Optimal Control Fast Search Planetary Landing Guidance Method

Abstract

This invention discloses a planetary landing guidance method based on rapid search for optimal control, belonging to the field of spacecraft guidance and control technology. The implementation method is as follows: The lander's dynamic model is decoupled into a controlled dynamic model and an uncontrolled dynamic model; an optimization model of the reachable region is constructed using thrust amplitude and thrust direction constraints as constraints, solving for the reachable region of controlled motion in a prediction time domain; a fuel consumption optimization model is constructed using different positions within the reachable region as virtual endpoints, and offline optimization is performed to obtain the optimal fuel consumption control for the lander to reach the specified virtual endpoint position. The optimal control is stored as an optimal control database, and the corresponding virtual endpoint state is stored as an endpoint state database; during landing, the uncontrolled motion is superimposed with the endpoint state database to obtain the lander's state prediction space, the optimal terminal state is searched, and the corresponding optimal control command in the optimal control database is obtained. Planetary landing guidance is then implemented based on the optimal control command.

Description

Technical Field

[0001] This invention relates to a spacecraft guidance method, and more particularly to a planetary landing guidance method based on optimal control and rapid search, belonging to the field of spacecraft guidance and control technology. Background Technology

[0002] Planetary exploration is a crucial means for humanity to understand the laws of the universe and achieve extraterrestrial survival. Precise landing technology on planetary surfaces is a key technology for planetary exploration activities and a prerequisite for missions such as in-situ exploration of extraterrestrial surfaces and sample return. The powered descent phase is a critical stage for planetary landing, determining whether the lander can safely and accurately reach the desired landing site. The trajectory during powered descent must meet various constraints, including constraints on position and velocity at the landing site, as well as thrust amplitude and direction constraints during landing. Furthermore, the limited fuel consumption of the lander and onboard computing resources also impose practical engineering constraints on the design of planetary landing guidance methods. Therefore, to achieve precise landing on planetary surfaces, it is necessary to develop landing guidance methods that can meet multiple constraints.

[0003] Existing research has focused on planetary landing guidance methods, primarily including nominal trajectory-based tracking guidance and nominal trajectory-less explicit guidance. While nominal trajectory-based tracking guidance can handle various constraints, the trajectory is typically pre-designed, resulting in poor adaptability to initial mission deviations. Nominal trajectory-less explicit guidance methods exhibit better adaptability to initial condition deviations but struggle to effectively handle complex constraints. Model predictive control (MMCC) combines the advantages of both methods, possessing the ability to address initial condition deviations and handle complex constraints. Its basic idea is to solve the optimal control problem in a finite-time domain online. However, due to the need for online solving of complex optimization problems, MMCC cannot guarantee meeting the real-time requirements of landing guidance. Therefore, to meet the demands of safe and precise planetary surface landing guidance, it is necessary to improve traditional planetary landing guidance methods and develop a method capable of handling complex constraints and possessing high real-time performance. Summary of the Invention

[0004] To address the conflict between handling complex constraints and meeting real-time requirements during the planetary dynamic descent phase, and aiming to achieve precise landing and reduced fuel consumption, this invention primarily aims to provide a planetary landing guidance method based on rapid optimal control search. The method decouples the lander's dynamic model into a controlled dynamic model and an uncontrolled dynamic model, solves for the reachable region of controlled motion in a predicted time domain, and obtains the optimal fuel consumption control at different positions within the reachable region offline. The optimal control and the lander's final state are stored as an optimal control database and a final state database, respectively. During landing, the uncontrolled motion and the final state database are superimposed to obtain the lander's state prediction space. The optimal terminal state is searched to obtain the corresponding optimal control command in the optimal control database, and planetary landing guidance is achieved based on the optimal control command.

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

[0006] The planetary landing guidance method for optimal control and rapid search disclosed in this invention includes the following steps:

[0007] Step 1: Establish a lander dynamic model in a fixed coordinate system at the planetary landing site, and decouple the lander dynamic model into a controlled dynamic model and an uncontrolled dynamic model. The controlled dynamic model corresponds to the motion of the lander when it is only subjected to thrust, and the uncontrolled dynamic model corresponds to the motion of the lander when it is only subjected to gravity.

