Target-oriented attitude planning method for asteroid-attached three-node flexible probe

Abstract

The asteroid-attached three-node flexible probe target-oriented attitude planning method disclosed by the present application belongs to the field of spacecraft attitude control and planning.The present application realizes the attitude description and dynamic constraint representation of the flexible three-node probe by establishing the flexible three-node deformation and internal force equation and constructing the node plane coupling dynamics model;the present application improves the RRT algorithm by constructing a local optimization expansion strategy, sets the terminal state corresponding to the target attitude as the expanded target state point, and enhances the purpose of the attitude path maneuver;the present application takes the distance to the target attitude as the optimization objective, and constructs a quadratic programming problem in combination with the node plane coupling dynamics model;the present application solves the quadratic programming problem by the improved RRT algorithm based on the local optimization expansion strategy, ensures the smooth and unwinding-free arrival at the target attitude under multiple constraints, can realize the smooth and stable attitude maneuver of the flexible probe, and realizes the flexible attachment of the asteroid probe.

Description

Technical Field

[0001] This invention relates to a target-guided attitude planning method for a three-node flexible probe attached to an asteroid, belonging to the field of spacecraft attitude control and planning technology. Background Technology

[0002] In a probe's landing and attachment mission to an asteroid, the stability of its attitude maneuvers, the safety of the attachment process, the feasibility of the landing site, and the environmental constraints of payload operation must be considered. The probe may face various attitude maneuvering requirements, such as using optical sensors to avoid brightly lit celestial objects, adjusting its attitude pointing while transmitting communication data to the orbiter, maneuvering to observe the surface environment during descent, and adjusting its attachment attitude based on terrain features. Stable attitude control and maneuvering path planning must be achieved under these requirements and environmental constraints to ensure a safe attachment at a suitable location. The probe needs to use its onboard sensors to perceive its current attitude in real time, use its thrusters to output control forces to execute attitude maneuvers, and complete overall autonomous attitude planning to achieve autonomous attitude control.

[0003] In asteroid attachment missions, the complex gravitational fields and diverse terrain features on the asteroid surface pose significant risks of bounce, overturning, and attitude control loss during the attachment and descent of the probe. Therefore, a flexible attachment technique is considered to achieve safe and stable attachment using a flexible probe. During attitude maneuvers, the flexible probe undergoes deformation, and its internal nodes are subject to internal forces and moments, making it difficult to predict their impact on the attitude path. Therefore, the flexible probe's flexible body model is simplified to a three-node-connecting beam system. The dynamic characteristics of the nodes and the flexible constraints they are subject to are analyzed, with each node and its control thrust serving as the planning object. Furthermore, in the attitude maneuvering model of the three-node flexible probe, the maneuvering path from the initial attitude maneuver to the target attitude must satisfy not only dynamic and bounded constraints but also pointing constraints. Attitude path planning methods can be categorized into geometric methods, nonlinear programming methods, polynomial methods, potential function methods, and stochastic programming methods. Among these, stochastic programming methods are widely used in autonomous attitude planning systems due to their high robustness.

[0004] In the developed asteroid attachment probe missions and spacecraft attitude planning methods, prior to the technology [1] (Zou, X., et al. Photometry of asteroid (101955) Bennu with OVIRS on OSIRIS-Rex[J]. Icarus, 2021, 358, 114183), NASA's OSIRIS-Rex probe adopted a "touch and go" control strategy to safely attach to and sample the asteroid Bennu. However, OSIRIS-Rex is a traditional rigid probe. In asteroid attachment missions, due to the weak gravitational field environment and the irregular surface of the asteroid, rigid probes are prone to bounce and loss of control during the attachment process, making control difficult.

[0005] In prior art [2] (Yu Zhen. Research on attitude maneuvering and active vibration suppression control of flexible spacecraft [D]. Nanjing University of Science and Technology, 2017), a method for attitude maneuvering path planning of flexible spacecraft based on spectrum analysis was proposed. From the perspective of spectrum analysis, the design idea of ​​vibration reduction attitude maneuvering path was proposed by analyzing the dynamic characteristics of flexible attachments. By analyzing the relationship between trapezoidal angular velocity path parameters, spectrum and maneuvering time, a method for selecting trapezoidal angular velocity path parameters was proposed. This method achieves the effect of suppressing and optimizing the vibration of flexible attachments of spacecraft in attitude maneuvering through attitude path planning.

[0006] In the prior art [3] (XU R,WU CQ,ZHU SY,et al.A rapid maneuver path planning method with complex sensor pointing constraints in the attitude space[J].Information Systems Frontiers,2017,19(4):945-953), RRT is used as the global planner, and the kinematics, dynamics and bounded constraints are transformed into linear constraints and solved by quadratic programming during local expansion. Obstacle detection is performed on the newly generated nodes to ensure that the pointing constraints are met. The rigid spacecraft is described as a point mass model. When this method is applied to the flexible body system, the control thrust causes flexible deformation, and the maneuver path planning of the flexible body has difficulties in solving the flexible constraints.

