Multi-node flexible lander modeling method for small celestial body landing

Abstract

The invention relates to a multi-node flexible lander modeling method for small celestial body landing. The multi-node flexible lander modeling method for small celestial body landing at least comprises the following steps: establishing a kinetic equation of each node of a multi-node flexible lander; constructing an action Hamiltonian function between the rigid nodes and a limiting action equation of flexible connection on the rigid nodes; establishing a mathematical dynamic model of the multi-node flexible lander; establishing a bounce dynamic model of the multi-node flexible lander; and executing jump suppression analysis of the multi-node flexible lander. The small celestial body landing-oriented multi-node flexible lander modeling method overcomes the weak gravitational characteristic of a small celestial body, multiple nodes increase fault tolerance and can well drive a flexible body to move, a kinetic equation of the designed lander is established, a spring damping structure and flexible design are adopted, and the small celestial body landing-oriented multi-node flexible lander modeling method has the advantages of being simple in structure and convenient to operate. The problem that the landing effect is poor due to excessive deformation of the flexible plate is solved, the overall design is simple, and implementation is high.

Description

Technical Field

[0001] The present invention relates to the field of aerospace, and in particular to a multi-node flexible lander modeling method for small celestial body landing. Background Art

[0002] Asteroids have the environmental characteristics of "microgravity and uncertainty". "Microgravity" means that the surface of an asteroid is a microgravity environment, the escape velocity is very low, and the lander is prone to bounce. "Uncertainty" means that there is little prior knowledge about asteroids. Before the probe arrives, we can only speculate on its rotation period, topography, surface physical properties, etc. Therefore, a number of new core technologies need to be further broken through. Among them, the key technologies that need to be broken through for new probes are urgently needed.

[0003] Prior art 1 proposes a configuration in which three detectors drive a flexible net, and studies its attachment stability, concluding that the landing effect of the designed detector is better than that of a rigid detector. However, the configuration designed in prior art 1 still has the bouncing of the rigid detector in the simulation scene.

[0004] Prior art 2 proposes a configuration of installing a flexible plate under a rigid probe, hoping to use the flexible plate to contact the satellite surface to achieve robust attachment. The simulation tool shows that the lander mainly dissipates the landing kinetic energy through contact. The deformable plate determines the contact mode under different landing postures. There is an optimal stiffness range for the plate, which can produce appropriate deformation to make the energy consumption greater. The optimal value depends on the landing speed, and dynamic similarity can be used in the design. According to the rebound stability evaluation, the flexible design has a more stable contribution than the rigid lander, and is also adaptive to terrain and inverted conditions. However, due to the simplicity of the selected structure, the performance of the proposed lander is still limited to the impact-dominated landing posture. Moreover, the deformable plate determines the contact mode under different landing postures. There is an optimal stiffness range for the plate, and once it exceeds the range, the effect may be worse.

[0005] Prior art 3 proposes a structure consisting of three thrust units and airbags connected to each other, and studies its control distribution method. However, the rigid nodes are too constrained, and the use of airbags makes the flexibility not thorough enough. It is essentially a rigid lander.

[0006] Prior art 4 uses this multi-legged configuration to achieve asteroid exploration. However, multi-legged robots with rigid-flexible coupling grippers have good application prospects in asteroid exploration under microgravity conditions. However, these robots usually have very complex structures, which brings great challenges to kinematic design. Summary of the invention

[0007] The present invention provides a multi-node flexible lander modeling method for small celestial body landing, aiming to solve at least one of the technical problems existing in the prior art.

[0008] The technical solution of the present invention is a multi-node flexible lander modeling method for small celestial body landing, which is applied to the multi-node flexible lander. The multi-node flexible lander includes at least three rigid nodes connected end to end in sequence, each rigid node is connected by a spring, and each rigid node can move in a small range under the influence of the spring. The multi-node flexible lander modeling method for small celestial body landing includes at least the following steps:

[0009] S100, establishing the dynamic equations of each node of the multi-node flexible lander;

[0010] S200, constructing the Hamiltonian function of rigid node interaction and equations for the limiting effects of flexible connections on rigid nodes;

[0011] S300, establish a mathematical dynamics model of a multi-node flexible lander;

[0012] S400, establish the bouncing dynamics model of multi-node flexible lander;

[0013] S500: Execute jump suppression analysis of the multi-node flexible lander.

