A path planning-based micro-satellite attitude maneuvering control method

Abstract

The application is suitable for the field of space control technology, and provides a micro-satellite attitude maneuver control method based on path planning, which comprises the following steps: establishing an attitude dynamics model of a micro-satellite according to obtained design parameters of the micro-satellite; planning an attitude maneuver path of the micro-satellite; designing an attitude maneuver controller; and under the action of the designed attitude maneuver controller, the micro-satellite performs attitude tracking according to the preset attitude maneuver path. In the application, an attitude dynamics model of a rigid body-flexible accessory-rigid body coupling system is established, the designed attitude maneuver path and the attitude maneuver controller can effectively suppress the vibration of a coiled stretching arm, and the attitude control precision of the micro-satellite is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of space control, and particularly relates to a micro-satellite attitude maneuver control method based on path planning. BACKGROUND

[0002] In recent years, micro-satellites play an increasingly important role in space application fields due to advantages such as light weight, small size, flexible launch mode, short development cycle and low cost. Under this background, space deployment mechanisms represented by coiled stretch arms are increasingly applied to satellite platforms to expand their functions. As a typical one-dimensional flexible deployment mechanism, the coiled stretch arm has advantages such as light weight, small power consumption and large deployment and folding ratio (up to 20:1), which is very important for micro-satellites with limited resources on the satellite and has a broad application prospect.

[0003] The micro-satellite with a coiled stretch arm refers to the connection of the satellite and the payload by using a flexible stretch arm, and the satellite platform, the coiled stretch arm and the payload form a rigid-flexible coupling system. Such a satellite has a broad application prospect in astronomical observation, space environment detection and new material space exposure test research. Due to the high coupling between the satellite rigid body and the coiled stretch arm, the vibration of the coiled stretch arm is easily caused in the satellite attitude maneuver process, and then the stability of the satellite platform and the control accuracy of the end payload are affected. The coiled stretch arm is different from flexible accessories such as solar panels and large antennas. It connects the satellite platform and the end payload in the form of a cantilever to form a rigid-flexible coupling system (i.e. a rigid-flexible coupling system), and the dynamic characteristics of the coiled stretch arm in the satellite attitude maneuver process are strong nonlinearity and multivariable coupling, which is a new challenge for satellite attitude maneuver control. However, there is little research on the micro-satellite with a coiled stretch arm in the field of attitude maneuver control in China, and there is no effective control method at present.

[0004] The application designs a micro-satellite attitude maneuver control method based on path planning, so as to effectively suppress the flexible vibration of the coiled stretch arm and ensure the satellite attitude maneuver control accuracy. SUMMARY

[0005] The purpose of the embodiment of the application is to provide a micro-satellite attitude maneuver control system based on path planning, which can effectively suppress the flexible vibration of the coiled stretch arm and ensure the satellite attitude control accuracy by designing an attitude maneuver path and adopting a sliding mode control rate based on an auxiliary compensator, so as to solve the problems mentioned in the background.

[0006] The embodiment of the application is implemented in the following way: a path planning-based micro-satellite attitude maneuver control method, the micro-satellite being composed of a cascaded satellite platform, a coiled stretchable arm and a terminal payload, the method comprising:

[0007] An attitude dynamics model of the micro-satellite is established according to the obtained design parameters of the micro-satellite;

[0008] An attitude maneuver path of the micro-satellite is planned;

[0009] An attitude maneuver controller is designed;

[0010] Under the action of the designed attitude maneuver controller, the micro-satellite performs attitude tracking according to the preset attitude maneuver path.

