Adaptive guidance method for landing on small, irregular celestial bodies with weak gravity

Abstract

This invention discloses an adaptive guidance method for landing on small, irregular celestial bodies with weak gravity, belonging to the field of deep space probe guidance technology. The implementation method is as follows: The probe's position and velocity are selected as state variables to establish a landing dynamics model; a performance function is introduced to determine the constraint boundary, giving allowable upper and lower bounds, and determining the steady-state value and convergence speed parameters of the performance function; by pre-setting the performance function and error transformation function, the trajectory tracking system with inequality constraints is converted into an unconstrained tracking system; the number of neural network nodes and Gaussian basis functions are set, and an RBFNN is used to approximate the uncertainty perturbation of the small celestial body's gravity as the distance between the probe and the landing point decreases; the uncertainty perturbation of the gravitational field fitted by the neural network is introduced into the adaptive guidance law, and the parameters of the adaptive guidance law are adaptively adjusted according to the probe's state, tracking error, and neural network fitting results to ensure the speed and high accuracy of trajectory tracking during landing.

Description

Technical Field

[0001] This invention relates to an adaptive guidance method for landing on small, irregular celestial bodies with weak gravity, belonging to the field of deep space probe guidance technology. Background Technology

[0002] Small body exploration is of great value for understanding the origin and evolution of the solar system, defending against near-Earth asteroid impacts, and verifying the latest deep space exploration technologies. As the complexity of small body exploration missions continues to increase, soft landing on the surface of small bodies has become one of the main methods of current exploration.

[0003] Due to the lack of prior information about asteroids, the gravitational pull of the small celestial body increases in uncertainty as the distance between the probe and the landing point decreases during the landing process. Secondly, landings in areas with higher scientific value or special resources and characteristics may be complex and dangerous, requiring not only precise attachment of the probe to the target landing point but also rapid and robust tracking of the nominal trajectory. In asteroid landing missions, using high-precision gravitational field models, such as polyhedral models, significantly increases the computational load on the onboard computer, affecting the real-time performance of landing trajectory tracking. Conversely, using spherical harmonic function models, which have lower computational requirements, results in a significant decrease in the accuracy of gravitational field calculations as the distance between the probe and the landing point decreases, affecting trajectory tracking accuracy. Furthermore, existing asteroid landing trajectory tracking and guidance methods have achieved good results in improving the accuracy and robustness of asteroid landing trajectory tracking, but they do not adequately consider the transient performance of the tracking system under complex and unknown conditions. The small celestial body landing guidance method that takes into account the preset performance can take into account both the steady-state and transient characteristics of the system, limit the trajectory tracking error within the designed performance function, prevent the risk of obstacle collision caused by excessive trajectory tracking error, and greatly increase the safety of the probe landing process. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive guidance method for landing on small, irregularly shaped celestial bodies with weak gravity. This method enables the detector to attach precisely to the target landing point and achieves rapid and robust tracking of the nominal trajectory. It prevents the landing position from deviating from the target landing point or the detector from colliding with obstacles due to excessive trajectory tracking errors, thereby increasing the safety of the detector landing process.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses an adaptive guidance method for landing on a weakly gravitationally irregular small celestial body. The method selects the probe's position and velocity as state variables and establishes a landing dynamics model in a fixed asteroid coordinate system. A performance function is introduced to determine constraint boundaries, providing upper and lower bounds for the allowable trajectory tracking error, and determining the steady-state value and convergence speed parameters of the performance function. By pre-setting the performance function and error transformation function, the trajectory tracking system with inequality constraints is converted into an unconstrained tracking system. The state variables of the probe after the conversion are designed to facilitate controller design. The number of neural network nodes and Gaussian basis functions are set, and an RBFNN is used to approximate the uncertainty perturbation caused by the gravitational field of the small celestial body as the distance between the probe and the landing point decreases, making the probe's dynamics model more accurate. The gravitational field uncertainty perturbation fitted by the neural network is introduced into the adaptive guidance law. The parameters of the adaptive guidance law are adaptively adjusted according to the probe's state, tracking error, and neural network fitting results, ensuring the speed and high accuracy of trajectory tracking during landing and effectively avoiding risks such as landing position deviation from the target landing point or probe collision with obstacles due to excessive trajectory tracking errors.