[0008] The specific implementation method of step one is as follows:

[0009] Define a fixed coordinate system O-XYZ for the landing point: with the landing point as the origin O, the OX axis points eastward to the local area, the OY axis points northward to the local area, and the OZ axis points towards the local zenith.

[0010] Ignoring the effects of planetary rotation and aerodynamic forces, and treating planetary gravitational acceleration as a constant, a dynamic model of the lander is established in a fixed coordinate system at the landing point:

[0011]

[0012] In the formula, r and v represent the position vector and velocity vector of the lander in the fixed coordinate system of the landing point, respectively; a represents the thrust acceleration vector of the lander; T represents the thrust vector of the lander; m represents the mass of the lander; g represents the gravitational acceleration vector of the planetary surface; and I represents the velocity vector of the lander. sp represents the specific impulse of the lander's engine, and g0 represents the numerical value of the gravitational acceleration at sea level.

[0013] According to the principle of motion independence, the lander's motion can be considered as the synthesis of two component motions driven by thrust and gravity respectively. These two component motions occur independently and do not interfere with each other. Integrating the position and velocity equations in equation (1) yields:

[0014]

[0015] In the formula, t represents the motion time, and r0 and v0 represent the position vector and velocity vector at the initial moment, respectively.

[0016] By analyzing the position and velocity equations as shown in equation (2), the dynamic equations are decoupled into a controlled dynamic model and an uncontrolled dynamic model, as shown in equations (3) and (4) respectively:

[0017]

[0018]

[0019] In the controlled dynamics model, the lander's initial position and velocity are both 0, and it is only affected by thrust; in the uncontrolled dynamics model, the lander's initial position and velocity are r0 and v0, respectively, and it is only affected by gravity.

[0020] Step 2: Set the prediction time domain. Based on the controlled dynamics model in Step 1, construct an optimization model for the reachable area with thrust amplitude and thrust direction constraints as constraints. Solve for the reachable area of ​​controlled motion within a prediction time domain using the optimization model. Using different positions within the reachable area as virtual endpoints, fuel consumption as the optimization objective, and thrust amplitude and thrust direction constraints as constraints, construct a fuel consumption optimization model. Obtain the optimal fuel consumption control for the lander to reach the specified virtual endpoint position through offline optimization based on the fuel consumption optimization model, and store the optimal control as an optimal control database and the corresponding virtual endpoint state as an endpoint state database.

[0021] The specific implementation method for step two is as follows:

[0022] The control constraints on the lander include thrust amplitude constraints and thrust direction constraints, as shown in equation (5):

[0023]

[0024] In the formula, T min and T max Let n represent the minimum and maximum thrust amplitudes, respectively. z θ represents the unit vector in the positive direction of the Z-axis. max This represents the maximum engine sway angle, which is defined as the maximum angle between the thrust vector and the positive Z-axis.

[0025] Set the prediction time domain to t NOffline solution for the controlled motion reachable region in the prediction time domain. Considering the rotational symmetry of thrust about the Z-axis, the two-dimensional reachable region of the lander in the first quadrant of XOZ can be solved first, and then the three-dimensional reachable region can be obtained by rotating it around the Z-axis. Based on the controlled dynamics model in step one, an optimization model for the two-dimensional reachable region is constructed with thrust amplitude constraints and thrust direction constraints as constraints, as shown in equation (6):

[0026]

[0027] In the formula, all vectors are two-dimensional vectors, x i and z i These represent the X and Z coordinates that the lander can reach, respectively. Different z-coordinates are selected. i The optimization yielded the farthest X-axis position that the lander could reach at this point. i coordinates (x) i ,z i The envelope formed by these two-dimensional reachable regions can be obtained by rotating around the Z-axis to obtain the three-dimensional reachable regions.

[0028] Select different locations r within the reachable area i As a virtual endpoint, with optimal fuel consumption as the optimization objective, and with the thrust amplitude constraint and thrust direction constraint as shown in Equation (5) as the constraint conditions, an optimization model as shown in Equation (7) is established. Based on the optimization model shown in Equation (7), the optimal fuel consumption control of the lander reaching the specified virtual endpoint position is obtained through offline optimization.

[0029]

[0030] In the formula, m0 represents the mass of the lander at the initial moment.