[0011] The path planning-based micro-satellite attitude maneuver control method provided by the embodiment of the application takes the micro-satellite with a coiled stretchable arm as a specific object, establishes a rigid-flexible coupling multi-body satellite dynamics model for rigid body-flexible accessory-rigid body, fully considers the structural mechanics characteristics of the coiled stretchable arm, and ensures the reliability and accuracy of the model; on the basis of the attitude maneuver path planning, the designed attitude maneuver path based on upper and lower limit time fixing can effectively reduce the maximum amplitude of the first three order modes of the system and the maximum amplitude of the defined internal vibration disturbance, and accelerate the time for the first three order modes and the internal vibration disturbance of the system to enter the error band, i.e., greatly reduce the excited coiled stretchable arm vibration; meanwhile, on the basis, the proposed compensator-based sliding mode controller can suppress the influence of the rigid-flexible coupling term, the nonlinear dynamic term, the parameter perturbation term and the external disturbance term on the closed-loop control system in a limited time, and improve the attitude control precision. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 A path planning-based micro-satellite attitude maneuver control method flowchart provided by the embodiment of the application;

[0013] Figure 2 A micro-satellite with a coiled stretchable arm in the embodiment of the application is shown in the schematic diagram;

[0014] Figure 3 An attitude maneuver path planning schematic diagram in the embodiment of the application is shown in the schematic diagram;

[0015] Figure 4 A compensator-based attitude maneuver controller principle block diagram in the embodiment of the application is shown in the schematic diagram;

[0016] Figure 5 A change curve of an error attitude angle in the attitude maneuver process in the embodiment of the application is shown in the schematic diagram;

[0017] Figure 6The change curve of the error angular velocity in the attitude maneuver process in the embodiment of the present application is provided as follows:

[0018] Figure 7 The change curve of the attitude tracking performance in the attitude maneuver process in the embodiment of the present application is provided as follows:

[0019] Figure 8 The change curve of the vibration interference of the coiled stretchable arm in the attitude maneuver process in the embodiment of the present application is provided as follows. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0021] As shown in the drawings, Figures 1-4 in the embodiment of the present application, Figure 1 a flow chart of a micro-satellite attitude maneuver control method based on path planning provided in the embodiment of the present application is provided as follows, Figure 2 a schematic diagram of a micro-satellite with a coiled stretchable arm in the embodiment of the present application is provided as follows, Figure 3 a schematic diagram of an attitude maneuver path planning in the embodiment of the present application is provided as follows, Figure 4 a principle block diagram of an attitude maneuver controller based on a compensator is provided as follows;

[0022] Figure 2 In the embodiment of the present application, the micro-satellite is composed of a cascaded satellite platform, a coiled stretchable arm and a terminal payload, wherein the satellite platform is regarded as a rigid body, the coiled stretchable arm is regarded as a flexible accessory, and the terminal payload is regarded as a rigid body, thus constituting a rigid-flexible coupled multi-body satellite system; the method comprises steps S100-S400:

[0023] S100, establishing an attitude dynamics model of the micro-satellite according to the obtained design parameters of the micro-satellite;

[0024] In this step, the design parameters of the micro-satellite include the moment of inertia of an equivalent load composed of the coiled stretchable arm and the terminal payload, the mass of the equivalent load, the moment of inertia of the satellite platform, the length of the coiled stretchable arm, the angular velocity of the satellite, the first three order modal coordinates of the coiled stretchable arm, the required control torque, the external interference torque, and the coefficients related to the energy dissipation function and the potential energy function, etc.

[0025] It can be understood that the satellite platform, the coiled stretchable arm and the terminal payload are all well-known in the art and will not be described in detail here;

[0026] In this step, the establishment of the attitude dynamics model of the micro-satellite can utilize the Lagrange mechanics to establish the second-order attitude dynamics model of the micro-satellite containing the coiled stretchable arm, so as to ensure the nonlinear and coupling characteristics of the model, and the dynamic equation of the second-order attitude dynamics model is as follows:

[0027]

[0028]

[0029] wherein, J = diag(J mx +J sx +m μ L 2 ,J my +J sy +m μ L 2 ,J mz +J sz ), the rotational inertia of the equivalent load composed of the coiled stretchable arm and the terminal payload is J s =[J sx J sy J sz ] T , the mass of the equivalent load is m μ , the rotational inertia of the satellite platform is J m =[J mx J my J mz ] T , the length of the coiled stretchable arm is L; ω b (t) = [ω bi (t)] ∈ R 3×1 represents the angular velocity of the satellite; are the first three modal coordinates of the coiled stretchable arm, respectively representing the bending along the X-axis and Y-axis of the satellite body and the rotation around the Z-axis; represents the required control torque, represents the external disturbance torque, K d and K c are coefficients related to the energy dissipation function and the potential energy function, respectively;