[0007] The adaptive guidance method for landing on small, irregular celestial bodies with weak gravity disclosed in this invention includes the following steps:

[0008] Step 1: Select the probe's position and velocity as state variables, and establish a landing dynamics model of the probe in the asteroid fixed coordinate system.

[0009] Choosing the probe's position and velocity as state variables, and assuming the small celestial body spins uniformly around its principal axis of maximum inertia, neglecting other disturbing forces, the probe's landing dynamics equations in the small celestial body's fixed coordinate system are expressed as:

[0010] (1)

[0011] Where r is the position vector of the detector, and v is the velocity vector of the detector. Let be the spin angular velocity vector of the small celestial body, g(r) be the gravitational acceleration of the small celestial body acting on the detector, the perturbation of the gravitational acceleration of the small celestial body is unknown and bounded, and its rate of change is also bounded, a c The control acceleration command is applied. Rewriting equation (1) in scalar form yields:

[0012] (2)

[0013] U represents the gravitational potential energy of the probe near the asteroid. , , Let a and b represent the partial derivatives of the gravitational potential energy in the three axes, respectively. cx a cy a czThese represent the control accelerations along the three axes, and all variables are expressed in a fixed coordinate system of the small celestial body. The trajectory tracking error during the probe's landing process is defined as e(t) = rr. d r d This refers to the nominal trajectory during the attachment process.

[0014] Step 2: Introduce a performance function to determine the constraint boundaries. Given the upper and lower bounds of the allowable track tracking error of the detector, determine the steady-state value and convergence speed parameters of the performance function. By pre-setting the performance function and error transformation function, the track tracking system with inequality constraints is transformed into an unconstrained tracking system. The detector state variables of the unconstrained tracking system facilitate the design of the controller.

[0015] For smooth continuous functions If the following conditions are met:

[0016] 1) Furthermore, it decreases strictly monotonically with respect to time t.

[0017] 2)

[0018] Then it is called a function For asteroid landing nonlinear systems, a preset performance function will be used. The design is as follows:

[0019] (3)

[0020] in , , For a pre-set positive number, This is the maximum allowable initial value for steady-state error. Let l be the steady-state value of the performance function as time approaches infinity, and let l determine the convergence rate of the performance function.

[0021] As shown in equations (4) and (5), by setting inequality constraints, the upper and lower bounds of the allowable trajectory tracking error of the detector are determined, so that the trajectory tracking error e(t) during the landing process reaches the preset steady-state performance and transient performance.

[0022] (4)

[0023] (5)

[0024] in Let e(0) be the overshoot suppression parameter. Directly processing nonlinear systems with inequality constraints is quite difficult; therefore, the error e(t) with inequality constraints is converted into an equivalent unconstrained error, as follows:

[0025] (6)

[0026] Where S is the error transformation function. To convert the error, the error conversion function is designed as follows:

[0027] (7)

[0028] According to the above formula:

[0029] (8)

[0030] Then we have:

[0031] (9)

[0032] make , After replacing the parameters, we have:

[0033] (10)

[0034] Let the error variable s be in the following form: constant parameter

[0035] (11)

[0036] Let the detector state variable be... The asteroid landing dynamics model can be simplified as follows:

[0037] (12)

[0038] in: , , Therefore:

[0039] in: , ; For system parameters, e = e(t) is used in the simplified expression. , i=1…6.

[0040] Step 3: Set the number of neural network nodes and Gaussian basis functions. Use radial basis neural networks to approximate the uncertainty perturbation caused by the gravity of small celestial bodies as the distance between the probe and the landing point decreases, so as to make the dynamic model of the probe more accurate.