[0014] Further, in step S100,

[0015] Based on port-Hamilton dynamics, the dynamic equations of each node of the multi-node flexible lander including N rigid nodes are determined as follows:

[0016]

[0017] Where N>2, q i =(x i ,y i , z i ) T represents the position of a rigid node, M i is the node quality, Represents the momentum of a node, Di is the third-order damping matrix, Di represents the damping of the node when it moves in three-dimensional space, is the damping coefficient, I3 is the 3D unit matrix, u i It is the limiting force of the flexible connection on the rigid node generated by the self-recovery ability of the flexible material.

[0018] Indicates the next H i P i Find the partial differential, Hi The Hamiltonian for a rigid node motion.

[0019] Furthermore, the Hamiltonian function H of any rigid node motion in the multi-node flexible lander is i for:

[0020]

[0021] Among them, M i is the node quality, represents the momentum of a node, H i is the Hamiltonian function of a rigid node motion. Since there is a flexible body between the rigid nodes, the force between the rigid nodes is equivalent to the interaction between the spring and the damper.

[0022] Further, in step S200,

[0023] Introducing undirected graphs Represents the connection relationship between rigid nodes, uses edge sets to represent the elasticity and damping between rigid nodes, and uses represents the length of the side, represents the speed of change of the length of the edge, then the interaction force F between the rigid nodes ij By an elastic potential energy function V(z ij )definition,

[0024] Therefore, the length of the side z ij The interaction force F between the rigid nodes ij They are:

[0025]

[0026] in, is the dissipative matrix, which represents the relative motion speed between rigid nodes. The spring deforms under the action of external force. After the external force is removed, the spring returns to its original shape.

[0027] Therefore, construct the Hamiltonian function of rigid node interaction That is, the elastic potential energy function V(z ij )for:

[0028]

[0029] Among them, z ij , are the actual length and the length without deformation of the spring, is the elastic constant of the spring,

[0030] The limiting effect of the flexible connection on the rigid node is expressed as:

[0031]

[0032] Among them, B is the adjacency matrix of the node, is the Kronecker product operator.

[0033] Further, in step S300,

[0034] Under the restriction of flexible connection, the mathematical dynamic model of the multi-node flexible lander is expressed as:

[0035]

[0036] in,

[0037]

[0038] After the introduction of flexible connections, each node of the multi-node flexible lander will not only have kinetic energy, but will also be affected by the potential energy of the flexible connections.

[0039] Further, in step S400,

[0040] The collision force is described by the nonlinear spring damping model and nonlinear damping function based on Hertz's law. The multi-node flexible lander is regarded as a mass point. When the multi-node flexible lander collides with the star surface during landing, it will bounce. The bouncing dynamics equation is:

[0041]

[0042] Among them, F N is the vertical reaction force, F t is the tangential reaction force, the vertical reaction force F N and the tangential reaction force F t Calculated by the continuous collision model, g z is the vertical gravitational constant, g z is the tangential gravitational constant.

[0043] Furthermore, the vertical reaction force F N for:

[0044]

[0045] Among them, k z is the contact rebound coefficient, c is the contact damping coefficient, δ is the collision penetration depth of the multi-node flexible lander into the star surface after contact with the star surface, v0 is the vertical velocity of the lander at the moment of contact, and e is the contact recovery coefficient.

[0046] Further, in step S500,

[0047] Based on the dynamic equations of each node of the multi-node flexible lander established by the pH system, under the constraints of the limiting effect equation of the sexual connection on the rigid nodes, the mathematical dynamic model composed of the total energy of the multi-node flexible lander spontaneously decays;

[0048] In the port-Hamilton dynamics of the multi-node flexible lander, the Hamiltonian function of the system is:

[0049]

[0050] Obviously, H(p i , z ij )≥0, and taking the derivative of the Hamilton function of the system, we get:

[0051]

[0052] Therefore, the energy of the entire system has a tendency to decay spontaneously. Under the control of the spontaneous recovery deformation characteristics of the flexible connection spring, the actual length of the spring will converge to its nominal length, that is, The kinetic energy of the multi-node flexible lander will be partially converted into the flexible connection potential energy, and its energy will decay spontaneously;

[0053] When there is a motion difference between the nodes, the flexible lander will have a conversion of kinetic energy and elastic potential energy, and then gradually consume the kinetic energy, thereby effectively suppressing the rebound.

