Adaptive Control Method for Relative Motion in Proximity Detection Missions of Small Spacecraft

Abstract

The present invention provides a relative motion adaptive control method for the close-range detection mission of small spacecrafts, which is characterized by the following steps: Step 1, regarding the close-range detection object as the target spacecraft and the small spacecraft as the service spacecraft, and constructing a relative orbit dynamics model between the two; Step 2, designing a full-process nominal flight trajectory according to the requirements of the close-range detection mission, including parameters of some key hover points, transfer trajectories between hover points, and transfer times; Step 3, respectively representing the relative orbit dynamics model and the nominal flight trajectory in state space; Step 4, regarding the nominal flight trajectory as the reference model and the relative orbit dynamics model as the controlled object, and designing a relative motion adaptive controller by using the adaptive control theory SAC. The present invention still has good control effects under the influence factors such as the existence of modeling uncertainty terms, unknown disturbances, and limited control capabilities in the controlled object.

Description

Technical Field

[0001] The present invention relates to the field of on-orbit servicing in space, and particularly to a relative motion control method for the approach detection mission of small spacecraft. Background Art

[0002] In the situation of increasingly tense space resources, on-orbit servicing is an essential means to solve various faults and accidents that occur during the on-orbit operation of spacecraft, replace failed components of spacecraft, and refuel spacecraft. However, on-orbit servicing has characteristics such as complex systems, numerous elements, and high sensitivity. Coupled with the particularity of the space environment, it faces numerous obstacles in engineering practice. Conducting close-range observation of space targets can make up for the deficiencies of ground observation imaging information, is an important means to obtain the on-orbit characteristics and state information of targets, and is also a necessary pre-stage for carrying out refined on-orbit servicing.

[0003] Close-range observation means that a spacecraft forms a relative motion trajectory that is convenient for observation within the close range of another spacecraft, realizes purposeful, continuous and orderly observation and monitoring of the characteristics and state of the spacecraft, so as to understand and master information such as the external shape, motion state, maneuver intention, and fault phenomenon of the spacecraft, and can provide information support and guarantee for on-orbit servicing in space. Summary of the Invention

[0004] The technical problem solved by the present invention is: aiming at the high-precision and strong robustness requirements of the control system during the approach detection process of small spacecraft, based on the simple adaptive control architecture, a novel joint design strategy for nominal trajectory planning and relative orbit control is proposed, and an adaptive controller with high precision and strong robustness is designed.

[0005] The technical solution of the present invention is as follows:

[0006] A relative motion adaptive control method for the approach detection mission of small spacecraft, characterized by including the following steps:

[0007] Step 1, regarding the approach detection object as the target spacecraft and the small spacecraft as the service spacecraft, and constructing a relative orbit dynamics model between the two;

[0008] Step 2, designing a full-process nominal flight trajectory according to the requirements of the approach detection mission, including parameters of some key hover points, transfer trajectories between hover points, and transfer times;

[0009] Step 3, respectively representing the relative orbit dynamics model and the nominal flight trajectory in state space;

[0010] Step 4: Consider the nominal flight trajectory as the reference model and the relative orbit dynamics model as the controlled object, and design a relative motion adaptive controller using the self-adaptive control theory SAC.

[0011] Furthermore, in the said Step 1, the specific process includes:

[0012] The relative dynamics equation derived based on the algebraic method is differentiated through the orbit dynamics in the inertial coordinate system and expressed in the target spacecraft LVLH orbit system to obtain the non-linear form of the relative dynamics equation:

[0013]

[0014] In the formula: the subscripts t and s respectively represent the target spacecraft and the servicing spacecraft, θ represents the true anomaly of the target spacecraft, μ is the gravitational constant of the earth,

[0015] Neglect the perturbation difference between the target spacecraft and the servicing spacecraft. At the same time, under the assumption of a nearly circular orbit and through the first-order approximation of the gravity field, the following relative motion equation, that is, the CW equation, is obtained:

[0016]

[0017] In the formula: n is the average angular velocity of the target spacecraft.

