Landing control method of tethered asteroid probe suitable for irregular gravitational field of asteroid

Abstract

The invention discloses a tethered asteroid probe landing control method suitable for an asteroid irregular gravitational field. The method comprises the following steps: under the condition that a detector and a lander in a tethered asteroid in an asteroid irregular gravitational field are separated, setting different expected trajectory strategies based on different descending stages of the lander; and designing a model prediction control algorithm based on different expected trajectory strategies set in different descent stages of the lander. The method solves the problems that in the landing process of a tethered asteroid detector of an asteroid irregular gravitational field, the tethered asteroid detector system dynamics is complex, and constraint conditions for ensuring safe flight of the detector and limiting the control capability of the detector exist; and the problem of establishing the optimal control of the asteroid landing trajectory planning is difficult to solve and the calculation speed is slow is solved.

Description

Technical Field

[0001] The present invention relates to the field of probe landing control technology, and in particular to a tethered asteroid probe landing control method suitable for the irregular gravitational field of an asteroid. Background Art

[0002] Asteroids, due to their small size, irregular shape, and the influence of surrounding celestial bodies, create a weak, irregular, and complex gravitational field in their immediate vicinity. Furthermore, their soft surface creates significant challenges for landing and attaching probes. Furthermore, asteroids' rapid spin and complex surface environment pose significant challenges to landing site planning, navigation, and control.

[0003] There are currently two main methods for asteroid exploration and landing: fixed landing and touch-and-leave. However, probes using the fixed landing method are prone to bouncing after landing, resulting in errors from the expected position and thus failing to achieve the expected results. While the touch-and-leave method is less prone to rebound and overturning problems, the sampling effect cannot be guaranteed due to its short contact time. In response to these two methods, a tethered asteroid probe scheme combining a space tethered asteroid probe system has been proposed. By making the probe hover at a certain distance from the asteroid surface, the lander is released to descend and land. A space tether connects the probe and the lander. Under the action of the lander's micro-thrust engine and the space tether, the lander can land on the asteroid surface and then carry out the exploration mission.

[0004] However, due to the flexible connection of the space tether, tethered asteroid probes are highly nonlinear and strongly coupled, significantly impacting both control of the lander and maintaining hovering. Furthermore, the weak, irregular, and complex gravitational field in the asteroid's near-space environment, as well as the influence of various celestial bodies in deep space, pose significant challenges to control of tethered asteroid probes. Current research approaches include closed-loop control and optimal trajectory planning, but several challenges remain. Due to the complex gravitational environment of the asteroid and the inaccuracy of its dynamic models, current closed-loop control methods lack applicability to irregular gravitational fields and unknown environments. Optimal trajectory methods, however, suffer from poor convergence due to their high dependence on the accuracy of initial estimates. Furthermore, the complex dynamics of tethered asteroid probe systems, coupled with constraints that ensure safe flight and limit control capabilities, make optimal control of asteroid landing trajectory planning difficult to solve and computationally slow.

[0005] This paper proposes a robust tracking model predictive control (MPC) controller based on tether tension control to achieve the landing of the probe, so as to ensure that the rope tension can remain stable while the lander can descend along the expected trajectory and at the expected speed. It can also better deal with the inaccuracy of the dynamic model caused by the irregular and complex gravitational field. Summary of the Invention

[0006] An embodiment of the present invention provides a landing control method for a tethered asteroid probe suitable for an asteroid with an irregular gravitational field, so as to at least solve the technical problems that the dynamics of the tethered asteroid probe system are relatively complex during the landing process of the tethered asteroid probe in the asteroid with an irregular gravitational field, and there are constraints to ensure the safe flight of the probe and limit the control capability of the probe, which makes it difficult to solve the optimal control problem of asteroid landing trajectory planning and the calculation speed is slow.

[0007] According to one aspect of an embodiment of the present invention, a landing control method for a tethered asteroid probe suitable for use in an irregular gravitational field of an asteroid is provided. The method may include: setting different desired trajectory strategies based on different descent phases of the lander when the probe is separated from the lander in the irregular gravitational field of the asteroid; designing a model predictive control algorithm based on the different desired trajectory strategies set for different descent phases of the lander; designing a cost function for the model predictive control algorithm based on the model predictive control algorithm and introducing second-order cone constraints to obtain optimal control forces for the probe, lander, and space tether in the tethered asteroid; and controlling the probe on the tethered asteroid to safely land based on the optimal control forces for the probe, lander, and space tether in the tethered asteroid.