[0041] In small body landing and exploration missions, using a high-precision polyhedral gravitational field model significantly increases the computational load on the onboard computer, affecting the real-time performance of landing trajectory tracking. Conversely, using a spherical harmonic function model with lower computational load results in a significant decrease in the accuracy of gravitational field calculations as the distance between the probe and the landing point decreases, affecting the accuracy of trajectory tracking. The following radial basis function neural network approximates the uncertainty perturbation D of the small body's gravity as the distance between the probe and the landing point decreases:

[0042] (13)

[0043] In the formula: , where m is the number of hidden layer nodes in the network. h j ( The basis functions are expressed using Gaussian functions as shown in equation (14):

[0044] (14)

[0045] In the formula: c j Let be the center vector of the j-th node in the network. Let be the base width value of node j.

[0046] This is the weight matrix of the neural network. This represents the approximation error of the neural network. The input to the neural network is taken as... Then the estimation of the uncertain term D It can be written as:

[0047] (15)

[0048] In the formula: This is for estimating the weight matrix of a neural network.

[0049] Step 4: Based on the approximation of the nonlinear uncertain perturbation in the attachment dynamics of small celestial bodies using RBFNN, an adaptive law is designed to estimate the upper bound of the error for the state variables after error transformation, ensuring the speed and high accuracy of trajectory tracking during landing.

[0050] Based on the approximation of the nonlinear uncertainty term in the attachment dynamics of small celestial bodies using RBFNN, and considering the upper bound of the approximation error... The following adaptive control law is introduced.

[0051] (16)

[0052] in: Indicates the upper bound of the approximation error The estimate is that K>0. , , , , Let be the parameters of the controller to be designed and the adaptive gain. The controller u designed using equation (16) makes s bounded, then... and Bounded positioning ultimately enables the probe to precisely attach to the target landing point of a small, irregularly shaped object with weak gravity, and allows for rapid and robust tracking of the nominal trajectory. This prevents the landing position from deviating from the target landing point or the probe from colliding with obstacles due to excessive trajectory tracking errors, thereby increasing the safety of the probe's landing process.

[0053] Beneficial effects:

[0054] 1. The adaptive guidance method for landing on a weakly gravitationally irregular small celestial body disclosed in this invention establishes a landing dynamic model of the probe in a fixed coordinate system of the asteroid, introduces a performance function to determine the constraint boundary, designs the upper and lower bounds of the allowable trajectory tracking error of the probe, and determines the steady-state value and convergence speed parameters of the performance function. By pre-setting the performance function and the error transformation function, the trajectory tracking control system with inequality constraints can be converted into an unconstrained control system. The converted unconstrained control system has an equivalent control effect to the control system with pre-set performance constraints before the conversion, so that the probe can simultaneously take into account the steady-state and transient characteristics of the system when landing on a small celestial body.

[0055] 2. The adaptive guidance method for landing on small, irregular celestial bodies with weak gravity disclosed in this invention sets the number of neural network nodes and Gaussian basis functions, and uses RBFNN to approximate the uncertainty perturbations caused by inaccurate gravitational field models during the probe landing process; the gravitational field uncertainty perturbations fitted by the neural network are introduced into the adaptive guidance law, and the parameters of the adaptive guidance law are adaptively adjusted according to the probe state, the rate of change of the state, and the fitting results of the neural network, ensuring the speed and high accuracy of trajectory tracking during the landing process, and effectively avoiding risks such as the landing position deviating from the target landing point or the probe colliding with obstacles due to excessive trajectory tracking errors. Attached Figure Description

[0056] Figure 1 This is a flowchart of the adaptive guidance method for landing on small, irregular celestial bodies with weak gravity, as disclosed in this invention.

[0057] Figure 2 This is a trajectory diagram of the probe landing on the surface of a small celestial body using the adaptive guidance method for landing on a weakly gravitationally irregular small celestial body disclosed in this invention.

[0058] Figure 3 shows the trajectory tracking error of the probe in the x-axis direction in the fixed coordinate system of the asteroid;

[0059] Figure 4 shows the trajectory tracking error of the probe in the y-axis direction in the fixed coordinate system of the asteroid.

