An attitude tracking control method for a probe orbiting an asteroid based on adaptive iterative learning

Abstract

The present invention belongs to the technical field of probe attitude tracking control, and specifically relates to a method for attitude tracking control of a probe orbiting an asteroid based on adaptive iterative learning. The method comprises the following steps: Step 1: The probe mathematical model outputs two state variables, namely attitude and angular velocity; Step 2: The attitude and angular velocity are fed back to the input of the control system, and the error attitude and error angular velocity are respectively subtracted from the given desired attitude and desired angular velocity; Step 3: A probe attitude tracking error system is established based on the two error states, where the uncertainty and external interference in the system are regarded as total disturbances and estimated using an adaptive law; Step 4: An attitude tracking controller is designed based on an adaptive iterative learning algorithm. The present invention proposes a design method for an adaptive iterative learning controller based on an all-wheel drive system approach and sliding mode control. The designed adaptive iterative learning controller has excellent control performance and a small number of adjustment parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of probe attitude tracking control, and in particular relates to a probe attitude tracking control method for flying around an asteroid based on adaptive iterative learning. Background Art

[0002] When a probe orbits an asteroid for observation, attitude control is required to ensure the payload on board remains stably pointed at the asteroid's surface. Due to the uncertainty of the gravitational field of an irregular asteroid, the probe must possess strong anti-interference capabilities during the orbital process due to the uncertain gravitational field and the influence of various complex perturbations such as solar gravity and light pressure. Furthermore, the asteroid's irregular shape and gravitational field distribution lead to a very complex dynamic environment nearby, requiring extremely high precision control capabilities to prevent the probe from escaping.

[0003] Iterative learning control can significantly suppress repeated disturbances during periodic operation and achieve high-precision control. The motion process of a probe flying around an asteroid and carrying out observation missions has the characteristics of repeated operation, so the research on iterative learning attitude tracking control is of great value. As the complexity of tasks increases, how to design more technically advanced adaptive iterative control methods based on the characteristics of different systems still needs to be explored in depth. To this end, the present invention proposes a probe attitude tracking control method based on adaptive iterative learning to fly around an asteroid. Summary of the Invention

[0004] The purpose of the present invention is to provide a probe attitude tracking control method for flyby of an asteroid based on adaptive iterative learning, so as to improve the robustness and adaptability of the attitude control system when the probe flies around an asteroid for observation. Probe attitude tracking control method based on adaptive iterative learning. First, a mathematical model of the probe attitude tracking error system is established based on the probe kinematic and dynamic equations. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. The total disturbance term in the adaptive law estimation model is constructed, and combined with the full drive system method and sliding mode control technology, an adaptive iterative learning attitude tracking control method is designed to ultimately achieve the purpose of high-precision flyby of an asteroid.

[0005] The technical solutions adopted by the present invention are as follows:

[0006] A method for attitude tracking control of a probe flying around an asteroid based on adaptive iterative learning includes the following steps:

[0007] Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω;

[0008] Step 2: Feedback the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and the error angular velocity Ω e ;

[0009] Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. To estimate;

[0010] Step 4: Design the posture tracking controller u based on the adaptive iterative learning algorithm.

[0011] Preferably, in step 1, a mathematical model of the attitude control system of the probe when it flies around the asteroid is first established, and the attitude kinematic equation of the probe is expressed as:

[0012]

[0013] Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula:

[0014] W(σ)=(1-σ T σ)I3+2σ × +2σσ T (2)

[0015] The attitude dynamics equation of the probe is expressed as

[0016]

[0017] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, Represents the total torque of the solar light pressure and solar gravitational interference on the detector, Ω × is a skew-symmetric matrix, defined as:

[0018]

[0019] Due to the uncertainty of internal parameters caused by factors such as the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as:

[0020] J=J0+ΔJ (4)

[0021] Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, and is calculated as:

[0022]

[0023]

[0024] Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, and R c Represents the distance from the probe's center of mass to the asteroid's center of mass, and defines the system parameter variables a and b as

[0025]

[0026] Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, and satisfies η represents the true anomaly, and ω0 represents the rotational angular velocity.