[0054] Furthermore, the present invention also proposes a multi-node flexible lander, which is applied to the multi-node flexible lander modeling method for landing on a small celestial body, and the multi-node flexible lander comprises:

[0055] The multi-node flexible lander includes at least three rigid nodes connected end to end in sequence, each rigid node is equipped with at least a sensing device and a scientific payload, the sensing device includes at least a combination of one or more of a wide and narrow field of view camera, a laser radar and an IMU, each rigid node is connected by a spring, and each rigid node can move in a small range under the pull of the spring.

[0056] Affected by the spring, the thrust output direction of the rigid node is single, and the thrust size is continuously controllable. The thrust direction can only be changed in a small range by changing the roll angle and pitch angle of the rigid node.

[0057] Furthermore, the present invention also proposes a computer-readable storage medium having program instructions stored thereon, and when the program instructions are executed by a processor, the multi-node flexible lander modeling method for small celestial body landing is implemented.

[0058] The beneficial effects of the present invention are:

[0059] The multi-node flexible lander modeling method for small celestial body landing overcomes the weak gravity characteristics of small celestial bodies. The multiple nodes not only increase the fault tolerance but also can well drive the movement of the flexible body. The dynamic equation of the designed lander is established. The spring damping structure and flexible design are adopted to overcome the problem of poor landing effect caused by excessive deformation of the flexible plate. The overall design is simple and has strong feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of the multi-node flexible lander modeling method for small body landing.

[0061] Figure 2 It is a schematic diagram of a multi-node flexible lander model in a multi-node flexible lander modeling method for small body landing.

[0062] Figure 3 It is a schematic diagram of the thrust output direction of a single node in the multi-node flexible lander modeling method for small body landing.

[0063] Figure 4 It is a schematic diagram of the force relationship between nodes in the multi-node flexible lander modeling method for small body landing.

[0064] Figure 5 It is a schematic diagram of the bouncing of a multi-node flexible lander in the multi-node flexible lander modeling method for landing on small celestial bodies.

[0065] Figure 6 It is a schematic diagram of the bounce suppression analysis of a multi-node flexible lander in the multi-node flexible lander modeling method for small-body landing.

[0066] Figure 7 This is a schematic diagram of the simulation of the conventional lander bouncing process in the multi-node flexible lander modeling method for small body landing.

[0067] Figure 8 This is the second schematic diagram of the simulation of the conventional lander bouncing process in the multi-node flexible lander modeling method for small body landing.

[0068] Fig. 9 It is the third schematic diagram of the simulation of the conventional lander bouncing process in the multi-node flexible lander modeling method for small body landing.

[0069] Fig.10 It is a schematic diagram of the topological connections of an embodiment of a multi-node flexible lander for attachment to a small celestial body.

[0070] Fig.11 It is a simulation process of an embodiment of a multi-node flexible lander for attachment to small celestial bodies.

[0071] Fig.12It is the simulation result of an embodiment of a multi-node flexible lander for attachment to a small celestial body. DETAILED DESCRIPTION

[0072] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention, so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other without conflict.

[0073] It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to the other feature, or it may be indirectly fixed or connected to the other feature. In addition, the descriptions of up, down, left, right, top, bottom, etc. used in the present invention are only relative to the relative positional relationship of the components of the present invention in the drawings.

[0074] In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art. The terms used in this specification are only for describing specific embodiments, not for limiting the present invention. The term "and / or" used herein includes any combination of one or more related listed items.

[0075] It should be understood that, although the terms first, second, third, etc. may be used to describe various elements in the present disclosure, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other. For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element.

[0076] Reference Figures 1 to 12 In some embodiments, the technical solution of the present invention is a multi-node flexible lander modeling method for small celestial body landing, which is applied to the multi-node flexible lander. The multi-node flexible lander includes at least three rigid nodes connected end to end in sequence, each rigid node is connected by a spring, and each rigid node can move in a small range under the influence of the spring. Figure 1 The multi-node flexible lander modeling method for small celestial body landing comprises at least the following steps:

[0077] S100, establishing the dynamic equations of each node of the multi-node flexible lander;

[0078] S200, constructing the Hamiltonian function of rigid node interaction and equations for the limiting effects of flexible connections on rigid nodes;

[0079] S300, establish a mathematical dynamics model of a multi-node flexible lander;

[0080] S400, establish the bouncing dynamics model of multi-node flexible lander;

[0081] S500: Execute jump suppression analysis of the multi-node flexible lander.