[0007] In the attitude maneuvering mission of a flexible probe attached to an asteroid, based on the flexible three-node structure and its motion characteristics, it is necessary to describe the relative positions of the nodes and the overall attitude orientation of the flexible body, determine the constraints of the flexible structure, and establish the relative motion equations of the nodes and the constraint dynamics model. Based on the attitude maneuvering model, and aiming for a smooth, non-back-rotating attitude maneuver to the target attitude under multiple constraints, a target-guided attitude planning method suitable for a three-node flexible probe attached to an asteroid is proposed. Summary of the Invention

[0008] To address the challenges of attitude maneuver control and attitude planning solutions for a three-node flexible asteroid attachment probe under multiple constraints, this invention primarily aims to provide a target-oriented attitude planning method. This method constructs a node-plane coupled dynamics model to describe the attitude and dynamic constraints of the flexible three-node probe. In a local optimization extension strategy, the terminal state corresponding to the target attitude is set as the extended target state point, enhancing the purposefulness of maneuvers along the attitude path. With shortening the distance to the target attitude as the optimization objective, a quadratic programming problem is constructed using the node-plane coupled dynamics model. This invention employs an improved RRT algorithm based on the local optimization extension strategy to ensure smooth and stable attitude maneuvers to the target attitude under multiple constraints, achieving smooth and stable attitude maneuvers for the flexible asteroid attachment probe and improving the stability and reliability of attitude maneuvers for flexible asteroid attachment.

[0009] This invention is achieved through the following technical solution:

[0010] This invention discloses a target-guided attitude planning method for a flexible asteroid-attached three-node probe. Based on the three-node structure and motion characteristics of the flexible body, the flexible three-node probe model is simplified into a three-node-connecting beam system. The influence of flexible connections and deformation on the internal forces of the three nodes is characterized, and equations for the deformation and internal forces of the flexible three nodes are established. The probe's attitude is represented by the angular relationship between the three-node planar fixed system and the inertial frame. A mapping relationship is established from the three-node positions to the overall planar attitude of the probe represented by quaternions. The relative positions of the nodes and the overall attitude pointing of the flexible probe are described using the three-node positions. Combining the deformation and internal force equations of the flexible three nodes, a nodal planar coupled dynamic model is constructed to achieve attitude description and dynamic constraint characterization of the flexible three-node probe. Based on the RRT algorithm, the RRT algorithm is improved by constructing a local optimization extension strategy. In the local optimization extension strategy, the terminal state corresponding to the target attitude is set as the extended target state point, enhancing the purposefulness of maneuvering along the attitude path. With shortening the distance to the target attitude as the optimization objective, a quadratic programming problem is constructed using a nodal-planar coupled dynamics model. Solving this quadratic programming problem ensures that the pointing constraints, bounded constraints of control force and angular velocity, and nodal-planar coupled dynamics constraints are simultaneously satisfied during the attitude maneuver. An improved RRT algorithm based on the local optimization extension strategy connects the extension process from the initial state point to the terminal state point to form a path, obtaining the attitude maneuver path, three-node motion trajectory, and control thrust that satisfy the pointing constraints, bounded constraints, and dynamic constraints. Based on this, a smooth and non-backflipping attitude maneuver to the target attitude is ensured under multiple constraints, enabling smooth and stable attitude maneuvers for flexible probes. This facilitates flexible attachment of asteroid probes and improves the stability and reliability of attitude maneuvers for flexible asteroid attachment.

[0011] The target guidance attitude planning method for a three-node flexible probe attached to an asteroid disclosed in this invention includes the following steps:

[0012] Step 1: Based on the three-node structure and motion characteristics of the flexible body, the flexible three-node detector model is simplified into a three-node-connecting beam system. This model can characterize the influence of flexible connections and deformation on the internal forces of the three nodes, establishing the deformation and internal force equations for the flexible three nodes. Based on these equations, using the relative displacement and deformation between nodes as input, the internal forces and moments between the nodes are calculated, facilitating the dynamic modeling of the flexible detector in Step 2.

[0013] Based on the three-node structure and motion characteristics of the flexible body, the deformation and internal force equations of the flexible three-node system are established. The flexible three-node detector model is simplified to a three-node-connecting beam system, that is, the flexible three-node detector model is simplified to three rigid body nodes connected in pairs by beam elements; the three nodes form the three vertices of an equilateral triangle with a side length of L0. The relative displacement and rotation between nodes are negligible quantities in spatial scale measurements, but are input quantities that need to be considered in mechanical analysis. The lumped mass method is used to equivalently concentrate the mass of the flexible surface on the nodes. The inertial coordinate system is {OXYZ}, the origin O is the center point of the equilateral triangle configuration when the flexible detector is not deformed, and the centroid of each node is O. i ,(i=1,2,3).