[0027] Preferably, in step 2, when the probe flies around the asteroid for observation, σ d and Ω d Represents the target posture and target angular velocity, and the relationship between the two is

[0028]

[0029] The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula

[0030]

[0031] The error angular velocity is defined as

[0032] ω=Ω-CΩ d (7)

[0033] Where: C represents the rotation matrix, which can be calculated by the following formula

[0034]

[0035] Where I3 represents a 3×3 identity matrix. Based on (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established:

[0036]

[0037] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, It represents the resultant torque of solar light pressure and solar gravitational interference on the detector;

[0038] Defining state variables Then the detector attitude tracking control error system model (8)-(9) is transformed into

[0039]

[0040] Where:

[0041]

[0042] in,

[0043]

[0044] Preferably, in step 3, in order to construct an adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system (10) has an upper bound, that is,

[0045] ||z||≤D (11) where: D is a time-varying and unknown parameter;

[0046] In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows:

[0047] s k =Kx k +a∫σ ek (12)

[0048] Where: K is a constant matrix that needs to be reasonably designed to ensure that the matrix KG is reversible, a>0 is the controller parameter; k∈Z + Represents the number of iterations, meaning: s k , x k and σ ek Represent the sliding surface, state variables and posture tracking error corresponding to the kth iteration respectively; taking the derivative of the sliding surface, we can get

[0049]

[0050] At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed using the full drive system method is

[0051]

[0052] z kFor the total disturbance, a differential adaptive law of the following form is designed to estimate the upper bound D of the total disturbance term:

[0053]

[0054] Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

[0055] Preferably, in step 4, the estimated value of the adaptive law (15) is used to design the switching control term of the sliding mode controller as:

[0056]

[0057] Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as

[0058]

[0059] In the formula and See (14) and (16) for the definition of

[0060] The technical effects achieved by the present invention are:

[0061] In the present invention, a design method of an adaptive iterative learning controller based on an all-wheel drive system method and sliding mode control is proposed; the designed adaptive iterative learning controller has the characteristics of excellent control performance and fewer adjustment parameters.

[0062] For a probe orbiting an asteroid, this paper considers both the uncertainty of moment of inertia parameters and the influence of external disturbances, designing a novel attitude tracking control method based on adaptive iterative learning technology. This method offers the advantages of high tracking accuracy and a small number of adjustment parameters. Simulation examples demonstrate the effectiveness of the proposed probe attitude tracking control method.

[0063] The present invention aims to improve the robustness and adaptability of the attitude control system of a probe during an observation orbit around an asteroid. A probe attitude tracking control method based on adaptive iterative learning is proposed. First, a mathematical model of the probe attitude tracking error system is established based on the probe's kinematic and dynamic equations. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. An adaptive law is constructed to estimate the total disturbance term in the model. Combined with the all-wheel drive system method and sliding mode control technology, an adaptive iterative learning attitude tracking control method is designed to ultimately achieve high-precision orbit around an asteroid. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1This is a flowchart of a method for attitude tracking control of a probe flying around an asteroid based on adaptive iterative learning in the present invention;

[0065] Figure 2 is the attitude error change curve under the action of the controller in the present invention;

[0066] Figure 3 is the error angular velocity variation curve under the action of the controller in the present invention;

[0067] Figure 4 It is the variation curve of the performance index along the iteration axis in the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is described in detail below with reference to the following examples. It should be understood that the following text is only used to describe one or more specific embodiments of the present invention and does not strictly limit the scope of protection of the present invention.

[0069] A method for attitude tracking control of a probe flying around an asteroid based on adaptive iterative learning includes the following steps:

[0070] Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω;

[0071] Step 2: Feedback the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and the error angular velocity Ω e ;

[0072] Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. To estimate;

[0073] Step 4: Design the posture tracking controller u based on the adaptive iterative learning algorithm.

[0074] In step 1, a mathematical model of the probe's attitude control system is first established when the probe is flying around the asteroid. The probe's attitude kinematic equation is expressed as:

[0075]

[0076] Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula:

[0077] W(σ)=(1-σT σ)I3+2σ × +2σσ T (2)

[0078] Where I3 represents a 3×3 unit matrix; the attitude dynamics equation of the detector is expressed as

[0079]

[0080] Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, Ω represents the combined torque of solar light pressure and solar gravitational interference on the probe. This interference torque may appear repeatedly during the probe's orbit. × is a skew-symmetric matrix, defined as:

[0081]

[0082] Due to the uncertainty of internal parameters caused by factors such as the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as:

[0083] J=J0+ΔJ (4)

[0084] Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, and is calculated as:

[0085]

[0086] Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, and R c Represents the distance from the probe's center of mass to the asteroid's center of mass, and defines the system parameter variables a and b as

[0087]

[0088] Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, and satisfies η represents the true anomaly, and ω0 represents the rotational angular velocity.

[0089] In step 2, when the probe flies around the asteroid for observation, it is required that the probe can accurately track the target attitude; the present invention uses σ d and Ω dRepresents the target posture and target angular velocity, and the relationship between the two is

[0090]

[0091] The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula

[0092]

[0093] The error angular velocity is defined as

[0094] ω=Ω-CΩ d (7)

[0095] Where: C represents the rotation matrix, which can be calculated by the following formula

[0096]

[0097] Where I3 represents a 3×3 identity matrix. Based on (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established:

[0098]

[0099] Defining state variables Then the detector attitude tracking control error system model (8)-(9) is transformed into

[0100]

[0101] Where:

[0102]

[0103] in,

[0104]

[0105] Since the attitude control of a probe flying around an asteroid has the characteristic of repeated operation, the adaptive iterative learning method will be used in the next section to design an attitude tracking control strategy for the probe flying around an asteroid; that is, the core goal of the present invention is to design a controller u so that the attitude tracking error system (10) of the asteroid probe flying around the asteroid is asymptotically stable.