[0008] Optionally, before setting different desired trajectory strategies based on different descent phases of the lander, the method further includes: Based on the scenario where a probe is about to land in an irregular gravitational field on a tethered asteroid, a dynamic model of the probe and lander in the tethered asteroid and a dynamic model of the space tether in the tethered asteroid are established; The dynamic model of the probe and lander in the tethered asteroid is:

[0009] Among them, among them, 、 and are the accelerations of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the velocities of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the positions of the probe or lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, For a probe or lander, the asteroid rotates approximately uniformly around the principal axis of maximum inertia, which is assumed to be the z axis. is the angular velocity of the asteroid's rotation around the z axis, is the gravitational vector in the asteroid’s inertial coordinate system, Indicates the tension of the tether. The acceleration caused by the solar pressure, is the gravitational error due to the asteroid shape error, is the mass of the probe and lander; The dynamic model of the space tether is:

[0010] in, is the electromechanical time constant, is the torque coefficient, is the moment of inertia converted into the motor shaft load, is the input voltage to the motor, is the armature resistance, is the natural length of the tether in the absence of tension, is the motor kinetic energy constant, is the release acceleration of the natural length of the tether in the absence of tension, is the release speed of the natural length of the tether in the absence of tension; Based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the position and velocity of the probe and lander in different directions of the inertial system of the asteroid's centroid and the release acceleration and release velocity of the tether in the tension-free state are determined.

[0011] Optionally, based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the expressions for determining the position and velocity of the probe and lander in different directions of the inertial system of the asteroid centroid and the release acceleration and release velocity of the tether in the tension-free state are:

[0012] in, is the position of the probe in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the probe in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, is the position of the lander in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, represent the values ​​of the gravitational vector in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; They represent the values ​​of the sunlight pressure in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; The control forces in the X, Y, and Z directions applied to the inertial system of the probe and the lander asteroid centroid, as well as the voltage value of the tether release motor.

[0013] Optionally, the expression for setting different desired trajectory strategies based on different descent stages of the lander is:

[0014] in, It is the period from the separation of the probe and the lander to the safe landing of the lander, that is, the actual running time. They are the time points during the landing process when the release changes from uniform speed to deceleration, the time points when the deceleration release enters the final low-speed landing stage, and the time points after landing; are the expected values ​​of lander velocity, lander position and tether length respectively; Respectively represent the set speed value of the uniform speed operation stage, is the simulation time step, is the time step that has been run, represents the expected value of the tether release velocity, Indicates the initial value of the lander position, represents the initial value of the tether length, represents the expected value of the tether length at the moment before time t, represents the expected value of the lander position at the moment before time t.

[0015] Alternatively, the expression of the model predictive control algorithm is:

[0016]

[0017] in, for A function, is the control input matrix, is the actual state matrix of the tethered asteroid probe system, is the cost function, is the index value of the matrix, is the terminal constraint function, is the maximum allowable control input, is the maximum allowed state value, is the state terminal set, is the expected state matrix of the probe and lander, and are respectively the prediction time domain and the control time domain of model predictive control, is the time point when the min function runs, for The actual state matrix of the tethered asteroid probe system at time, for The input matrix is ​​controlled at all times. is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the actual state matrix of the tethered asteroid probe system at the time point when the min function runs, is the state of the tethered asteroid probe system at time k, is the state of the tethered asteroid probe system on N, where N is the prediction time domain.

[0018] Optionally, the cost function expression of the model predictive control algorithm is:

[0019] in, is the cost function, t is the simulation time, , , are the expected state matrices of the probe and lander, Q and R are both positive semi-definite matrices, and T is the transpose.

[0020] Optionally, the expression of the second-order cone constraint is:

[0021]

[0022] in, where f is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the state of the tethered asteroid probe system at time k+i, is the control input of the tethered asteroid probe system at time k+i, is the expected state of the tethered asteroid probe system, where k is the current initial time of the tethered asteroid probe performing iterative optimization, N is the prediction time domain, , is the surface normal vector of the preset landing point, The actual trajectory and The angle of are the coordinates of the target landing point and the lander release position, For terminal sets.