[0082] The beneficial effects of the present invention are:

[0083] The multi-node flexible lander modeling method for small celestial body landing overcomes the weak gravity characteristics of small celestial bodies. The multiple nodes not only increase the fault tolerance but also can well drive the movement of the flexible body. The dynamic equation of the designed lander is established. The spring damping structure and flexible design are adopted to overcome the problem of poor landing effect caused by excessive deformation of the flexible plate. The overall design is simple and has strong feasibility.

[0084] Specifically, the exploration of small celestial bodies is one of the cutting-edge topics of deep space exploration today. It can provide clues to the formation and evolution of the solar system and has important guiding significance for studying the origin of life on Earth. Its scarce material resources may become a treasure trove for future development and utilization. With the development of human science and technology, the detection methods of small celestial bodies have also gradually evolved from early ground-based astronomical observations and close-range flyby observations to attachment and sampling and return. In recent years, Japan's Hayabusa2 mission and the United States' OSIRIS-Rex mission (the sample return capsule has successfully returned to Earth on September 24, 2023) have set off a climax of asteroid sampling and return exploration. my country also plans to launch "Tianwen-2" in 2025 to carry out a sampling and return mission for small celestial bodies.

[0085] In the sampling and return mission of small celestial bodies, the landing process is the key to the success or failure of the mission. Due to the different morphologies of small celestial bodies, their gravitational fields are usually irregular and weak, so conventional landers will face the risk of landing bounce. "Hayabusa 1" failed in its first landing on the Isokawa asteroid because its posture was skewed before landing. After two slight bounces, the sampler and the front end of the solar sail touched the ground together, causing it to accidentally enter the safety mode; and the Philae lander carried by the "Rosetta" also had a landing bounce due to braking problems in the final stage of landing, and ultimately failed to successfully fall into the illuminated area as planned, causing it to enter permanent hibernation after only a few dozen hours of observation. Secondly, due to the great differences in the surface structural characteristics of various small celestial bodies, their surface structures can be stardust soil, gravel or hard stones, etc., and humans have relatively limited knowledge of them. Therefore, the landing and attachment system of small celestial bodies needs to have greater adaptability. The overall implementation plan for deep space exploration before 2030 released by my country lists asteroid exploration as one of the priorities of my country's future deep space exploration, and puts forward new requirements for probe landing and attachment technology, requiring further breakthroughs in adhesion, attachment stability and mechanism reliability.

[0086] The compliance and impact resistance of flexible soft robots are very consistent with the needs of landing on small celestial bodies. First of all, flexible soft robots are deformable, so they are less likely to be damaged when in contact with the surface of a star. Secondly, a soft lander can dissipate the landing impact better than a rigid body when in contact with the surface of a star, thereby reducing the bounce of the lander. By embedding multiple robots with maneuverability into the flexible body, the flexible body can be driven to move, and the landing impact can be further dissipated through the collaboration of multiple nodes. In summary, the present invention proposes a multi-node flexible lander, and from the perspective of energy, studies the bounce suppression problem of the multi-node flexible lander, and clarifies the bounce suppression mechanism of the multi-node flexible lander.

[0087] Further, in step S100,

[0088] Based on port-Hamilton dynamics, the dynamic equations of each node of the multi-node flexible lander including N rigid nodes are determined as follows:

[0089]

[0090] Where N>2, q i =(x i ,y i , z i ) T represents the position of a rigid node, M i is the node quality, Represents the momentum of a node, Di is the third-order damping matrix, Di represents the damping of the node when it moves in three-dimensional space, is the damping coefficient, I3 is the 3D unit matrix, u i It is the limiting force of the flexible connection on the rigid node generated by the self-recovery ability of the flexible material.

[0091] Indicates the next H i P i Find the partial differential, H i The Hamiltonian for a rigid node motion.

[0092] Specifically, refer to Figure 2 and Figure 3 The flexible multi-node lander is planned to be connected by springs and rigid nodes. Each node is equipped with wide and narrow field of view cameras, lidar, IMU and other sensing equipment and scientific payloads. The node can move in a small range under the influence of the spring. However, due to the influence of the spring, the thrust output direction of the node is single, and the thrust size is continuously controllable. The thrust direction can be changed in a small range only by changing the roll angle and pitch angle of the node.