[0030] In the formula, the definitions of H, ω b (t) × and M J are as follows:

[0031]

[0032]

[0033] M J = diag(m μm μ ,J sz );

[0034] Thus, the error dynamics equation of the micro-satellite can be obtained as follows:

[0035]

[0036] where q e (t)=[q ei (t)]∈R 3×1 is the vector part of the error quaternion, ω e (t)=ω b (t)-ω d (t)=[ω ei (t)]∈R 3×1 is the error angular velocity, and ω d (t)=[ω di (t)]∈R 3×1 is the expected angular velocity of the satellite, is the interference caused by the vibration of the coiled stretchable arm; in the formula, J1=J-HM J -1 H T , are the damping matrix and the stiffness matrix respectively, ξ i ,ω fi (i=1,2,3) are the damping coefficients and the modal frequencies respectively, which can be measured through experiments;

[0037] In one example of the embodiment, for the convenience of subsequent design of the attitude maneuver controller, the error dynamics equation is arranged as follows:

[0038]

[0039] where Δ(t) is an equivalent interference term composed of the rigid-flexible coupling effect and the external interference.

[0040] S200, planning an attitude maneuver path of the micro-satellite;

[0041] In this step, the attitude maneuver path of the micro-satellite can be designed based on the sinusoidal function attitude maneuver path planning; on this basis, the attitude maneuver time of the path planning in the sinusoidal function attitude maneuver path is kept unchanged, and the attitude maneuver path based on the upper and lower limit time-fixed is designed;

[0042] S300, designing an attitude maneuver controller;

[0043] S400, under the action of the designed attitude maneuver controller, the micro-satellite performs attitude tracking according to the preset attitude maneuver path;

[0044] The specific control flow of the attitude maneuver controller can refer to Figure 4 which will not be described in detail here.

[0045] In an example of an embodiment, the planning of the attitude maneuver path is implemented by the following steps:

[0046] S201: Calculate the maximum angular velocity value and the angular acceleration value that can be reached by the attitude maneuver path based on the sine function, which are

[0047]

[0048]

[0049] wherein V s_max is the maximum angular velocity value, a s_max is the maximum angular acceleration value, V allowed_max represents the maximum angular velocity value that can be reached during the satellite attitude maneuver process, T s1 is the time of the acceleration segment in the attitude maneuver process.

[0050] S202: Calculate the uniform speed segment time of the attitude maneuver path based on the sine function, which is

[0051]

[0052]

[0053]

[0054] wherein the total maneuver angle is is the minimum value of the angle that can be reached by the designed softening vibration avoidance path, T s2 is the time of the uniform speed segment in the attitude maneuver process.

[0055] S203: According to the path parameters determined in steps S201 and S202, and according to the integral law of the planning graph and the sine function, the angular position trajectory is obtained.

[0056] S204: Design an attitude maneuver path based on the upper and lower limit time fixed, which can be divided into variable acceleration segments, uniform acceleration segments, variable acceleration segments and variable deceleration segments, uniform deceleration segments, and variable deceleration segments according to the angular velocity; define the variable acceleration segments and the variable deceleration segments as quarter sine functions, and the attitude maneuver angular acceleration is

[0057]

[0058] In one example, on the basis of the path planning based on the sine function, the additional conditions of the maneuvering process are: the maximum value of the attitude maneuvering angular acceleration is a n_max = ka s_max , where 0 < k < 1.

[0059] S205: Calculate the variable acceleration section time of the attitude maneuvering path based on the upper and lower time-fixed values:

[0060]

[0061] After the attitude maneuvering acceleration is completed by using the attitude maneuvering path based on the upper and lower time-fixed values, the speed value reached should be equal to the speed value reached after the attitude maneuvering acceleration is completed by using the path based on the sine function; then the expression of the variable acceleration section time is

[0062]

[0063] S206: Calculate the variable deceleration section time of the attitude maneuvering path based on the upper and lower time-fixed values:

[0064]

[0065] After the attitude maneuvering deceleration is completed by using the attitude maneuvering path based on the upper and lower time-fixed values, the effect reached by using the path based on the sine function should be realized, that is, the speed is zero; then the expression of the variable deceleration section time is

[0066]

[0067] S207: On the basis of the path planning based on the sine function, the attitude angular acceleration variation law of the path based on the upper and lower time-fixed values is obtained by using steps S205 and S206, and then the angular position trajectory is obtained according to the planning graph and the sine function variation law.