[0023] Beneficial effects of the present invention: This paper proposes a landing control method for a tethered asteroid probe suitable for the irregular gravitational field of an asteroid. A dynamic model of the tethered asteroid probe relative to the asteroid's inertial coordinate system is established. Taking into account the uncertainty of the asteroid model and other celestial perturbations, a robust model predictive control algorithm is designed to ensure that the tethered asteroid probe descends along the desired trajectory. The algorithm also derives and calculates the upper limits of model uncertainty and celestial perturbations under the premise of robustness. This method is applicable to various irregular and complex gravitational fields and has the following advantages: (1) The release and landing process of the tethered asteroid probe was analyzed, and a Newtonian dynamics model of the tethered asteroid probe was established, which has a clearer model expression effect.

[0024] (2) Considering multiple sources of disturbance, a robust model predictive control algorithm is designed to ensure that the tethered asteroid probe can smoothly descend along the expected trajectory. The model uncertainty and the upper limit of celestial disturbances under the premise of robustness are derived and calculated, making the algorithm applicable to various irregular and complex weak gravitational field environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a flow chart of a tethered asteroid probe landing control method applicable to an asteroid's irregular gravitational field according to an embodiment of the present invention; Figure 2 is a schematic diagram of an example of an irregular and complex gravitational field in the near-space of an asteroid applicable according to an embodiment of the present invention; Figure 3 is a schematic diagram of components of a tethered asteroid probe applicable to an embodiment of the present invention; Figure 4 Schematic diagram of the coordinate system of a tethered asteroid probe system established according to an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0027] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and to describe a specific order or sequence. It should be understood that the terms used in this way are interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or inherent to these processes, methods, products or devices.

[0028] Example 1 According to an embodiment of the present invention, a tethered asteroid probe landing control method suitable for an asteroid with an irregular gravitational field is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer tethered asteroid probe system comprising at least one set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0029] Figure 1 FIG. 1 is a flow chart of a tethered asteroid probe landing control method applicable to an asteroid's irregular gravitational field according to an embodiment of the present invention. Figure 1 As shown, the method may include the following steps: Step S101 , when the probe and the lander in the tethered asteroid are separated in the irregular gravitational field of the asteroid, different expected trajectory strategies are set based on different descent stages of the lander.

[0030] In the technical solution provided in step S101 of the present invention, before setting different desired trajectory strategies for different descent phases of the lander, it is set to obtain the initial state parameters of the main spacecraft, the lander, and the space tether at the separation moment. Figure 2 Schematic diagram of an example of an irregular and complex gravitational field in near-space of an asteroid applicable to an embodiment of the present invention.

[0031] Step S102: Design a model predictive control algorithm based on different desired trajectory strategies set for different descent stages of the lander.

[0032] In the technical solution provided in the above step S102 of the present invention, a model predictive control algorithm is designed according to different expected trajectory strategies set in different descent stages of the lander.

[0033] Step S103: Based on the model predictive control algorithm, a cost function of the model predictive control algorithm is designed and a second-order cone constraint is introduced to obtain the optimal control force of the probe, lander and space tether in the tethered asteroid.

[0034] In the technical solution provided in step S103 of the present invention, based on the model predictive control algorithm, a cost function of the model predictive control algorithm is designed and a second-order cone constraint is introduced to solve the model predictive control algorithm to determine the optimal control force of the probe, lander and space tether in the tethered asteroid.

[0035] Step S104: Based on the optimal control force of the probe, lander and space tether in the tethered asteroid, the probe of the tethered asteroid is controlled to land safely.

[0036] In the technical solution provided in the above step S104 of the present invention, based on the optimal control force of the probe, lander and space tether in the tethered asteroid, the probe of the tethered asteroid is controlled to maintain a hovering position during the landing process, and the lander can land along a predetermined orbit.

[0037] The above method of this embodiment is further introduced below.