[0093] Furthermore, the Hamiltonian function H of any rigid node motion in the multi-node flexible lander is i for:

[0094]

[0095] Among them, M i is the node quality, represents the momentum of a node, H i is the Hamiltonian function of a rigid node motion. Since there is a flexible body between the rigid nodes, the force between the rigid nodes is equivalent to the interaction between the spring and the damper.

[0096] Reference Figure 4 , taking the force relationship between node 1 and node 2 as an example, Figure 4 Where F1 and F2 are the interaction forces between nodes. q1 and q2 are the displacements of node 1 and node 2, respectively. m1 and m2 are the masses of node 1 and node 2, respectively. 12 is the distance between nodes. k is the spring elastic coefficient and d is the spring damping coefficient.

[0097] Further, in step S200,

[0098] Introducing undirected graphs Represents the connection relationship between rigid nodes, uses edge sets to represent the elasticity and damping between rigid nodes, and uses represents the length of the side, represents the speed of change of the length of the edge, then the interaction force F between the rigid nodes ij By an elastic potential energy function V(z ij )definition,

[0099] Therefore, the length of the side z ij The interaction force F between the rigid nodes ij They are:

[0100]

[0101] in, is the dissipative matrix, which represents the relative motion speed between rigid nodes. The spring deforms under the action of external force. After the external force is removed, the spring returns to its original shape.

[0102] Therefore, construct the Hamiltonian function of rigid node interaction That is, the elastic potential energy function V(z ij )for:

[0103]

[0104] Among them, z ij , are the actual length and the length without deformation of the spring, is the elastic constant of the spring,

[0105] The limiting effect of the flexible connection on the rigid node is expressed as:

[0106]

[0107] Among them, B is the adjacency matrix of the node, is the Kronecker product operator.

[0108] Further, in step S300,

[0109] Under the restriction of flexible connection, the mathematical dynamic model of the multi-node flexible lander is expressed as:

[0110]

[0111] in,

[0112]

[0113] After the introduction of flexible connections, each node of the multi-node flexible lander will not only have kinetic energy, but will also be affected by the potential energy of the flexible connections.

[0114] Further, refer to Figure 5 In the step S400,

[0115] The collision force is described by the nonlinear spring damping model and nonlinear damping function based on Hertz's law. The multi-node flexible lander is regarded as a mass point. When the multi-node flexible lander collides with the star surface during landing, it will bounce. The bouncing dynamics equation is:

[0116]

[0117] Among them, F N is the vertical reaction force, F t is the tangential reaction force, the vertical reaction force F N and the tangential reaction force F t Calculated by the continuous collision model, g z is the vertical gravitational constant, g z is the tangential gravitational constant.

[0118] Further, refer to Figure 5 , vertical reaction force F N for:

[0119]

[0120] Among them, k zis the contact rebound coefficient, c is the contact damping coefficient, δ is the collision penetration depth of the multi-node flexible lander into the star surface after contact with the star surface, v0 is the vertical velocity of the lander at the moment of contact, and e is the contact recovery coefficient.

[0121] Further, refer to Figure 6 In step S500,

[0122] Based on the dynamic equations of each node of the multi-node flexible lander established by the pH system, under the constraints of the limiting effect equation of the sexual connection on the rigid nodes, the mathematical dynamic model composed of the total energy of the multi-node flexible lander spontaneously decays;

[0123] In the port-Hamilton dynamics of the multi-node flexible lander, the Hamiltonian function of the system is:

[0124]

[0125] Obviously, H(p i , z ij )≥0, and taking the derivative of the Hamilton function of the system, we get:

[0126]

[0127] Therefore, the energy of the entire system has a tendency to decay spontaneously. Under the control of the spontaneous recovery deformation characteristics of the flexible connection spring, the actual length of the spring will converge to its nominal length, that is, The kinetic energy of the multi-node flexible lander will be partially converted into the flexible connection potential energy, and its energy will decay spontaneously;

[0128] When there is a motion difference between the nodes, the flexible lander will have a conversion of kinetic energy and elastic potential energy, and then gradually consume the kinetic energy, thereby effectively suppressing the rebound.

[0129] Specifically, the port-Hamilton (pH system) was established by Van der Schaft as an energy-based approach to describe and model nonlinear systems in various fields.