[0106] In step 3, in order to construct the adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system (10) has an upper bound, that is,

[0107] ||z||≤D (11) where: D is a time-varying and unknown parameter;

[0108] In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows:

[0109] s k =Kx k +a∫σ ek (12)

[0110] Where: K is a constant matrix that needs to be reasonably designed to ensure that the matrix KG is reversible, a>0 is the controller parameter, k∈Z + Represents the number of iterations; taking the derivative of the sliding surface, we can get

[0111]

[0112] At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed using the full drive system method is

[0113]

[0114] In practical applications, the total disturbance z k The value of is difficult to obtain; therefore, the present invention designs the following form of differential adaptive law to estimate the upper bound D of the total disturbance term:

[0115]

[0116] Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

[0117] In step 4, the estimated value of the adaptive law (15) is used to design the switching control term of the sliding mode controller as follows:

[0118]

[0119] Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as

[0120]

[0121] In the formula and The definitions of are given in (14) and (16).

[0122] The present invention is verified in the simulation experiment.

[0123] The designed control method was applied to attitude control during a probe's flyby of an asteroid to verify its effectiveness and superiority. In this invention, we considered the NEAR probe orbiting the asteroid Eros 433. High-precision attitude and pointing control is required when the probe is orbiting the asteroid and observing it. The parameters of Eros 433 are shown in Table 1.

[0124] Table 1: Parameters of asteroid Eros 433

[0125]

[0126] The moment of inertia of the detector is

[0127]

[0128] The uncertainty of the moment of inertia is set to ΔJ = 0.1J0. Assume that the total torque of the disturbance acting on the detector is:

[0129]

[0130] The initial attitude and angular velocity of the detector are:

[0131] σ(0)=[0.553-0.894-0.988] T

[0132] and

[0133] Ω(0)=

[000] T rad / s

[0134] The desired posture is:

[0135] σ d =0.01[cos(0.2t)sin(0.2t)sin(0.1t)] T

[0136] Using the above formula, the desired angular velocity can be obtained by formula (5); in addition, the parameters of controller (17) are set to γ ​​= 0.01, η = 5, a = 0.3, K = 0.4 [I3 I3].

[0137] First, the simulation comparison results of the 1st iteration and the 10th iteration under the action of controller (17) are given. Figure 2 The following are the curves of the attitude tracking error changing with time at the 1st iteration and the 10th iteration. Figure 3 The curves of error angular velocity changing with time at the 1st iteration and the 10th iteration are given.

[0138] pass Figure 2 as well as Figure 3It can be seen that even if there are factors such as uncertainty in the moment of inertia parameters, external interference, and the gravitational torque of other celestial bodies, the controller (17) can still make the state of the detector attitude tracking error system converge to zero. Moreover, Figure 2 as well as Figure 3 The results show that as the number of iterations increases, the overshoot of the attitude tracking error curve and the error angular velocity curve decreases, and the required adjustment time is also reduced. In other words, the performance of the attitude tracking control system is effectively improved through multiple iterative learning of the controller.

[0139] In order to further illustrate the role of the adaptive iterative learning controller, the following performance indicators are defined:

[0140] max t∈[0,T] ||ω k (t)||(deg / s) (52)

[0141] The index (52) represents the maximum value of the error angular velocity during each iteration. Figure 4 The curve of performance index changing with the number of iterations is given.

[0142] Figure 4 The simulation curve in shows that the value of index (52) decreases monotonically with the increase of the number of iterations. Each iterative learning further reduces the maximum value of the error angular velocity. The above simulation results prove the convergence of the proposed algorithm.

[0143] In the present invention, a design method of an adaptive iterative learning controller based on an all-wheel drive system method and sliding mode control is proposed; the designed adaptive iterative learning controller has the characteristics of excellent control performance and fewer adjustment parameters.

[0144] For a probe orbiting an asteroid, this paper considers both the uncertainty of moment of inertia parameters and the influence of external disturbances, designing a novel attitude tracking control method based on adaptive iterative learning technology. This method offers the advantages of high tracking accuracy and a small number of adjustment parameters. Simulation examples demonstrate the effectiveness of the proposed probe attitude tracking control method.