[0038] As an optional embodiment, before setting different desired trajectory strategies based on different descent phases of the lander in step S101, the method further includes: establishing a dynamic model of the probe and the lander in the tethered asteroid and a dynamic model of the space tether in the tethered asteroid based on a scenario in which the probe is about to land in an irregular gravitational field; The dynamic model of the probe and lander in the tethered asteroid is:

[0039] in, 、 and are the accelerations of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the velocities of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the positions of the probe or lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, For a probe or lander, the asteroid rotates approximately uniformly around the principal axis of maximum inertia, which is assumed to be the z axis. is the angular velocity of the asteroid's rotation around the z axis, is the gravitational vector in the asteroid’s inertial coordinate system, Indicates the tension of the tether. The acceleration caused by the solar pressure, is the gravitational error due to the asteroid shape error, is the mass of the probe and lander; The dynamic model of the space tether is:

[0040] in, is the electromechanical time constant, is the torque coefficient, is the moment of inertia converted into the motor shaft load, is the input voltage to the motor, is the armature resistance, is the natural length of the tether in the absence of tension, is the motor kinetic energy constant, is the release acceleration of the natural length of the tether in the absence of tension, is the release speed of the natural length of the tether in the absence of tension; Based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the position and velocity of the probe and lander in different directions of the inertial system of the asteroid's centroid and the release acceleration and release velocity of the tether in the tension-free state are determined.

[0041] In this embodiment, Figure 3 Schematic diagram of components of a tethered asteroid probe applicable to an embodiment of the present invention, such as Figure 3 As shown in the figure, the tethered asteroid probe mainly consists of three parts: the probe, the space tether and the lander. The probe and the lander can be regarded as mass points. Figure 4 : is a schematic diagram of a coordinate system of a tethered asteroid probe system established according to an embodiment of the present invention, such as Figure 4 As shown, I-XYZ is defined as an inertial system with the origin I located at the centroid of the asteroid, and its three axes correspond to the principal axes of minimum, intermediate and maximum moments of inertia, respectively. O-XYZ is defined as the coordinate system of the probe body, where the z-axis is along the direction of the maximum principal axis of inertia of the probe, the x-axis is along the direction of the minimum principal axis of inertia of the probe, and the y-axis and the other two axes form a right-handed coordinate system.

[0042] The motion equation of the tethered asteroid dynamics model in the inertial coordinate system I-XYZ can be expressed as follows:

[0043]

[0044] in, , and are the position vector and velocity vector of the tethered asteroid probe in the inertial frame, is the gravitational vector in the asteroid’s inertial coordinate system, Indicates the tension of the tether. The acceleration caused by the solar pressure, is the gravitational error due to the asteroid shape error, is the mass of the probe and lander, Using relative motion:

[0045] in, is the rotational angular velocity variable of the tethered asteroid probe in the asteroid inertial coordinate system, is the rate of change of the asteroid's rotational angular velocity vector. However, considering that most asteroids are basically in a fixed-axis rotation state and their angular velocity changes very slowly, this paper focuses on short-term asteroid landing missions, which can be regarded as asteroids in a permanent EULER rotation state.

[0046] In this order , so the formula

[0047] can be transformed into:

[0048] Considering the tethered asteroid probe Movement in direction, i.e. , are the position data of the main spacecraft (1) and the lander (2) in the X, Y, and Z directions respectively, and the asteroid rotates approximately uniformly around the principal axis of maximum inertia, which is assumed to be the z axis. is the angular velocity of the asteroid's rotation around the z axis, so , we can obtain the dynamic models of probes and landers in tethered asteroids.

[0049] The tether release dynamics of a tethered asteroid probe are modeled. The tether is released by a winch in the host spacecraft (the probe) with a radius of The relationship between the motor parameters and voltage, tether length, and release speed can be obtained by using a permanent magnet DC motor drive:

[0050] Since the rope is assumed to be an elastic but incompressible rod, the tension in the rope is calculated from the difference between the actual length of the rope and its natural length according to Hooke's law:

[0051] Where E is the Young's modulus of the tether and A is the cross-sectional area of ​​the tether. And according to The T being solved only represents the magnitude of the tension. The tether pulls on the probe and the lander are equal in magnitude and opposite in direction. is the elastic coefficient of the tether.

[0052] As an optional embodiment, based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the expressions for determining the position and velocity of the probe and lander in different directions in the inertial frame of the asteroid's centroid and the release acceleration and release velocity of the tether in the tension-free state are:

[0053] in, is the position of the probe in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the probe in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, is the position of the lander in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, represent the values ​​of the gravitational vector in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; They represent the values ​​of the sunlight pressure in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; The control forces in the X, Y, and Z directions applied to the inertial system of the probe and the lander asteroid centroid, as well as the voltage value of the tether release motor.