[0130] Specifically, refer to Figure 6 For a conventional lander, as it gradually approaches the star surface, the gravitational potential energy is gradually converted into kinetic energy. When the lander contacts the surface, a collision occurs and energy is exchanged, accompanied by energy loss. The energy loss is mainly composed of the friction work between the surface weathering layer and the lander, and the internal force work of the lander's own elastic deformation. Therefore, the kinetic energy of the lander after the impact is This energy will push the lander away from the surface of the star. Until the lander reaches a height h from the star surface, at which time the lander will move toward the star surface again under the action of gravity, and its collision energy is It is worth noting that due to the collision energy loss exists, so Then the kinetic energy of the lander will become smaller and smaller after each collision, so its bounce height will become lower and lower, and finally converge to the star surface.

[0131] For a multi-node flexible lander, due to the existence of flexible connections, part of the system kinetic energy will be converted into flexible connection potential energy, that is, Therefore, under the same conditions, the impact kinetic energy of the node will be less than that of the conventional lander, and the gravitational potential energy that can be converted will also be reduced, so the bounce height of the multi-node flexible lander will be less than that of the conventional lander. Secondly, the conventional lander can only consume kinetic energy through collision, while the flexible connection of the multi-node flexible lander can also consume kinetic energy.

[0132] Therefore, the following theorem is deduced: Considering the multi-node lander dynamic model based on the pH system, under the control of the flexible connection, the total energy of the closed-loop system has the characteristic of spontaneous decay.

[0133] Hamiltonian function of the system By taking the derivative, we can see that the energy of the entire system has a tendency to spontaneously decay. That is to say, under the control of the spontaneous recovery deformation characteristics of the flexible connection, the kinetic energy of the multi-node flexible lander will be partially converted into the flexible connection potential energy, and its energy will spontaneously decay. Through the above analysis, we can draw the following conclusions: when there is a motion difference between the nodes, the flexible lander will have a conversion of kinetic energy and elastic potential energy, and then gradually consume kinetic energy, thereby effectively suppressing rebound.

[0134] Reference Figure 7 , showing the speed change of a single-node lander during the landing process with initial speeds of -2m / s, -3m / s, and -4m / s respectively.

[0135] Reference Figure 8 , showing the height change of a single-node lander during the landing process with initial speeds of -2m / s, -3m / s, and -4m / s respectively.

[0136] Reference Fig. 9 , showing the change in kinetic energy of a single-node lander during the landing process with initial speeds of -2m / s, -3m / s, and -4m / s respectively.

[0137] Through the above analysis, the following conclusions can be drawn: when there is a difference in motion between nodes, the flexible lander will have a conversion of kinetic energy and elastic potential energy, and then gradually consume kinetic energy, thereby effectively suppressing the rebound. The premise of using a missile with multiple nodes and a flexible connection structure is that there are differences in motion between nodes, and this condition is relatively easy to meet. As mentioned earlier, due to errors in the navigation and control systems, as well as the influence of irregular gravitational fields, differences in motion between nodes are inevitable. In addition, as shown in the figure, considering that the surface terrain of a small celestial body is complex and may be composed of soft sand or hard rock, when in contact with the surface of the celestial body, the rebound coefficients received by the nodes are bound to be different, which will also lead to differences in motion between nodes.

[0138] Furthermore, the present invention also proposes a multi-node flexible lander, which is applied to the multi-node flexible lander modeling method for landing on a small celestial body, and the multi-node flexible lander comprises:

[0139] The multi-node flexible lander includes at least three rigid nodes connected end to end in sequence, each rigid node is equipped with at least a sensing device and a scientific payload, the sensing device includes at least a combination of one or more of a wide and narrow field of view camera, a laser radar and an IMU, each rigid node is connected by a spring, and each rigid node can move in a small range under the pull of the spring.

[0140] Affected by the spring, the thrust output direction of the rigid node is single, and the thrust size is continuously controllable. The thrust direction can only be changed in a small range by changing the roll angle and pitch angle of the rigid node.

[0141] In a specific embodiment, the multi-node flexible lander includes five rigid nodes connected end to end in sequence.

[0142] The present invention proposes a new type of multi-node rigid-flexible coupling lander. The rigid-flexible coupling can overcome the weak gravitational characteristics of small celestial bodies. The multiple nodes increase the fault tolerance and can well drive the movement of flexible bodies. Compared with the problem of the difficulty in establishing dynamics in the prior art 4, this scheme has established the dynamic equations of the designed lander; compared with the prior art 1, the design of the present invention is simpler and more feasible; compared with the prior art 2, the present invention does not select a flexible plate, but selects a spring damping structure, which overcomes the problem of poor landing effect caused by excessive deformation of the flexible plate; compared with the prior art 3, the design of the present invention is more flexible.

