows:
wherein,
representing the overall uncertainty of the system,
an integral term of an angular velocity tracking error is introduced, and a nonsingular integral terminal sliding mode surface is designed as follows:
wherein, ω is e ＝ω s -ω d Indicating the angular velocity of error, s q ＞s p > 0 is a positive number to be designed,
is a positive definite diagonal matrix;
based on avoiding the actuator saturation, the anti-saturation auxiliary system is designed as follows:
wherein Δ u = sat (u) c )-u c Is an input to the auxiliary system, u c Is a control law to be designed; eta is the state of the auxiliary system, k η ,k η2 ,k η3 ,γ η ,ε η Are parameters of auxiliary systems to be designed and are all normal values
Based on the bounded nature of the external disturbance, the integrated uncertainty δ is expressed as:
||δ||≤b 0 +b 1 ||ω s ||+b 2 ||ω s || 2
≤bL
wherein, b 0 ＝(h 0 +h 3 )，b 1 ＝h 1 ，b 2 ＝h 2 ，b＝max{b 0 ,b 1 ,b 2 ,b 3 }，L＝1+||ω s ||+||ω s || 2 ，h i (i = 0.. 3) represents an uncertainty parameter upper bound;
the design adaptive update law is as follows:
wherein,
is an estimate of b, ξ 1 And xi 2 Is a normal value;
and is provided with
Is a normal value
Based on an attitude dynamics equation of a service spacecraft, a nonsingular integral terminal sliding mode surface, an anti-saturation auxiliary system and comprehensive uncertainty of the system, an attitude controller for pointing tracking is designed as follows:
wherein,
to expect angular acceleration, k 1 、k 2 And α is a normal number.
7. The method according to any one of claims 1 to 6, further comprising:
controlling the relative position of the service spacecraft by the control quantity output by the MPC controller aiming at the relative position through a C-W equation;
and controlling the attitude dynamics equation by using the control quantity output by the pointing tracking attitude controller.
8. A tracking control apparatus that considers input saturation and motion constraints, the apparatus comprising: a first build portion, a second build portion, a third build portion, a first design portion, an acquisition portion, and a second design portion, wherein,
the first build portion configured to build a desired translation for a desired distance between a serving spacecraft and a target spacecraft;
the second building portion configured to build the desired attitude of the serving spacecraft for a line of sight angular pointing constraint between the serving spacecraft and a target spacecraft;
the third construction part is configured to construct constraint conditions of translation and rotation aiming at task requirements in an on-orbit service process;
the first design part is configured to construct a Model Predictive Control (MPC) controller aiming at relative position with the aim of minimizing fuel and tracking error based on the constraint conditions of the expected translation and the translation;
the acquisition part is configured to acquire an expected angular velocity through an MPC angular velocity planning module based on an expected attitude and a rotation constraint condition of the service spacecraft;
the second design part is configured to design an adaptive anti-saturation sliding mode controller according to the expected angular speed, and process a control moment saturation problem through an anti-saturation auxiliary system so as to obtain an attitude controller for pointing tracking.
9. A computing device, wherein the computing device comprises: a communication interface, a memory and a processor; the various components are coupled together by a bus system; wherein,
the communication interface is used for receiving and sending signals in the process of receiving and sending information with other external network elements;
the memory for storing a computer program operable on the processor;
the processor, when executing the computer program, is configured to perform the steps of the tracking control method according to any of claims 1 to 7 taking into account input saturation and motion constraints.
10. A computer storage medium, characterized in that the computer storage medium stores a tracking control program considering input saturation and motion constraints, and the tracking control program considering input saturation and motion constraints realizes the steps of the tracking control method considering input saturation and motion constraints according to any one of claims 1 to 7 when being executed by at least one processor.
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