[0031] All virtual endpoint positions r i The lander arrived at r i v at time i The lander's fuel consumption Δm is stored in the endpoint state database, corresponding to the optimal control acceleration a. i The optimal control acceleration a is stored in the optimal control database for easy storage. i Discretized into the optimal control acceleration sequence a i,j Store the data, where j = 1, 2, ..., t N / t g , t g Indicates the guidance period, t N It is t g Integer multiples of.

[0032] Step 3: During the landing process, the state of the lander after undergoing a predicted uncontrolled motion is calculated based on the uncontrolled dynamics model. The final state of the uncontrolled motion is superimposed with the endpoint state database obtained in Step 2 to generate a state prediction space for the lander within a predicted time domain. State points in the state prediction space that violate control constraints due to mass changes are removed. The mass of the lander within a predicted time domain is approximated as a constant. A fuel consumption correction factor α is constructed based on the ratio of the lander's mass at the current moment to its mass at the initial moment, and fuel consumption is corrected based on the fuel consumption correction factor α. The optimal state is searched by traversing the state prediction space to obtain the corresponding optimal control command in the optimal control database. Planetary landing guidance is implemented based on the optimal control command.

[0033] The specific implementation method for step three is as follows:

[0034] At time t during the landing process, the state of the lander after undergoing a predicted uncontrolled motion in the time domain is calculated according to the uncontrolled dynamics model, as shown in equation (8):

[0035]

[0036] In the formula, r u v u and m u These represent the position vector, velocity vector, and mass of the lander after a predicted uncontrolled motion in the time domain, respectively.

[0037] The final state of uncontrolled motion is superimposed with the final state of controlled motion in the endpoint state database to generate the state prediction space X of the lander at time t in a prediction time domain. N As shown in equation (9):

[0038] X N ={(r N ,v N ,m N )|r N =r u +r i ,v N =v u +v i ,m N =m u -Δm i ,i=1,2,...,n} (9)

[0039] In the formula, r N v N and m N These represent the position vector, velocity vector, and mass of the lander after a prediction time domain, respectively, and n represents the number of controlled final states in the final state database.

[0040] Considering that the initial mass of the lander in equation (7) is m0, and the variable in the optimal control database is acceleration a, when the mass of the lander decreases to m(t) at time t, the optimal control acceleration a in the optimal control database partially satisfies the lower limit constraint of thrust amplitude. e At this point, the constraint condition is no longer satisfied, that is:

[0041]

[0042] For a e To predict the lander's state in space X N The corresponding state point X e These are eliminated to ensure that the optimal control satisfies the thrust constraint. At this time, the state prediction space X is as shown in equation (11):

[0043] X = X N -X e (11)

[0044] During landing, the rate of change of the lander's mass is proportional to the thrust amplitude, and the thrust amplitude is proportional to the lander's mass. Therefore, changes in the lander's mass also affect the fuel consumption value in the state prediction space X. The lander's mass in a prediction time domain is approximated as a constant, and a fuel consumption correction factor α is constructed based on the ratio of the lander's mass at the current moment to its mass at the initial moment, as shown in equation (12).

[0045]

[0046] At time t during the landing process, the performance indicators are selected as shown in equations (13)-(15):

[0047]

[0048]

[0049]

[0050] In the formula, λ<0 represents the fuel consumption weighting coefficient, k represents the speed weighting coefficient, and r x r y and r z These represent the current positions of the lander's three axes, v and v'. x v y and v z t represents the three-axis velocities of the lander at the current moment. go This represents the remaining flight time of the lander, and d>0 is a constant to prevent Q from becoming singular.

[0051] Based on the performance indices shown in equations (13) to (15), the optimal state X is searched by traversing the lander state prediction space X. *In the optimal state X * The corresponding optimal control sequence a in the optimal control database i,j The first item a i,1 For optimal control, drive the lander toward the target point.

[0052] The terminal state prediction and optimal control search described above are performed once in each guidance cycle. Planetary landing guidance is performed based on the optimal control command obtained from the search until the lander reaches the target landing point.