[0060] Figure 5 shows the trajectory tracking error of the probe in the z-axis direction in the fixed coordinate system of the asteroid. Detailed Implementation

[0061] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0062] Numerical simulations were conducted using 25143 Itokawa as the target asteroid, which has a size of (0.535 × 0.294 × 0.209) km. In the fixed coordinate system of the asteroid, the initial position r0 of the probe's center of mass is [-22.85, -134.77, 255.24] m, the initial velocity v0 is [0.01, 0.02, -0.02] m / s, the target landing point is [-44.73, -84.18, 85.94] m, and the transfer time t... f Set to 240s. The nominal landing trajectory of the probe is designed using the ZEM / ZEV guidance law. Through preset performance function parameters, the maximum trajectory tracking error of the probe in the three axes is 0.8m; the initial position error is [-0.45, -0.6, -0.2]m. The neural network adaptive controller parameters are designed as follows: K=3.2. , , , , .

[0063] like Figure 1 As shown in the example, the adaptive guidance method for landing on small, irregular celestial bodies with weak gravity disclosed in this example has the following specific implementation steps:

[0064] Step 1: Select the probe's position and velocity as state variables, and establish a landing dynamics model of the probe in the asteroid fixed coordinate system.

[0065] Choosing the probe's position and velocity as state variables, and assuming the small celestial body spins uniformly around its principal axis of maximum inertia, neglecting other disturbing forces, the probe's landing dynamics equations in the small celestial body's fixed coordinate system are expressed as:

[0066] (17)

[0067] Where r is the position vector of the detector, and v is the velocity vector of the detector. Let be the spin angular velocity vector of the small celestial body, g(r) be the gravitational acceleration of the small celestial body acting on the detector, the perturbation of the gravitational acceleration of the small celestial body is unknown and bounded, and its rate of change is also bounded, a c The applied control acceleration command. Rewriting the above equation in scalar form yields:

[0068] (18)

[0069] U represents the gravitational potential energy of the probe near the asteroid. , , Let a and b represent the partial derivatives of the gravitational potential energy in the three axes, respectively. cx a cy a cz These represent the control accelerations along the three axes, and all variables are expressed in a fixed coordinate system of the small celestial body. The trajectory tracking error during the probe's landing process is defined as e(t) = rr. d r d This refers to the nominal trajectory during the attachment process.

[0070] Step 2: Introduce a performance function to determine the constraint boundaries. Given the upper and lower bounds of the allowable trajectory tracking error of the detector, determine the steady-state value and convergence speed parameters of the performance function. By pre-setting the performance function and error transformation function, the trajectory tracking system with inequality constraints is transformed into an unconstrained tracking system. The state variables of the transformed detector are designed to facilitate the design of the controller.

[0071] For smooth continuous functions If the following conditions are met:

[0072] 1) Furthermore, it decreases strictly monotonically with respect to time t.

[0073] 2)

[0074] Then it is called a function For asteroid landing nonlinear systems, a preset performance function will be used. The design is as follows:

[0075] (19)

[0076] in , , For a pre-set positive number, The maximum allowable initial value for steady-state error is set to 0.8m. Let l be the steady-state value of the performance function as time approaches infinity. l determines the convergence rate of the performance function, and its value is set to 0.2.

[0077] As shown in equations (20) and (21), by setting inequality constraints, the upper and lower bounds of the allowable trajectory tracking error of the detector are determined, so that the trajectory tracking error e(t) during the landing process reaches the preset steady-state performance and transient performance.

[0078] (20)

[0079] (twenty one)

[0080] in Let e(0) be the overshoot suppression parameter. Directly processing nonlinear systems with inequality constraints is quite difficult; therefore, the error e(t) with inequality constraints is converted into an equivalent unconstrained error, as follows:

[0081] (twenty two)

[0082] Where S is the error transformation function. To convert the error, the error conversion function is designed as follows:

[0083] (twenty three)

[0084] According to the above formula:

[0085] (twenty four)

[0086] Then we have:

[0087] (25)

[0088] make , After replacing the parameters, we have:

[0089] (26)

[0090] Let the error variable s be in the following form: constant parameter

[0091] (27)

[0092] Let the detector state variable be... The asteroid landing dynamics model can be simplified as follows:

[0093] (28)

[0094] in: , , Therefore:

[0095] For simplicity, e = e(t) in the formula. , For system parameters, , ; i=1…6.