[0143] In order to further verify whether the multi-node flexible lander has the ability to suppress bounce, the following simulation experiment is constructed based on the bounce dynamics and lander dynamics: First, the landing bounce simulation of a single-node lander is established, and its parameter settings are shown in Table 1.

[0144] Table 1 Simulation parameter settings

[0145] parameter gravitational Coefficient of Rebound Initial Speed Initial Height Node quality Elastic modulus Damping coefficient Numeric <![CDATA[0.0008m / s 2 ]]> 20 -2m / s 5m 30kg 0.001 0.05

[0146] Then, refer to Fig.10 , a landing bounce simulation of a flexible lander with 5 nodes is established, each node will have a flexible connection with the other 4 nodes, where ε ij Represents the connection relationship between nodes, such as ε 12 Represents the connection between node 1 and node 2.

[0147] Reference Fig.11 , is the simulation process at different times, where the arrows indicate the velocity direction and magnitude of each node at the current time. When T = 0s, each node starts to fall with different initial velocities; as time goes on, each node touches the ground one after another and rebounds. When T = 1500s, the entire bouncing process ends, and each node lands stably on the surface of the small celestial body.

[0148] Reference Fig.12 , (a) shows the height change of each node of the multi-node flexible lander and the conventional single-node lander during the landing process. (b) shows the change of the spring length between the nodes of the multi-node flexible lander. (c) shows the change of the kinetic energy of each node of the multi-node flexible lander. (d) shows the change of the overall elasticity of the multi-node flexible lander. In summary, the results of the simulation experiments show that the rebound height of each node of the multi-node flexible lander is only about 4 meters, compared with the rebound height of 5.5 meters of the traditional single-node lander. This clearly shows that the multi-node flexible lander effectively suppresses the landing rebound. Compared with traditional landers, the kinetic energy of the multi-node flexible lander dissipates significantly faster. This can be attributed to the initial height difference between the nodes, which causes relative motion between them, refer to Fig.12 (b) This relative motion causes deformation in the flexible material, generating elastic potential energy, see Fig.12 (d), thus, accelerating the dissipation of the lander’s kinetic energy and suppressing the rebound of each node.

[0149] Furthermore, the present invention also proposes a computer-readable storage medium having program instructions stored thereon, and when the program instructions are executed by a processor, the multi-node flexible lander modeling method for small celestial body landing is implemented.

[0150] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the scope of protection of the present disclosure. All should belong to the protection scope of the present invention. Within the protection scope of the present invention, its technical scheme and / or implementation method can have various modifications and changes.

Claims

1. A multi-node flexible lander modeling method for small celestial body landing, applied to a multi-node flexible lander, wherein the multi-node flexible lander comprises at least three rigid nodes connected end to end in sequence, each rigid node is connected by a spring, and each rigid node can move in a small range under the pull of the spring, characterized in that: The multi-node flexible lander modeling method for small celestial body landing comprises at least the following steps: S100, establishing the dynamic equations of each node of the multi-node flexible lander; S200, constructing the Hamiltonian function of rigid node interaction and equations for the limiting effects of flexible connections on rigid nodes; S300, establish a mathematical dynamics model of a multi-node flexible lander; S400, establish the bouncing dynamics model of multi-node flexible lander; S500: Execute jump suppression analysis of the multi-node flexible lander.

2. The multi-node flexible lander modeling method for small celestial body landing according to claim 1 is characterized in that: In the step S100, Based on port-Hamilton dynamics, the dynamic equations of each node of the multi-node flexible lander including N rigid nodes are determined as follows: Where N>2, q i =(x i ,y i , z i ) T represents the position of a rigid node, M i is the node quality, represents the momentum of a node, Di is the third-order damping matrix, Di represents the damping of the node when it moves in three-dimensional space, di is the damping coefficient, I3 is the three-dimensional unit matrix, u i It is the limiting force of the flexible connection on the rigid node generated by the self-recovery ability of the flexible material. Indicates the next H i P i Find the partial differential, H i The Hamiltonian for the motion of a rigid node.