[0053] Beneficial effects:

[0054] 1. To address the challenges of planetary landings involving multiple constraints, such as thrust amplitude and directional constraints, this invention discloses a planetary landing guidance method based on rapid optimal control search. This method calculates the lander's reachable zone offline and solves for the optimal fuel consumption control that satisfies thrust constraints within that zone. This solution is stored in an optimal control database, and the optimal control is searched online to ensure that all searched control quantities satisfy the constraints. During landing, the optimal control search range is dynamically adjusted based on changes in the lander's mass, and fuel consumption data is corrected, further ensuring that planetary landing guidance does not violate control constraints. This invention's guidance method solves for optimal control that satisfies constraints offline and corrects data online, guaranteeing that the lander's control constraints are met.

[0055] 2. Addressing the practical constraints of limited computing and storage capabilities of planetary lander computers, this invention discloses a planetary landing guidance method based on rapid optimal control search. This method decouples the lander's dynamic model into a controlled dynamic model and an uncontrolled dynamic model, storing only data related to controlled motion in the endpoint state database. This reduces the data storage and computational load of the onboard computer. Using different locations within the reachable zone as virtual endpoints, fuel consumption as the optimization objective, and thrust amplitude and direction constraints as conditions, a fuel consumption optimal control optimization model is constructed. The optimization problem is solved offline based on this model. During landing, only two databases need to be accessed and the optimal control search performed, eliminating the need for online optimization problem solving and reducing the workload of the onboard computer. This guidance method has low computational load and fast search speed, meeting the computational performance constraints of the onboard computer.

[0056] 3. The optimal control rapid search planetary landing guidance method disclosed in this invention, based on achieving the beneficial effects 1 and 2, can achieve planetary landing guidance under optimal fuel consumption conditions. At the same time, the landing position accuracy and velocity accuracy of the lander meet the terminal constraints, enabling precise landing on the planetary surface. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the optimal control fast search planetary landing guidance method disclosed in this invention.

[0058] Figure 2 This is a distribution diagram of the optimal acceleration amplitude in the optimal control database;

[0059] Figure 3 The three-axis position curves of the lander;

[0060] Figure 4 The three-axis velocity curves of the lander;

[0061] Figure 5 The total thrust amplitude curve of the lander;

[0062] Figure 6 The curve shows the sway angle of the lander's engine. Detailed Implementation

[0063] 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.

[0064] To verify the feasibility of the method, a simulation of a planetary landing guidance method based on optimal control and rapid search is performed, taking a Mars lander landing mission as an example. The probe starts from the initial position r0 = [2000, 0, 1500]. T (Unit: m) The system enters the powered descent phase for Mars landing, with an initial velocity of v0 = [100, 0, -75]. T (Unit: m / s). The initial mass of the lander is m = 1905 kg, and the set flight time is t. f =200s, maximum engine thrust T max =13258N, minimum thrust T min = 4971N, maximum engine sway angle θ max =30°, engine specific impulse I sp =225s, Earth's gravitational acceleration at sea level g0 = 9.80665m / s² 2 The gravitational acceleration on the surface of Mars is g = [0, 0, -3.72]. T (Unit: m / s) 2 ).

[0065] like Figure 1 As shown in the figure, the specific implementation steps of the optimal control fast search planetary landing guidance method disclosed in this embodiment are as follows:

[0066] Step 1: Establish a lander dynamic model in a fixed coordinate system at the planetary landing site, and decouple the lander dynamic model into a controlled dynamic model and an uncontrolled dynamic model. The controlled dynamic model corresponds to the motion of the lander when it is only subjected to thrust, and the uncontrolled dynamic model corresponds to the motion of the lander when it is only subjected to gravity.

[0067] The specific implementation method of step one is as follows:

[0068] Define a fixed coordinate system O-XYZ for the landing point: with the landing point as the origin O, the OX axis points eastward to the local area, the OY axis points northward to the local area, and the OZ axis points towards the local zenith.

[0069] Ignoring the effects of planetary rotation and aerodynamic forces, and treating planetary gravitational acceleration as a constant, a dynamic model of the lander is established in a fixed coordinate system at the landing point:

[0070]

[0071] In the formula, r and v represent the position vector and velocity vector of the lander in the fixed coordinate system of the landing point, respectively; a represents the thrust acceleration vector of the lander; T represents the thrust vector of the lander; m represents the mass of the lander; and g = [0, 0, -3.72]. T (Unit: m / s) 2 ) represents the gravitational acceleration vector on the surface of Mars, I sp =225s represents the specific impulse of the lander engine, g0 = 9.80665m / s 2 This represents the numerical value of gravitational acceleration at sea level on Earth.