[0018] Furthermore, in the said Step 2, the full-process nominal flight trajectory designed according to the requirements of the proximity detection mission includes: the design of the nominal flight trajectory takes into account many constraint factors such as technical characteristics, mission requirements, and safety limitations, and is designed in two forms: linear translation and elliptical fly-around. At the same time, in order to make the segmented trajectories transition smoothly, a hover mode is introduced at the key points.

[0019] Furthermore, in the said Step 2, for the design of the linear translation trajectory with fixed start and end positions, the polynomial interpolation principle is adopted, and the mathematical description of the nominal trajectory is expressed as a polynomial function related to the relative position l, relative velocity and time:

[0020]

[0021] In the formula, a n 、a n-1 、...、a1 and a0 represent the interpolation coefficients of the nth-degree polynomial,

[0022] For the determination of the interpolation coefficients of the nth-degree polynomial, at least n + 1 equations are required. Besides the boundary information l(t0) = l0 and l(t f ) = l f ), the derivatives of each order of the relative position l are introduced to construct the remaining n - 1 boundary conditions to uniquely determine the interpolation coefficients of the polynomial.

[0023] Furthermore, in the step 2, the construction of the remaining n - 1 boundary conditions by introducing the derivatives of the relative position l includes

[0024] Furthermore, the design of the elliptical flying-around trajectory is basically the same as the design method of the linear translation trajectory. The difference is that in the design of the elliptical flying-around trajectory, the flying-around angle θ and its derivatives are used as interpolation variables, and the process of determining the interpolation polynomial coefficients is the same as that of the linear translation.

[0025] Furthermore, in the step 3, expressing the relative orbit dynamics model and the nominal flight trajectory as state-space expressions includes:

[0026] The relative orbit dynamics model is expressed as a state-space expression of the relative position Δr and the relative velocity Δv:

[0027]

[0028] The nominal flight trajectory is expressed as a state-space expression of the relative motion vector X and :

[0029]

[0030] Furthermore, in the step 4, the specific process includes:

[0031] Based on the SAC theory, if the controlled object in Equation (4) wants to achieve asymptotic tracking of the reference model in Equation (5), its control input is expressed as:

[0032]

[0033] In the formula, e y represents the error between the controlled object and the reference model, x m represents the state of the reference model, u m represents the input signal of the reference model, K e 、K x and K u respectively represent time-varying gain matrices with respect to e y 、x m and u m and are expressed in the following forms:

[0034]

[0035]

[0036]

[0037] In the formula, Γ e 、Γx and Γ u Determine the matrix coefficients for adaptability, and σ is used to eliminate the influence of external disturbances on the control gain.

[0038] Beneficial effects:

[0039] In view of the relative motion modeling and control problems of on-orbit spacecraft, the present invention designs a relative motion adaptive control method. Through embodiments, it shows that this control method still has good control effects under the influence factors such as the existence of modeling uncertainty terms, unknown disturbances, and limited control capabilities in the controlled object. Description of the drawings

[0040] Figure 1 is a flowchart of the relative motion adaptive control method for the close-proximity detection mission of microspacecraft according to the present invention;

[0041] Figure 2 is a schematic diagram of the absolute motion in the inertial system and the relative motion in the target orbit system;

[0042] Figure 3 is a schematic diagram of the controller framework based on the SAC theory;

[0043] Figure 4 is a schematic diagram of the simulation system framework for verifying the adaptive controller designed by the present invention;

[0044] Figure 5 is the motion trajectory of the tracker in the LVLH orbit coordinate system of the target;

[0045] Figure 6 is the relationship between the motion state of the tracker and time;

[0046] Figure 7 is the relationship between the control quantity of the tracker and time;

[0047] Figure 8 is the relationship between the control error of the adaptive controller and time. Specific implementation manners

[0048] The following will combine Figures 1 to 8 to further describe in detail a relative motion adaptive control method for the close-proximity detection mission of microspacecraft according to the present invention.

[0049] Figure 1 is a flowchart of the relative motion adaptive control method for the close-proximity detection mission of microspacecraft according to the present invention. As Figure 1 shown, the present invention provides a relative motion adaptive control method for the close-proximity detection mission of microspacecraft, and this method includes the following steps:

[0050] Step 1: Regarding the approaching detection object as the target spacecraft and the microsatellite as the servicing spacecraft, a relative orbital dynamics model between the two is constructed.