3. The multi-node flexible lander modeling method for small celestial body landing according to claim 2 is characterized in that: The Hamiltonian function H of any rigid node motion in the multi-node flexible lander i for: Among them, M i is the node quality, represents the momentum of a node, H i is the Hamiltonian function of a rigid node motion. Since there is a flexible body between the rigid nodes, the force between the rigid nodes is equivalent to the interaction between the spring and the damper.

4. The multi-node flexible lander modeling method for small celestial body landing according to claim 1 is characterized in that: In the step S200, Introducing undirected graphs Represents the connection relationship between rigid nodes, uses edge sets to represent the elasticity and damping between rigid nodes, and uses represents the length of the side, represents the speed of change of the length of the edge, then the interaction force F between the rigid nodes ij By an elastic potential energy function V(z ij )definition, Therefore, the length of the side z ij The interaction force F between the rigid nodes ij They are: in, is the dissipative matrix, which represents the relative motion speed between rigid nodes. The spring deforms under the action of external force. After the external force is removed, the spring returns to its original shape. Therefore, construct the Hamiltonian function of rigid node interaction That is, the elastic potential energy function V(z ij )for: Among them, z ij are the actual length and the length without deformation of the spring, is the elastic constant of the spring, The limiting effect of the flexible connection on the rigid node is expressed as: Among them, B is the adjacency matrix of the node, is the Kronecker product operator.

5. The multi-node flexible lander modeling method for small celestial body landing according to claim 1, characterized in that: In the step S300, Under the restriction of flexible connection, the mathematical dynamic model of the multi-node flexible lander is expressed as: in, After the introduction of flexible connections, each node of the multi-node flexible lander will not only have kinetic energy, but will also be affected by the potential energy of the flexible connections.

6. The multi-node flexible lander modeling method for small celestial body landing according to claim 1 is characterized in that: In the step S400, The collision force is described by the nonlinear spring damping model and nonlinear damping function based on Hertz's law. The multi-node flexible lander is regarded as a mass point. When the multi-node flexible lander collides with the star surface during landing, it will bounce. The bouncing dynamics equation is: Among them, F N is the vertical reaction force, F t is the tangential reaction force, the vertical reaction force F N and the tangential reaction force F t Calculated by the continuous collision model, g z is the vertical gravitational constant, g z is the tangential gravitational constant.

7. The multi-node flexible lander modeling method for small celestial body landing according to claim 6 is characterized in that: Vertical reaction force F N for: Among them, k z is the contact rebound coefficient, c is the contact damping coefficient, δ is the collision penetration depth of the multi-node flexible lander into the star surface after contact with the star surface, v0 is the vertical velocity of the lander at the moment of contact, and e is the contact recovery coefficient.

8. The multi-node flexible lander modeling method for small celestial body landing according to claim 1, characterized in that: In step S500, Based on the dynamic equations of each node of the multi-node flexible lander established by the pH system, under the constraints of the limiting effect equation of the sexual connection on the rigid nodes, the mathematical dynamic model composed of the total energy of the multi-node flexible lander spontaneously decays; In the port-Hamilton dynamics of the multi-node flexible lander, the Hamiltonian function of the system is: Obviously, H(p i , z ij )≥0, and taking the derivative of the Hamilton function of the system, we get: Therefore, the energy of the entire system has a tendency to decay spontaneously. Under the control of the spontaneous recovery deformation characteristics of the flexible connection spring, the actual length of the spring will converge to its nominal length, that is, The kinetic energy of the multi-node flexible lander will be partially converted into the flexible connection potential energy, and its energy will decay spontaneously; When there is a motion difference between the nodes, the flexible lander will have a conversion of kinetic energy and elastic potential energy, and then gradually consume the kinetic energy, thereby effectively suppressing the rebound.

9. A multi-node flexible lander, characterized in that: The multi-node flexible lander modeling method for small celestial body landing as described in any one of claims 1 to 8, wherein the multi-node flexible lander comprises: The multi-node flexible lander includes at least three rigid nodes connected end to end in sequence, each rigid node is equipped with at least a sensing device and a scientific payload, the sensing device includes at least a combination of one or more of a wide and narrow field of view camera, a laser radar and an IMU, each rigid node is connected by a spring, and each rigid node can move in a small range under the pull of the spring. Affected by the spring, the thrust output direction of the rigid node is single, and the thrust size is continuously controllable. The thrust direction can only be changed in a small range by changing the roll angle and pitch angle of the rigid node. 10 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions implement the method according to any one of claims 1 to 8 when executed by a processor.

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