[0072] According to the principle of motion independence, the lander's motion can be considered as the synthesis of two component motions driven by thrust and gravity respectively. These two component motions occur independently and do not interfere with each other. Integrating the position and velocity equations in equation (1) yields:

[0073]

[0074] In the formula, t represents the motion time, and r0 and v0 represent the position vector and velocity vector at the initial moment, respectively.

[0075] By analyzing the position and velocity equations as shown in equation (2), the dynamic equations are decoupled into a controlled dynamic model and an uncontrolled dynamic model, as shown in equations (3) and (4) respectively:

[0076]

[0077]

[0078] In the controlled dynamics model, the lander's initial position and velocity are both 0, and it is only affected by thrust; in the uncontrolled dynamics model, the lander's initial position and velocity are r0 and v0, respectively, and it is only affected by gravity.

[0079] Step 2: Define the prediction time domain. Based on the controlled dynamics model in Step 1, construct an optimization model for the reachable region using thrust amplitude and thrust direction constraints as conditions. Solve for the reachable region of controlled motion within a prediction time domain using the optimization model. Using different locations within the reachable region as virtual endpoints, fuel consumption as the optimization objective, and thrust amplitude and thrust direction constraints as conditions, construct a fuel consumption optimization model. Obtain the optimal fuel consumption control for the lander to reach the specified virtual endpoint position through offline optimization using the fuel consumption optimization model. Store the optimal control in an optimal control database and the corresponding virtual endpoint state in an endpoint state database. The specific implementation method of Step 2 is as follows:

[0080] The control constraints on the lander include thrust amplitude constraints and thrust direction constraints, as shown in equation (5):

[0081]

[0082] In the formula, T min =4971N and T max =13258N represents the minimum and maximum thrust amplitudes, respectively, n z θ represents the unit vector in the positive direction of the Z-axis. max =30° indicates the maximum engine sway angle.

[0083] Set the prediction time domain to t N =10s. An offline solution is performed for the controlled motion reachable region in the prediction time domain. Considering the rotational symmetry of the thrust about the Z-axis, the two-dimensional reachable region of the lander in the first quadrant of XOZ can be solved first, and then the three-dimensional reachable region can be obtained by rotating it around the Z-axis. Based on the controlled dynamics model in step one, an optimization model for the two-dimensional reachable region is constructed with thrust amplitude constraints and thrust direction constraints as constraints, as shown in equation (6):

[0084]

[0085] In the formula, all vectors are two-dimensional vectors, x i and z i These represent the X and Z coordinates that the lander can reach, respectively. Different z-coordinates are selected. i In this example, z i =130,140,150,…,350, Optimization yields the farthest X-axis position x that the lander can reach at this point. i coordinates (x) i ,z i The envelope formed by these two-dimensional reachable regions can be obtained by rotating around the Z-axis to obtain the three-dimensional reachable regions.

[0086] Select different locations r within the reachable area iAs a virtual endpoint, with optimal fuel consumption as the optimization objective, and using the thrust amplitude and thrust direction constraints shown in Equation (5) as constraints, an optimization model as shown in Equation (7) is established. Based on the optimization model shown in Equation (7), offline optimization is performed to obtain the optimal fuel consumption control for the lander to reach the specified virtual endpoint position. In this example, the virtual endpoint constitutes a set... Where C represents the three-dimensional reachable region.

[0087]

[0088] In the formula, m0 = 1905 kg represents the mass of the lander at the initial moment.

[0089] All virtual endpoint positions r i The lander arrived at r i v at time i The lander's fuel consumption Δm i Stored as a final state database, the corresponding optimal control acceleration a i The optimal control acceleration a is stored in the optimal control database for easy storage. i Discretized into the optimal control acceleration sequence a i,j Store the data, where j = 1, 2, ..., t N / t g , t g =1s indicates the guidance period.