[0051] In the above Step 1, the relative orbital dynamics model between the target spacecraft and the servicing spacecraft is derived by the algebraic method. Figure 2 As shown in the schematic diagram of the absolute motion in the inertial system and the relative motion in the target orbital system, as Figure 2 shown, the relative dynamics equation derived based on the algebraic method is a classic model for studying relative motion guidance and control. By taking the difference of the orbital dynamics in the inertial coordinate system and expressing it in the target spacecraft's LVLH orbital system, the non-linear form of the relative dynamics equation can be obtained:

[0052]

[0053] In the formula: the subscripts t and s represent the target spacecraft and the servicing spacecraft respectively, θ represents the true anomaly of the target spacecraft, and μ is the gravitational constant of the earth.

[0054] Neglecting the perturbation difference between the target spacecraft and the servicing spacecraft, and under the assumption of a nearly circular orbit, and through the first-order approximation of the gravity field, a very simple relative motion equation can be obtained, that is, the CW equation:

[0055]

[0056] In the formula: n is the average angular velocity of the target spacecraft.

[0057] Equation (2) is a special case of Equation (1), and the subsequent design is carried out for Equation (2).

[0058] Step 2: Design a full-process nominal flight trajectory according to the requirements of the approaching detection mission, including some key hover points, the transfer trajectories between the hover points, and parameters such as the transfer time, etc.

[0059] In the above Step 2, the design of the nominal flight trajectory involves many constraint factors such as technical characteristics, mission requirements, and safety limitations. It can usually be designed in two forms: linear translation and elliptical orbiting. At the same time, in order to make the segmented trajectories transition smoothly, a hover mode can be introduced at the key points.

[0060] For the design of the linear translation trajectory with fixed start and end positions, the polynomial interpolation principle can be used. The mathematical description of the nominal trajectory is expressed as a polynomial function related to the relative position l, relative velocity and time:

[0061]

[0062] In the formula, a n 、a n-1,..., a1 and a0 represent the interpolation coefficients of an nth-degree polynomial.

[0063] For the determination of the interpolation coefficients of an nth-degree polynomial, at least n+1 equations are required, and the available boundary information is only l(t0) = l0 and l(t f ) = l f , so it is necessary to introduce the derivatives of each order of the relative position l to construct the remaining n-1 boundary conditions to uniquely determine the interpolation coefficients of the polynomial, such as and so on.

[0064] The design method of the elliptical fly-around trajectory is basically the same as that of the linear translation trajectory. The difference is that in the design of the elliptical fly-around trajectory, the fly-around angle θ and its derivatives of each order are used as interpolation variables, and the determination process of the interpolation polynomial coefficients is the same as that of the linear translation.

[0065] Step 3, represent the relative orbit dynamics model and the nominal flight trajectory as state-space expressions;

[0066] Furthermore, in the said Step 3, represent the relative orbit dynamics model and the nominal flight trajectory as state-space expressions, where:

[0067] The relative orbit dynamics model can be represented as a state-space expression of the relative position Δr and the relative velocity Δv:

[0068]

[0069] Represent the nominal flight trajectory as a state-space expression of the relative motion vector X and :

[0070]

[0071] Step 4, regard the nominal flight trajectory as the reference model, regard the relative orbit dynamics model as the controlled object, and design the relative motion adaptive controller by using the adaptive control theory (SAC).

[0072] In the said Step 4, combining the control system framework of the simple adaptive control theory (SAC), regard the nominal flight trajectory as the reference model, regard the relative orbit dynamics model as the controlled object, and design the relative motion controller of the spacecraft, Figure 3 is the schematic diagram of the controller framework based on the SAC theory, as shown in Figure 3 shown, and in its specific process:

[0073] Based on the SAC theory, if the controlled object in Equation (4) wants to achieve asymptotic tracking of the reference model in Equation (5), then its control input can be expressed as:

[0074]

[0075] where, e y represents the error between the controlled object and the reference model, x m represents the state of the reference model, u m represents the input signal of the reference model, K e 、K x and K u respectively represent time-varying gain matrices with respect to e y 、x m and u m and are expressed in the following form:

[0076]

[0077]

[0078]

[0079] where, Γ e 、Γ x and Γ u are matrix coefficients that determine the adaptability, and σ is used to eliminate the influence of external disturbances on the control gain.