[0054] As an optional embodiment, in step S101, the expression for setting different desired trajectory strategies based on different descent stages of the lander is:

[0055] in, It is the period from the separation of the probe and the lander to the safe landing of the lander, that is, the actual running time. They are the time points during the landing process when the release changes from uniform speed to deceleration, the time points when the deceleration release enters the final low-speed landing stage, and the time points after landing; are the expected values ​​of lander velocity, lander position and tether length respectively; Respectively represent the set speed value of the uniform speed operation stage, is the simulation time step, is the time step that has been run, represents the expected value of the tether release velocity, Indicates the initial value of the lander position, represents the initial value of the tether length, represents the expected value of the tether length at the moment before time t, represents the expected value of the lander position at the moment before time t.

[0056] In this embodiment, the initial state parameters of the main spacecraft, the lander, and the space tether are first obtained at the separation moment, and different desired trajectory strategies are set according to different descent stages.

[0057] As an optional embodiment, in step S102, the expression of the model predictive control algorithm is:

[0058] in, for A function, is the control input matrix, is the actual state matrix of the tethered asteroid probe system, is the cost function, is the index value of the matrix, is the terminal constraint function, is the maximum allowable control input, is the maximum allowed state value, is the state terminal set, is the expected state matrix of the probe and lander, and are respectively the prediction time domain and the control time domain of model predictive control, is the time point when the min function runs, for The actual state matrix of the tethered asteroid probe system at time, for The input matrix is ​​controlled at all times. is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the actual state matrix of the tethered asteroid probe system at the time point when the min function runs, is the state of the tethered asteroid probe system at time k, is the state of the tethered asteroid probe system on N, where N is the prediction time domain.

[0059] In this embodiment, based on the model predictive control algorithm, the state of the three is within the constraints of the following equations for a period of time after the terminal lander lands:

[0060] in, is the terminal constraint function, is the state terminal set, is the expected state matrix of the main spacecraft and the lander, is the control input matrix. is the actual state matrix of the tethered asteroid probe system, and They are respectively the prediction time domain and the control time domain of model predictive control.

[0061] As an optional embodiment, in step S103, the cost function expression of the model predictive control algorithm is:

[0062] in, is the cost function, t is the simulation time, , , are the expected state matrices of the probe and lander, Q and R are both positive semi-definite matrices, and T is the transpose.

[0063] This embodiment simultaneously considers the asteroid's irregular gravitational field, the effects of solar pressure, various other errors, and disturbances caused by celestial bodies, achieving stable landing control despite multiple sources of disturbance. Different phases have different operational states: the uniform descent phase prioritizes rate control and position, while the decelerated descent phase prioritizes acceleration control and position control. The landing hold phase prioritizes position and velocity maintenance. Based on this division, a cost function is designed.

[0064] As an optional embodiment, in step S103, the expression of the second-order cone constraint is:

[0065] in, where f is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the actual state of the tethered asteroid probe system at time k+i, is the state of the tethered asteroid probe system at time k+i, is the control input of the tethered asteroid probe system at time k+i, is the expected state of the tethered asteroid probe system, where k is the current initial time of the tethered asteroid probe performing iterative optimization, N is the prediction time domain, , is the surface normal vector of the preset landing point, The actual trajectory and The angle of are the coordinates of the target landing point and the lander release position, For terminal sets.

[0066] In this embodiment, in order to ensure that there is an optimal solution to the optimization problem, a second-order cone constraint is introduced to obtain a global optimal solution. The introduced second-order cone constraint is essentially a cone constraint, which can be judged to be a convex constraint. According to the properties of the convex constraint, the optimal solution obtained by solving the optimization problem is the global optimal solution.

[0067] Derive robustness conditions for computational algorithms.

[0068] The derived equation of state (dynamic model of the probe and lander in a tethered asteroid) is quadratically continuously differentiable. Furthermore, according to the proposed second-order cone constraints, the constraint set of state variables is closed, and the constraint set of control variables is compact. The designed desired trajectory is within the constraint set and is therefore reachable.