[0090] Step 3: During the landing process, the state of the lander after undergoing a predicted uncontrolled motion is calculated based on the uncontrolled dynamics model. The final state of the uncontrolled motion is superimposed with the endpoint state database obtained in Step 2 to generate a state prediction space for the lander within a predicted time domain. State points in the state prediction space that violate control constraints due to mass changes are removed. The mass of the lander within a predicted time domain is approximated as a constant. A fuel consumption correction factor α is constructed based on the ratio of the lander's mass at the current moment to its mass at the initial moment, and fuel consumption is corrected based on the fuel consumption correction factor α. The optimal state is searched by traversing the state prediction space to obtain the corresponding optimal control command in the optimal control database. Planetary landing guidance is implemented based on the optimal control command.

[0091] The specific implementation method for step three is as follows:

[0092] At time t during the landing process, the state of the lander after undergoing a predicted uncontrolled motion in the time domain is calculated according to the uncontrolled dynamics model, as shown in equation (8):

[0093]

[0094] In the formula, r u v u and mu These represent the position vector, velocity vector, and mass of the lander after a predicted uncontrolled motion in the time domain, respectively.

[0095] The final state of uncontrolled motion is superimposed with the final state of controlled motion in the endpoint state database to generate the state prediction space X of the lander at time t in a prediction time domain. N As shown in equation (9):

[0096] X N ={(r N ,v N ,m N )|r N =r u +r i ,v N =v u +v i ,m N =m u -Δm i ,i=1,2,...,n} (9)

[0097] In the formula, r N v N and m N These represent the position vector, velocity vector, and mass of the lander after a prediction time domain, respectively, and n = 1969128 represents the number of controlled motion final states in the final state database.

[0098] Considering that the initial mass of the lander in equation (7) is m0, and the variable in the optimal control database is acceleration a, when the mass of the lander decreases to m(t) at time t, the optimal control acceleration a in the optimal control database partially satisfies the lower limit constraint of thrust amplitude. e At this point, the constraint condition is no longer satisfied.

[0099]

[0100] For a e To predict the lander's state in space X N The corresponding state point X e These are eliminated to ensure that the optimal control satisfies the thrust constraint. At this time, the state prediction space X is as shown in equation (11):

[0101] X = X N -X e (11)

[0102] During landing, the rate of change of the lander's mass is proportional to the thrust amplitude, and the thrust amplitude is proportional to the lander's mass. Therefore, changes in the lander's mass also affect the fuel consumption value in the state prediction space X. The lander's mass in a prediction time domain is approximated as a constant, and a fuel consumption correction factor α is constructed based on the ratio of the lander's mass at the current moment to its mass at the initial moment, as shown in equation (12).

[0103]

[0104] At time t during the landing process, the performance indicators are selected as shown in equations (13)-(15):

[0105]

[0106]

[0107]

[0108] In the formula, λ<0 represents the fuel consumption weighting coefficient, in this example λ=-500, k represents the speed weighting coefficient, in this example k=100, r x r y and r z These represent the current positions of the lander's three axes, v and v'. x v y and v z t represents the three-axis velocities of the lander at the current moment. go This represents the remaining flight time of the lander. d>0 is a constant to prevent Q from becoming singular. In this example, d=0.01.

[0109] Based on the performance indices shown in equations (13) to (15), the optimal state X is searched by traversing the lander state prediction space X. * In the optimal state X * The corresponding optimal control sequence a in the optimal control database i,j The first item a i,1 For optimal control, drive the lander toward the target point.

[0110] The terminal state prediction and optimal control search described above are performed once in each guidance cycle. Planetary landing guidance is performed based on the optimal control command obtained from the search until the lander reaches the target landing point.

[0111] Figure 2 The optimal acceleration amplitude distribution diagram in the optimal control database is given when the virtual endpoint in the endpoint state database is located in the XOZ plane. Figure 3 The three-axis position curves of the lander are given, where r x r y and r zThese represent the three-axis position components of the lander in the fixed coordinate system of the planetary landing site. Figure 4 The three-axis velocity curves of the lander are given, where v x v y and v z The three-axis velocity components of the lander in the fixed coordinate system of the planetary landing point are represented respectively. It can be seen that the lander achieved a precise landing that satisfies the terminal constraints. Figure 5 The total thrust amplitude curve of the lander is given. Figure 6 The engine sway angle curve is presented, defined as the angle between the lander's thrust direction and the positive Z-axis. It can be seen that the thrust amplitude and direction constraints are satisfied throughout the landing process. The average time for searching for optimal control per guidance cycle is 7.29 ms, with a maximum time of 8.34 ms, meeting the real-time requirements of guidance. Simulations show that the designed guidance method is suitable for planetary landing missions.