[0080] The following introduces the application process of the present invention in combination with specific embodiments:

[0081] Figure 4 is a schematic diagram of the simulation system framework for verifying the adaptive control method designed by the present invention. The simulation system framework shown in Figure 4 is built to verify the adaptive control method designed by the present invention. In the simulation verification process, the RK-4 numerical integration method for the J2 perturbation equation is used to simulate the spacecraft orbit dynamics, and the integration step size is 0.05 s; the relative position and velocity obtained by absolute position and velocity calculation are used to simulate the relative measurement information of the tracker to the target; the control period of the control system is designed to be 1 s, and the control acceleration limit is -0.003 m / s 2 ~0.003 m / s 2 .

[0082] At the initial moment, the tracker is located 500 m behind the target on the same orbit, and the initial six orbital elements of the two are respectively:

[0083] Target spacecraft: a = 6778.140 km, e = 0.001, i = 42.000°, Ω = 123.536°, ω T = 69.000°, f T = 298.467°.

[0084] Service spacecraft: a = 6778.140 km, e = 0.001, i = 41.999°, Ω = 123.536°, ωT = 69.000°, f T = 298.463°.

[0085] The nominal trajectory is designed to approach linearly from 500 m behind to 200 m behind, hover at a fixed point 200 m behind, fly around quickly at 200 m, and hover at a fixed point 200 m in front. The four segments take 1000 s, 200 s, 1000 s, and 200 s respectively. By interpolating the nominal trajectory using a cubic polynomial, the reference input signal can be obtained.

[0086] The SAC controller parameters are designed as Γ e = [I3 I3] × e -8 , Γ xm = [I3 I3] × e -10 , Γ um = [I3 I3], σ = 0.0001, where I3 is a 3x3 identity matrix. In addition, to reduce the adaptive adjustment time of the SAC controller, the and values are selected as the initial values of the gain matrices such as K e (t), K x (t), and K u (t). The specific parameters are shown in the following formula:

[0087]

[0088]

[0089]

[0090] Based on the above simulation initial orbit conditions and control system parameters, simulation verification is carried out. Figure 5 The motion trajectory of the tracker in the target's LVLH orbit coordinate system is given. As Figure 5 shown, under the action of the corresponding controller, the tracker can achieve the tasks of approaching and flying around the target for observation. Figure 6 The relationship between the motion state of the tracker and time is given. As Figure 6 shown, under the action of the corresponding controller, the motion trajectory of the tracker is highly consistent with the designed nominal trajectory. Figure 7 The relationship between the control quantity of the tracker and time is given. As Figure 7 shown, the control quantity of the tracker can cope with the output saturation characteristics of the actuator in engineering practice, and has the feasibility of engineering implementation. Figure 8 The relationship between the control error of the adaptive controller and time is given. As Figure 8 shown, under the action of the corresponding controller, the error between the actual flight state and the nominal state of the tracker is small, indicating that this control method has the feasibility of engineering application.

[0091] In the above relative motion adaptive control method for the close-range detection mission of small spacecrafts of the present invention, by using the simple adaptive control theory, a novel combined design strategy for nominal trajectory planning and relative orbit control is proposed, an adaptive controller with the characteristics of high precision and strong robustness is designed, and the performance of the controller is verified through specific embodiments, indicating that the controller still has good control effects under the influence factors such as the existence of modeling uncertainty terms, unknown disturbances and limited control capabilities in the controlled object.

[0092] The above embodiments are only used to illustrate the content of the present invention. In addition to the above embodiments, the present invention has other embodiments. All technical solutions formed by equivalent replacement or equivalent deformation fall within the protection scope of the present invention.