[0069] Since asteroids are small in size and are far away from other celestial bodies in deep space, it is reasonable to assume that the gravitational field generated by asteroids and the disturbances caused by the influence of other celestial bodies have an upper limit, that is, for any time t, ,in is a positive constant. Stable operation is important for the proposed method (determining the position and velocity of the probe and lander in different directions of the inertial system of the asteroid's centroid and ) For the tethered asteroid probe system, the following state error feedback controller is designed:

[0070] in, , According to the new U, the state solution can be derived from this controller, the vector range of e, is the error feedback matrix, is the state error matrix, is the optimization parameter after the error feedback matrix is ​​introduced, To introduce the comprehensive control force after error feedback, They represent the components of the probe and lander in the X, Y, and Z directions, as well as the components applied to the tether release motor.

[0071] is the state error range, T is the prediction time domain, is a natural number, and , are the diagonal elements of matrices Q and R, .

[0072] And according to the designed second-order cone constraint, the necessary parameter definitions are given

[0073]

[0074] When the above conditions are met, for the proposed tethered asteroid probe system, at any time t, , there exists a control input that satisfies the conditions , the following conditions are met:

[0075] in, is the sampling time, .

[0076] Similarly, the sampling time interval is reasonably designed to meet its robustness requirements, and its sampling interval meets:

[0077] In the embodiment of the present invention, when the probe and lander in the tethered asteroid are separated in the irregular gravitational field of the asteroid, different expected trajectory strategies are set based on the different descent stages of the lander; based on the different expected trajectory strategies set in the different descent stages of the lander, a model predictive control algorithm is designed; based on the model predictive control algorithm, a cost function of the model predictive control algorithm is designed and a second-order cone constraint is introduced to obtain the optimal control force of the probe, lander and space tether in the tethered asteroid; based on the optimal control force of the probe, lander and space tether in the tethered asteroid, the probe of the tethered asteroid is controlled to land safely, thereby solving the problem of irregular asteroid. The dynamics of the tethered asteroid probe system during the landing of the tethered asteroid probe in the gravitational field is relatively complex, and there are constraints to ensure the safe flight of the probe and limit the control ability of the probe, which leads to the technical problem that it is difficult to solve the optimal control problem of asteroid landing trajectory planning and the calculation speed is slow. A robust tracking model pre-estimation controller based on tether tension control is proposed to realize the landing of the probe, so as to ensure that the lander can follow the expected trajectory and expected speed during the descent, while the rope tension can remain stable, and can better deal with the problem of inaccurate dynamic model caused by irregular and complex gravitational fields.

[0078] The serial numbers of the above embodiments of the present invention are for description only and do not represent the advantages or disadvantages of the embodiments.

[0079] In the above embodiments of the present invention, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0080] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only exemplary. For example, the division of units can be a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0081] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple units. Some or all of the units may be selected to achieve the purpose of the present embodiment according to actual needs.

[0082] In addition, the functional units in various embodiments of the present invention may be integrated into a first processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0083] The above are only preferred embodiments of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A tethered asteroid probe landing control method suitable for an asteroid with irregular gravitational fields, characterized in that: include: In the case of separation of the probe and the lander in the tethered asteroid in the irregular gravitational field of the asteroid, different expected trajectory strategies are set based on the different descent stages of the lander; Design a model predictive control algorithm based on different desired trajectory strategies set during the lander's descent phases; Based on the model predictive control algorithm, the cost function of the model predictive control algorithm is designed and the second-order cone constraint is introduced to obtain the optimal control force of the probe, lander and space tether in the tethered asteroid; Based on the optimal control force of the probe, lander and space tether in the tethered asteroid, the probe on the tethered asteroid is controlled to land safely.