[0112] 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. A planetary landing guidance method based on optimal control and rapid search, characterized in that: Includes the following steps, Step 1: Establish a lander dynamic model in a fixed coordinate system at the planetary landing point, and decouple the lander dynamic model into a controlled dynamic model and an uncontrolled dynamic model. The controlled dynamic model corresponds to the motion of the lander when it is only subjected to thrust, and the uncontrolled dynamic model corresponds to the motion of the lander when it is only subjected to gravity. The specific implementation method of step one is as follows: Define a fixed coordinate system O-XYZ for the landing point: with the landing point as the origin O, the OX axis points east to the local area, the OY axis points north to the local area, and the OZ axis points to the local zenith. Ignoring the effects of planetary rotation and aerodynamic forces, and treating planetary gravitational acceleration as a constant, a dynamic model of the lander is established in a fixed coordinate system at the landing point: In the formula, r and v represent the position vector and velocity vector of the lander in the fixed coordinate system of the landing point, respectively; a represents the thrust acceleration vector of the lander; T represents the thrust vector of the lander; m represents the mass of the lander; g represents the gravitational acceleration vector of the planetary surface; and I represents the velocity vector of the lander. sp This represents the specific impulse of the lander's engine, and g0 represents the numerical value of the gravitational acceleration at sea level. According to the principle of motion independence, the lander's motion can be viewed as the synthesis of two component motions driven by thrust and gravity respectively. These two component motions occur independently and do not interfere with each other. Integrating the position and velocity equations yields: In the formula, t represents the motion time, and r0 and v0 represent the position vector and velocity vector at the initial moment, respectively; By analyzing the position and velocity equations as shown in equation (2), the dynamic equations are decoupled into a controlled dynamic model and an uncontrolled dynamic model, as shown in equation (2). Japanese style As shown: In the controlled dynamics model, the lander's initial position and velocity are both 0, and it is only affected by thrust; in the uncontrolled dynamics model, the lander's initial position and velocity are r0 and v0, respectively, and it is only affected by gravity. Step 2: Set the prediction time domain. Based on the controlled dynamics model in Step 1, construct an optimization model for the reachable area with thrust amplitude and thrust direction constraints as constraints. Solve for the reachable area of ​​controlled motion within a prediction time domain using the optimization model. Using different locations within the reachable area as virtual endpoints, fuel consumption as the optimization objective, and thrust amplitude and thrust direction constraints as constraints, construct a fuel consumption optimization model. Obtain the optimal fuel consumption control for the lander to reach the specified virtual endpoint position through offline optimization based on the fuel consumption optimization model. Store the optimal control as an optimal control database and the corresponding virtual endpoint state as an endpoint state database. The specific implementation method for step two is as follows: The control constraints on the lander include thrust amplitude constraints and thrust direction constraints, as shown in the equation. As shown: In the formula, T min and T max Let n represent the minimum and maximum thrust amplitudes, respectively. z θ represents the unit vector in the positive Z-axis direction. max This represents the maximum engine sway angle, which is defined as the maximum angle between the thrust vector and the positive Z-axis. Set the prediction time domain to t N Offline solution for the reachable region of controlled motion in the prediction time domain; considering the rotational symmetry of thrust about the Z-axis, the two-dimensional reachable region of the lander in the first quadrant of XOZ can be solved first, and then the three-dimensional reachable region can be obtained by rotating it around the Z-axis; based on the controlled dynamics model in step one, an optimization model of the two-dimensional reachable region is constructed with thrust amplitude constraints and thrust direction constraints as constraints, as shown in the equation. As shown: In the formula, all vectors are two-dimensional vectors, x i and z i These represent the X and Z coordinates that the lander can reach, respectively. Different z-coordinates are selected. i The optimization yielded the farthest X-axis position that the lander could reach at this point. i coordinates (x) i ,z i The envelope formed by this is the two-dimensional reachable region, and the three-dimensional reachable region can be obtained by rotating it around the Z-axis. Select different locations r within the reachable area i As a virtual endpoint, with optimal fuel consumption