[0096] Step 3: Set the number of neural network nodes and Gaussian basis functions. Use radial basis neural networks to approximate the uncertainty perturbation caused by the gravity of small celestial bodies as the distance between the probe and the landing point decreases, so as to make the dynamic model of the probe more accurate.

[0097] In small body landing and exploration missions, using a high-precision polyhedral gravitational field model significantly increases the computational load on the onboard computer, affecting the real-time performance of landing trajectory tracking. Conversely, using a spherical harmonic function model with lower computational load results in a substantial decrease in the accuracy of gravitational field calculations as the distance between the probe and the landing point decreases, impacting trajectory tracking accuracy. The following radial basis function neural network approximates the uncertainty perturbation D caused by the decreasing distance between the probe and the landing point in the gravitational field of the small body:

[0098] (29)

[0099] In the formula: , where m is the number of hidden layer nodes in the network. h j ( The basis functions are expressed in Gaussian form as shown in equation (30):

[0100] (30)

[0101] In the formula: c j Let be the center vector of the j-th node in the network. Let be the base width value of node j.

[0102] This is the weight matrix of the neural network. This represents the approximation error of the neural network. The input to the neural network is taken as... Then the estimation of the uncertain term D It can be written as:

[0103] (31)

[0104] In the formula: This is for estimating the weight matrix of a neural network.

[0105] Step 4: Based on the approximation of the nonlinear uncertain perturbation in the attachment dynamics of small celestial bodies using RBFNN, an adaptive law is designed to estimate the upper bound of the error for the state variables after error transformation, ensuring the speed and high accuracy of trajectory tracking during landing.

[0106] Based on the approximation of the nonlinear uncertainty term in the attachment dynamics of small celestial bodies using RBFNN, and considering the upper bound of the approximation error... The following adaptive control law is introduced.

[0107] (32)

[0108] in: Indicates the upper bound of the approximation error The estimate is that K>0. , , , , The controller parameters and adaptive gain to be designed are as follows: K = 3.2. , , , , If the controller u designed using equation (32) makes s bounded, then and Bounded positioning ultimately enables the probe to precisely attach to the target landing point of a small, irregularly shaped object with weak gravity, and allows for rapid and robust tracking of the nominal trajectory. This prevents the landing position from deviating from the target landing point or the probe from colliding with obstacles due to excessive trajectory tracking errors, thereby increasing the safety of the probe's landing process.

[0109] Landing on smaller asteroids places higher demands on nominal trajectory tracking accuracy and landing error. Figure 2 , 3 As can be seen from points 4 and 5, the small celestial body landing neural network adaptive control method disclosed in this invention can simultaneously take into account the steady-state and transient characteristics of the system. The probe trajectory tracking error is always kept within the range of 0.8m and eventually converges to 0.05m. The probe has high landing accuracy and can effectively prevent the risk of obstacle collision caused by excessive trajectory tracking error, greatly increasing the safety of the probe landing process.