Claims

1. A relative motion adaptive control method for the close - proximity exploration mission of small spacecraft, characterized in that, It includes the following steps: Step 1: Regarding the approaching detection object as the target spacecraft and the microsatellite as the servicing spacecraft, a relative orbit dynamics model between the two is constructed. Step 2: Design a full-process nominal flight trajectory according to the requirements of the approaching detection mission, including parameters of some key hover points, transfer trajectories between hover points, and transfer times. Step 3: Represent the relative orbit dynamics model and the nominal flight trajectory in state space respectively. Step 4: Regarding the nominal flight trajectory as the reference model and the relative orbit dynamics model as the controlled object, use the adaptive control theory SAC to design a relative motion adaptive controller. In the said Step 3, representing the relative orbit dynamics model and the nominal flight trajectory as state space expressions includes: The relative orbit dynamics model is represented as a state space expression of relative position Δr and relative velocity Δv: Represent the nominal flight trajectory as the relative motion vector X and State-space expression of: In the said Step 4, the specific process includes: Based on the SAC theory, if the controlled object in Equation (4) wants to achieve asymptotic tracking of the reference model in Equation (5), its control input is expressed as: where, e y represents the error between the controlled object and the reference model, x m represents the state of the reference model, u m represents the input signal of the reference model, K e 、K x and K u respectively represent the time-varying gain matrices with respect to e y 、x m and u m and are expressed in the following form: where Γ e , Γ x and Γ u are matrix coefficients that determine adaptability, and σ is used to eliminate the influence of external disturbances on the control gain.

2. The relative motion adaptive control method for the close-proximity detection mission of a small spacecraft according to claim 1, characterized in that In the said Step 1, the specific process includes: The relative dynamics equation derived based on the algebraic method is subtracted by the orbit dynamics in the inertial coordinate system and expressed in the target spacecraft's LVLH orbit system to obtain the non-linear form of the relative dynamics equation. Where: the subscripts t and s represent the target spacecraft and the servicing spacecraft respectively, θ represents the true anomaly of the target spacecraft, μ is the Earth's gravitational constant, x, y, and z are the three-axis position components in the target spacecraft's LVLH orbit system, f x , f y , f z represent the components of the acceleration in the x, y, and z axis directions in the target spacecraft's LVLH orbit system, r t , r s represent the distances from the centers of mass of the target spacecraft and the servicing spacecraft to the center of the Earth respectively. Neglecting the perturbation difference between the target spacecraft and the servicing spacecraft, and under the assumption of a nearly circular orbit, the following relative motion equation, namely the CW equation, is obtained through the first-order approximation of the gravity field: Where: n is the average angular velocity of the target spacecraft.

3. The relative motion adaptive control method for the close-proximity detection mission of a small spacecraft according to claim 2, characterized in that In the said Step 2, designing a full-process nominal flight trajectory according to the requirements of the approaching detection mission includes: The design of the nominal flight trajectory takes into account many constraint factors such as technical characteristics, mission requirements, and safety limitations, and is designed in two forms: linear translation and elliptical fly-around. At the same time, to make the transition between segmented trajectories smooth, a hover mode is introduced at key points.

4. The relative motion adaptive control method for the approach detection mission of a small spacecraft according to claim 3, characterized in that In the said step 2, for the design of the linear translation trajectory with fixed start and end positions, the polynomial interpolation principle is adopted, and the mathematical description of the nominal trajectory is expressed as a polynomial function related to the relative position l, relative velocity and time: where a n , a n-1 ,..., a1 and a0 represent the interpolation coefficients of the nth-degree polynomial, For the determination of the interpolation coefficients of an n-th degree polynomial, at least n + 1 equations are required. Beyond the boundary information l(t0) = l0 and l(t f ) = l f , the derivatives of various orders of the relative position l are introduced to construct the remaining n - 1 boundary conditions so that the interpolation coefficients of the polynomial are uniquely determined.

5. The relative motion adaptive control method for the approaching detection mission of a micro spacecraft according to claim 4, characterized in that In the said step 2, the construction of the remaining n - 1 boundary conditions by introducing the derivatives of various orders of the relative position l includes 6. The relative motion adaptive control method for the approaching detection mission of a micro spacecraft according to claim 4, wherein, The design method of the elliptical fly-around trajectory is basically the same as that of the linear translation trajectory. The difference is that in the design of the elliptical fly-around trajectory, the fly-around angle θ and its derivatives of each order are used as interpolation variables, and the determination process of the interpolation polynomial coefficients is the same as that of the linear translation.

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