[0068] In one embodiment, on the basis of step S200, a sliding mode controller based on a compensator is designed, and then the attitude maneuvering controller of the microsatellite is obtained; the design of the attitude maneuvering controller is realized by the following steps:

[0069] S301: Design a nominal controller for the undisturbed system;

[0070] The sliding mode control law based on the compensator is designed as:

[0071] u(t) = J1[u N (t) + u C (t) + u S (t)];

[0072] where u N(t) is a nominal controller designed for the interference-free system, u C (t) is a compensator designed for the uncertainty term caused by the rigid-flexible coupling effect and external disturbance, u S (t) is a sliding mode controller designed for the coupling nonlinear term of the error angular velocity and the desired angular velocity.

[0073] In one example of the embodiment, the nominal controller is designed as:

[0074]

[0075] S302: A compensator is designed for the uncertainty caused by the rigid-flexible coupling effect and external disturbance. Specifically, it includes:

[0076] S3021: A nonlinear observer is designed to satisfy:

[0077]

[0078] wherein, α(t) represents the measurable state of the micro-satellite control system with a coiled stretchable arm, δ e (t) = ω e (t) - α(t) represents the measurement error. In the formula, k2, k3, k4 are normal numbers to be determined, which can be determined by a finite number of experiments, is the estimated value of δ e (t), y(t) = k2δ e (t), is the measurable y(t) numerical differential, is the observation error, τ e (e(t)) represents a nonlinear function, which can be specifically represented as τ e (e(t)) = [|e1| τ sign(e1), |e2| τ sign(e2), |e3| τ sign(e3)], τ is a normal value satisfying 0 < τ < 1.

[0079] S3022: Based on the nonlinear observer, a compensator is designed as:

[0080]

[0081] wherein, k1 is a normal number to be determined.

[0082] S303: A sliding mode controller is designed for the coupling nonlinear term of the error angular velocity and the desired angular velocity. Specifically, the sliding mode surface is designed as s = cq e + ω e , and the sliding mode controller can be designed as: where c is a constant.

[0083] In one embodiment, a simulation experiment is performed on a micro-satellite with a coiled deployable boom, which is composed of a satellite platform, a coiled deployable boom and a terminal payload, and the relevant parameters are as follows:

[0084] J m = diag(1.5, 2.5, 0.7) kg·m 2

[0085] J s = diag(0.2, 0.2, 0.4) kg·m 2

[0086] J = diag(9.7, 10.7, 1.1) kg·m 2

[0087] m μ = 2 kg

[0088] L = 2 m

[0089] ξ = diag(0.086, 0.089, 0.091)

[0090] ω f = diag(0.3214, 0.3978, 1.2380) rad / s

[0091] The controller parameters are as follows:

[0092] k1 = 2, k2 = 3, k3 = 4, k4 = 5, τ = 0.5

[0093] c = 1

[0094] k = 50

[0095] ε = 0.01

[0096] η(0) = [-0.1 m 0.1 m 10° π / 180] T

[0097]

[0098] α(0) = [0 0 0] T

[0099]

[0100] The initial attitude Euler angle is set to [0° 50° 0°] T , and the desired attitude Euler angle is [30° 0° 30°] T, the initial attitude angular velocity and the desired attitude angular velocity are both 0, the simulation time is 200s, the external disturbance in the disturbance torque is assumed to be a mixed signal of periodic disturbance of two frequencies and constant disturbance, which can be expressed as

[0101]

[0102] Figures 5-8 The simulation result of the micro-satellite attitude maneuver control method based on path planning shows that the satellite can realize fast attitude maneuver control, can track the planned attitude maneuver path well, can effectively suppress the flexible vibration of the coiled stretchable arm, and can improve the control precision of the satellite platform.