[0110] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive guidance method for landing on small, irregular celestial bodies with weak gravity, characterized in that: Includes the following steps, Step 1: Select the probe's position and velocity as state variables, and establish a landing dynamics model of the probe in the asteroid fixed coordinate system; Step 1 is implemented as follows: Choosing the probe's position and velocity as state variables, and assuming the small celestial body spins uniformly around its principal axis of maximum inertia, neglecting other disturbing forces, the probe's landing dynamics equations in the small celestial body's fixed coordinate system are expressed as: （1） Where r is the position vector of the detector, and v is the velocity vector of the detector. Let be the spin angular velocity vector of the small celestial body, g(r) be the gravitational acceleration of the small celestial body acting on the detector, the perturbation of the gravitational acceleration of the small celestial body is unknown and bounded, and its rate of change is also bounded, a c To apply the control acceleration command; writing equation (1) in scalar form, we get: （2） U represents the gravitational potential energy of the probe near the asteroid. , , Let a and b represent the partial derivatives of the gravitational potential energy in the three axes, respectively. cx a cy a cz These represent the control accelerations along the three axes, and all variables are expressed in a fixed coordinate system of the small celestial body. The trajectory tracking error during the probe's landing process is defined as e(t) = rr. d r d The nominal trajectory during the attachment process; Step 2: Introduce a performance function to determine the constraint boundary. Given the upper and lower bounds that the detector trajectory tracking error can be allowed, determine the steady-state value of the performance function and the convergence speed parameter of the performance function; by pre-setting the performance function and the error transformation function, the trajectory tracking system with inequality constraints is converted into an unconstrained tracking system. Step 2 is implemented as follows: For smooth continuous functions If the following conditions are met: 1) Furthermore, it is strictly monotonically decreasing with respect to time t; 2) Then it is called a function For asteroid landing nonlinear systems, a preset performance function will be used. The design is as follows: （3） in , , For a pre-set positive number, This is the maximum allowable initial value for steady-state error. Let l be the steady-state value of the performance function as time approaches infinity, and let l determine the convergence rate of the performance function. As shown in equations (4) and (5), by setting inequality constraints, the upper and lower bounds of the allowable trajectory tracking error of the detector are determined, so that the trajectory tracking error e(t) during the landing process reaches the preset steady-state performance and transient performance. （4） （5） in Let e(0) be the overshoot suppression parameter. Directly processing nonlinear systems with inequality constraints is quite difficult; therefore, the error e(t) with inequality constraints is converted into an equivalent unconstrained error, as follows: （6） Where S is the error transformation function. To convert the error, the error conversion function is designed as follows: （7） According to the above formula: （8） Then we have: （9） make , After replacing the parameters, we have: （10） Let the error variable s be of the following form: constant parameter （11） Let the detector state variable be... The asteroid landing dynamics model can be simplified as follows: （12） in: , , Therefore: For simplicity, the formula e = e(t) is used. ,in: For system parameters, , , i=1…6; Step 3: Set the number of neural network nodes and Gaussian basis functions. Use radial basis neural networks to approximate the uncertainty perturbation caused by the gravity of small celestial bodies as the distance between the probe and the landing point decreases, so as to make the dynamic model of the probe more accurate. Step 3 is implemented as follows: The following radial basis function neural network is used to approximate the uncertainty perturbation D caused by the gravity of the small celestial body as the distance between the probe and the landing point decreases: （13） In the formula: m is the number of hidden layer nodes in the network; h j ( The basis functions are expressed using Gaussian functions as shown in equation (14): （14） In the formula: c j Let be the center vector of the j-th node in the network. Let be the base width value of node j. This is the weight matrix of the neural network. The neural network approximation error is used; the neural network input is taken as... Then the estimation of the uncertain term D Written as: （15） In the formula: This is for estimating the weight matrix of a neural network; Step 4: Based on the approximation of the nonlinear uncertain perturbation in the attachment dynamics of small celestial bodies using RBFNN, an adaptive law is designed to estimate the upper bound of the error for the state variables after error transformation, ensuring the speed and high accuracy of trajectory tracking during landing. Step 4 is implemented as follows: Based on the approximation of the nonlinear uncertainty term in the attachment dynamics of small celestial bodies using RBFNN, and considering the upper bound of the approximation error... The following adaptive control law is introduced. （16） in: Indicates the upper bound of the approximation error The estimate is that K>

0. , , , , Let be the parameters of the controller to be designed and the adaptive gain; the controller u designed by equation (16) makes s bounded, then and Bounded positioning ultimately enables the probe to precisely attach to the target landing point of a small, irregularly shaped object with weak gravity, and allows for rapid and robust tracking of the nominal trajectory. This prevents the landing position from deviating from the target landing point or the probe from colliding with obstacles due to excessive trajectory tracking errors, thereby increasing the safety of the probe's landing process.

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