2. The method according to claim 1, characterized in that Before setting different desired trajectory strategies based on different descent phases of the lander, the method further includes: Based on the scenario where a probe is about to land in an irregular gravitational field on a tethered asteroid, a dynamic model of the probe and lander in the tethered asteroid and a dynamic model of the space tether in the tethered asteroid are established; The dynamic model of the probe and lander in the tethered asteroid is: in, 、 and are the accelerations of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the velocities of the probe or lander in the X, Y, and Z directions of the inertial system at the centroid of the asteroid, are the positions of the probe or lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, For a probe or lander, the asteroid rotates approximately uniformly around the principal axis of maximum inertia, which is assumed to be the z axis. is the angular velocity of the asteroid's rotation around the z axis, is the gravitational vector in the asteroid’s inertial coordinate system, Indicates the tension of the tether. The acceleration caused by the solar pressure, is the gravitational error due to the asteroid shape error, is the mass of the probe and lander; The dynamic model of the space tether is: in, is the electromechanical time constant, is the torque coefficient, is the moment of inertia converted into the motor shaft load, is the input voltage to the motor, is the armature resistance, is the natural length of the tether in the absence of tension, is the motor kinetic energy constant, is the release acceleration of the natural length of the tether in the absence of tension, is the release speed of the natural length of the tether in the absence of tension; Based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the position and velocity of the probe and lander in different directions of the inertial system of the asteroid's centroid and the release acceleration and release velocity of the tether in the tension-free state are determined.

3. The method according to claim 2, characterized in that Based on the dynamic model of the probe and lander in the tethered asteroid and the dynamic model of the space tether, the expressions for determining the position and velocity of the probe and lander in different directions of the inertial system of the asteroid's centroid and the release acceleration and release velocity of the tether in the absence of tension are: in, is the position of the probe in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the probe in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, is the position of the lander in the X, Y, and Z directions of the inertial system of the asteroid's centroid, is the velocity of the lander in the X, Y, and Z directions of the inertial system of the asteroid’s centroid, represent the values ​​of the gravitational vector in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; They represent the values ​​of the sunlight pressure in the X, Y, and Z directions of the inertial system of the probe and the lander asteroid centroid respectively; The control forces in the X, Y, and Z directions applied to the inertial system of the probe and the lander asteroid centroid, as well as the voltage value of the tether release motor.

4. The method according to claim 1, wherein The expression for setting different expected trajectory strategies based on different descent stages of the lander is: in, It is the period from the separation of the probe and the lander to the safe landing of the lander, that is, the actual running time. They are the time points during the landing process when the release changes from uniform speed to deceleration, the time points when the deceleration release enters the final low-speed landing stage, and the time points after landing; are the expected values ​​of lander velocity, lander position and tether length respectively; Respectively represent the set speed value of the uniform speed operation stage, is the simulation time step, is the time step that has been run, represents the expected value of the tether release velocity, Indicates the initial value of the lander position, represents the initial value of the tether length, represents the expected value of the tether length at the moment before time t, represents the expected value of the lander position at the moment before time t.

5. The method according to claim 1, wherein The expression of the model predictive control algorithm is: in, for A function, is the control input matrix, is the actual state matrix of the tethered asteroid probe system, is the cost function, is the index value of the matrix, is the terminal constraint function, is the maximum allowable control input, is the maximum allowed state value, is the state terminal set, is the expected state matrix of the probe and lander, and are respectively the prediction time domain and the control time domain of model predictive control, is the time point when the min function runs, for The actual state matrix of the tethered asteroid probe system at time, for The input matrix is ​​controlled at all times. is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the actual state matrix of the tethered asteroid probe system at the time point when the min function runs, is the state of the tethered asteroid probe system at time k, is the state of the tethered asteroid probe system on N, where N is the prediction time domain.

6. The method according to claim 1, wherein The cost function expression of the model predictive control algorithm is: in, is the cost function, t is the simulation time, , , are the expected state matrices of the probe and lander, Q and R are both positive semi-definite matrices, and T is the transpose.

7. The method according to claim 1, characterized in that The expression of the second-order cone constraint is: in, where f is the dynamic equation of the dynamic model of the probe and lander in the tethered asteroid, is the actual state of the tethered asteroid probe system at time k+i, is the state of the tethered asteroid probe system at time k+i, is the control input of the tethered asteroid probe system at time k+i, is the expected state of the tethered asteroid probe system, where k is the current initial time of the tethered asteroid probe performing iterative optimization, N is the prediction time domain, , is the surface normal vector of the preset landing point, The actual trajectory and The angle of are the coordinates of the target landing point and the lander release position, For terminal sets.

8. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method of claim 1.

9. A computer-readable storage medium, characterized in that Computer-executable instructions are stored, and when the instructions are executed, they are used to implement the method of claim 1.

10. A computer program product, characterized in that The invention comprises computer executable instructions, which are used to implement the method of claim 1 when the instructions are executed.

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