[0103] The embodiment provides a micro-satellite attitude maneuver control method based on path planning, establishes a rigid-flexible coupling multi-body satellite dynamics model of rigid body-flexible accessory-rigid body, fully considers the structural mechanical characteristics of the coiled stretchable arm, and guarantees the reliability and accuracy of the model; on the basis of the attitude maneuver path planning based on a sine function, the designed attitude maneuver path based on upper and lower limit time fixing can effectively reduce the maximum amplitude of the first three modes of the system and the maximum amplitude of the defined internal vibration disturbance, and can accelerate the time of the first three modes of the system and the internal vibration disturbance into the error band, namely, can greatly reduce the excited coiled stretchable arm vibration; on the basis, the proposed sliding mode controller (namely, the attitude maneuver controller) based on a compensator can suppress the influence of the rigid-flexible coupling term, the nonlinear dynamic term, the parameter perturbation term and the external disturbance term on the closed-loop control system in a limited time, and improve the attitude control precision; the embodiment takes the micro-satellite with the coiled stretchable arm as a specific object, the proposed control method has strong applicability, simple structure and small calculation amount, and is easy to realize in engineering.

[0104] The above-described embodiments only express several embodiments of the present application, which are described in detail and specifically, but should not be understood as the limitation of the patent scope of the present application. It should be noted that, for ordinary skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the patent protection scope of the present application should be subject to the appended claims.

[0105] The above only describes the preferred embodiments of the present application and should not be used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A path planning based micro-satellite attitude maneuver control method, the micro-satellite is composed of a cascaded satellite platform, a coiled stretch arm and an end payload, characterized in that, The method comprises: According to the obtained design parameters of the micro-satellite, an attitude dynamics model of the micro-satellite is established; The attitude maneuver path of the micro-satellite is planned; An attitude maneuver controller is designed; Under the action of the designed attitude maneuver controller, the micro-satellite performs attitude tracking according to the preset attitude maneuver path; In the step of establishing the attitude dynamics model of the micro-satellite according to the obtained design parameters of the micro-satellite, the attitude dynamics model of the micro-satellite is established by using Lagrange mechanics equation; The error dynamics equation of the attitude dynamics model is: ； wherein, is the error angular velocity, denotes the angular velocity of the micro-satellite, is the desired angular velocity of the micro-satellite; is the equivalent disturbance term composed of the uncertain terms caused by the rigid-flexible coupling effect and the external disturbance; , is the moment of inertia of the equivalent load composed of the coiled stretchable arm and the end payload, is the mass of the equivalent load, is the moment of inertia of the satellite platform, is the length of the coiled stretchable arm, ; denotes the required control moment, denotes the external disturbance moment, is the disturbance caused by the vibration of the coiled stretchable arm, , are the damping matrix and the stiffness matrix, respectively, and are the coefficients related to the energy dissipation function and the potential energy function, respectively, are the damping coefficient and the modal frequency, respectively; wherein , and are defined as follows: ， ， ； The step of planning the attitude maneuver path of the micro-satellite comprises: The attitude maneuver path based on the sine function is selected; The attitude maneuver time of the attitude maneuver path is kept unchanged, and the attitude maneuver path based on the upper and lower limit time is designed, which can be divided into variable acceleration section, uniform acceleration section, variable acceleration section and variable deceleration section, uniform deceleration section and variable deceleration section according to angular velocity; The attitude maneuver controller satisfies: ， wherein, is a nominal controller designed for the interference-free system, is a compensator designed for the uncertainty term caused by the rigid-flex coupling effect and external disturbance, is a sliding mode controller designed for the coupling nonlinear term of the error angular velocity and the desired angular velocity.

2. The method of claim 1, wherein, The nominal controller satisfies: 。 3. The method of claim 1, wherein, The compensator is set according to the nonlinear observer, and the nonlinear observer satisfies: ， wherein, represents a measurement error, is a constant to be determined, is an estimated value of , , is a measurable numerical differentiation, is an observation error, denotes a nonlinear function, is a normal value satisfying ; Based on the nonlinear observer, a compensator is designed: wherein is a normal number to be determined; The sliding mode controller satisfies: wherein, is a constant.

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