as the optimization objective, and with thrust amplitude and thrust direction constraints as shown in Equation (5) as the constraint conditions, the following equation is established: The optimization model shown is used to obtain the optimal fuel consumption control of the lander when it reaches the specified virtual endpoint position through offline optimization based on the optimization model shown in Equation (7); In the formula, m0 represents the mass of the lander at the initial moment; All virtual endpoint positions r i The lander arrived at r i v at time i The lander's fuel consumption Δm is stored in the endpoint state database, corresponding to the optimal control acceleration a. i The optimal control acceleration a is stored in the optimal control database for ease of storage. i Discretized into the optimal control acceleration sequence a i,j Store the values, where j = 1, 2, …, t. N / t g , t g Indicates the guidance period, t N It is t g Integer multiples of; Step 3: During the landing process, the state of the lander after undergoing a predicted uncontrolled motion is calculated based on the uncontrolled dynamics model. The final state of the uncontrolled motion is superimposed with the endpoint state database obtained in Step 2 to generate a state prediction space for the lander within a predicted time domain. State points in the state prediction space that violate control constraints due to mass changes are removed. The mass of the lander within a predicted time domain is approximated as a constant. A fuel consumption correction factor α is constructed based on the ratio of the lander's mass at the current moment to its mass at the initial moment, and fuel consumption is corrected based on the fuel consumption correction factor α. The optimal state is searched by traversing the state prediction space to obtain the corresponding optimal control command in the optimal control database. Planetary landing guidance is implemented based on the optimal control command. The specific implementation method for step three is as follows: At time t during the landing process, based on the uncontrolled dynamics model, the state of the lander after undergoing a predicted uncontrolled motion in the time domain is calculated, as shown in the equation. As shown: In the formula, r u v u and m u These represent the position vector, velocity vector, and mass of the lander after a predicted uncontrolled motion in the time domain, respectively. The final state of uncontrolled motion is superimposed with the final state of controlled motion in the endpoint state database to generate the state prediction space X of the lander at time t in a prediction time domain. N , as shown As shown: In the formula, r N v N and m N These represent the position vector, velocity vector, and mass of the lander after a prediction time domain, respectively, and n represents the number of controlled final states in the final state database. Considering the formula The initial mass of the lander is taken as m0, and the variable in the optimal control database is acceleration a. Therefore, when the lander mass decreases to m(t) at time t, the optimal control acceleration a in the optimal control database partially satisfies the lower limit constraint of thrust amplitude. e At this point, the constraint condition is no longer satisfied, that is: For a e To predict the lander's state in space X N The corresponding state point X e Eliminating these ensures that optimal control satisfies the thrust constraint, at which point the state prediction space X is as shown in the equation. As shown: During landing, the rate of change of the lander's mass is proportional to the thrust amplitude, which in turn is proportional to the lander's mass. Therefore, changes in the lander's mass also affect the fuel consumption value in the state prediction space X. Approximating the lander's mass as a constant within a prediction time domain, a fuel consumption correction factor α is constructed based on the ratio of the current lander mass to its initial mass, as shown in the equation. As shown: At time t during the landing process, select the formula as follows: - The performance indicators shown are: In the formula, The fuel consumption weighting coefficient is represented by k, the speed weighting coefficient is represented by r. x r y and r z These represent the current positions of the lander's three axes, v and v'. x v y and v z t represents the three-axis velocities of the lander at the current moment. go This represents the remaining flight time of the lander, and d > 0 is a constant to prevent Q from becoming singular; Based on the performance indices shown in equations (13) to (15), the optimal state X is searched by traversing the lander state prediction space X. * In the optimal state X * The corresponding optimal control sequence a in the optimal control database i,j The first item a i,1 For optimal control, drive the lander toward the target point; In each guidance cycle, a terminal state prediction and optimal control search are performed. Based on the optimal control command obtained from the search, planetary landing guidance is performed until the lander reaches the target landing point.

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