[0145] The present invention aims to improve the robustness and adaptability of the attitude control system of a probe during an observation orbit around an asteroid. A probe attitude tracking control method based on adaptive iterative learning is proposed. First, a mathematical model of the probe attitude tracking error system is established based on the probe's kinematic and dynamic equations. Taking into account factors such as the uncertainty of the probe's moment of inertia parameters and the repetitive interference torque it is subjected to, the attitude tracking error system model is converted into a general nonlinear system model. An adaptive law is constructed to estimate the total disturbance term in the model. Combined with the all-wheel drive system method and sliding mode control technology, an adaptive iterative learning attitude tracking control method is designed to ultimately achieve high-precision orbit around an asteroid.

[0146] The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.

Claims

1. A method for tracking the attitude of a probe orbiting an asteroid based on adaptive iterative learning, characterized by: The following steps are involved: Step 1: First, the detector mathematical model outputs two state variables, namely attitude σ and angular velocity Ω; Step 2: Feedback the attitude σ and angular velocity Ω back to the input of the control system and compare them with the given desired attitude σ d and the desired angular velocity Ω d Subtract and get the error posture σ e and the error angular velocity Ω e ; Step 3: Establish the detector attitude tracking error system based on the two error states. The uncertainty and external interference in the system are regarded as the total disturbance. To estimate; Step 4: Design the posture tracking controller u based on the adaptive iterative learning algorithm; In step 1, a mathematical model of the probe's attitude control system is first established when the probe is flying around the asteroid. The probe's attitude kinematic equation is expressed as: Where: is the modified Rodriguez parameter, represents the angular velocity of the detector, W(σ) is calculated by the following formula: W(σ)=(1-σ T σ)I3+2σ × +2ss T (2) The attitude dynamics equation of the probe is expressed as Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, Represents the total torque of the solar light pressure and solar gravitational interference on the detector, Ω × is a skew-symmetric matrix, defined as: Due to the uncertainty of internal parameters caused by the rotation of the detector's own load and fuel consumption during operation, the moment of inertia J is expressed as: J=J0+ΔJ (4) Where: J0 is a known symmetric positive definite matrix, ΔJ represents the uncertain part of the moment of inertia J; In addition, in the probe attitude dynamics equation (3), It represents the component of the gravitational torque on the detector in the fixed coordinate system, and is calculated as: Where: c mn is the mnth term in the rotation matrix C, where m is the asteroid gravity coefficient, and R c Represents the distance from the probe's center of mass to the asteroid's center of mass, and defines the system parameter variables a and b as Where: R0 is the reference radius of the asteroid, C 20 and C 22 is the spherical harmonic coefficient, I is the longitude of the detector, and satisfies η represents the true anomaly, ω0 represents the rotational angular velocity; In step 2, when the probe flies around the asteroid for observation, σ d and Ω d Represents the target posture and target angular velocity, and the relationship between the two is The actual pose of the detector σ and the target pose σ d The error between e Calculated by the following formula The error angular velocity is defined as ω=Ω-CΩ d (7) Where: C represents the rotation matrix, which can be calculated by the following formula Where I3 represents a 3×3 identity matrix. Based on formulas (6) and (7), the attitude kinematics equation (1) and the attitude dynamics equation (3), the following detector attitude tracking error system model is established: Where: represents the moment of inertia of the detector, is the control torque vector acting on the three main axes of the detector, It represents the resultant torque of solar light pressure and solar gravitational interference on the detector; Defining state variables Then the detector attitude tracking control error system model formula (8)-formula (9) is transformed into Where: in, In step 3, in order to construct the adaptive iterative learning controller, it is assumed that the total disturbance term of the detector attitude tracking error system formula (10) has an upper bound, that is, ||z||≤D (11) where: D is a time-varying and unknown parameter; In order to utilize the all-wheel drive system approach, the sliding surface is designed as follows: s k =Kx k +a∫σ ek (12) Where: K is a constant matrix that needs to be reasonably designed to ensure that the matrix KG is reversible, a>0 is the controller parameter; k∈Z + Represents the number of iterations, meaning: s k , x k and σ ek Represent the sliding surface, state variables and posture tracking error corresponding to the kth iteration respectively; taking the derivative of the sliding surface, we can get At this time, let the total disturbance z in the above formula be k is zero, the equivalent control term of sliding mode control designed using the full drive system method is z k For the total disturbance, a differential adaptive law of the following form is designed to estimate the upper bound D of the total disturbance term: Where: γ is a constant, representing the adaptive factor, Represents the estimated value of the upper bound D.

2. The method for tracking the attitude of a probe flying around an asteroid based on adaptive iterative learning according to claim 1, characterized in that: In step 4, the estimated value of the adaptive law formula (15) is used to design the switching control term of the sliding mode controller as follows: Where: η is a positive number; Based on the above results, the adaptive iterative learning posture tracking controller is designed as In the formula and The definition of is given in formula (14) and formula (16).

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