[0014] Define a beam element with length L, elastic modulus E, and shear modulus G. The equivalent cross-sectional area is A, moments of inertia are I and I', and polar moment of inertia is J. Let the two nodes of the beam element be j and k, and the nodal forces and moments be {F}. xj ,F yj ,F zj M xj M yj M zj ,F xk ,F yk ,F zk M xk M yk M zk}, the nodal displacements and nodal rotations are {u xj ,u yj ,u zj ,θ xj ,θ yj ,θ zj ,u xk ,u yk ,u zk ,θ xk ,θ yk ,θ zk The stiffness equation for the beam element is:

[0015]

[0016] In the formula: K ~ (L, E, G, A, I, I', J)

[0017] Establish three fixed connections {O} on the three nodes respectively. i X i Y i Z i The wavy line represents the reference value for the undeformed configuration. In the undeformed configuration, shaft and The shaft is located at In the plane, Shaft point to ( Shaft point to ), shaft edge The plane normal points upwards from the detector. The axes form a right-handed rectangular coordinate system.

[0018] {O i X i Y i Z i The direction cosine matrix relative to the inertial frame {OXYZ} is A. i When the detector deforms, the rigid body node j rotates. Rotate to {O i X i Y i Z i The direction cosine matrix of this rotation for

[0019]

[0020] In an inertial frame, the relative displacement of the nodes when the detector deforms.

[0021]

[0022] In the beam element jk between nodes j and k, the nodal displacements are:

[0023] u x1 (12) =u y1 (12) =u z1 (12) =u x1 (13) =u y1 (13) =u z1 (13) =0 (4)

[0024]

[0025]

[0026]

[0027]

[0028] Let u=[u x2 (12) u y2 (12)u z2 (12) θ x2 θ y2 θ z2 u x3 (13) u y3 (13) u z3 (13) θ x3 θ y3 θ z3 ] T In the formula θ xi θ yi θ zi Rigid body i around axis, axis, The amount of rotation of the axis. Coordinate system. In the diagram, the resultant internal forces and resultant internal moments acting on beams 12 and 13 at node 1 are:

[0029]

[0030] The resultant internal forces and resultant internal moments of beams 12 and 23 acting on node 2 are:

[0031]

[0032] The resultant internal forces and resultant internal moments of beams 13 and 23 acting on node 3 are:

[0033]

[0034] Equations (9)-(11) combined form the deformation and internal force equations of a flexible three-node system.

[0035]

[0036] In the formula, the unit of force is N, the unit of torque is N·mm, the unit of displacement is mm, and the unit of rotation angle is rad.

[0037] Step 2: Represent the detector's attitude by the angular relationship between the three-node planar fixed frame and the inertial frame. Establish a mapping relationship between the three-node positions and the overall planar attitude of the detector represented by quaternions. Use the three-node positions to describe the relative positions of the nodes and the overall attitude orientation of the flexible detector. Based on this mapping relationship, and combined with the flexible three-node deformation and internal force equations from Step 1, construct a nodal planar coupled dynamic model. This nodal planar coupled dynamic model enables the attitude description and dynamic constraint characterization of the flexible three-node detector, facilitating the planning and solution of attitude maneuvering paths, three-node motion trajectories, and control thrust in Step 3.

[0038] For flexible three-node detectors, describing the overall planar attitude of the detector using quaternions or other angular quantities presents the following problems:

[0039] 1) The attitude description using quaternions or other angular quantities requires that the control input be a force rectangle, while the equivalent torque of the three-node detector at the center of mass can only be generated by the thrust coupling produced by the three-node thrusters.

[0040] 2) During attitude maneuvers, the flexible body deforms as the relative positions of the nodes change, the position of the equivalent center of mass in the inertial frame and the overall rotational inertia change dynamically, and the overall attitude is affected by the flexible internal forces.

[0041] 3) The three-node detector uses three nodes as the control objects, and quaternions or other angular quantities cannot describe the movement law of the nodes.

[0042] The overall planar attitude of the detector is described using three-node positions instead of quaternions or angle quantities. The positions (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) of the three nodes in the inertial frame represent the fixed system {O} established based on the plane composed of the three nodes. b X b Y b Z b The orientation of}. Fixed connection to the origin O. b Coinciding with the origin of the inertial frame, X b axis and Y b The axis lies in the O1O2O3 plane, X b The axis is O b Pointing to O1, Z b The axis points upwards along the normal of the O1O2O3 plane, Y b Axis and X b Z b This forms a right-handed rectangular coordinate system.

[0043] The mapping relationship between the three node positions of the detector (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) and the overall planar attitude of the detector represented by quaternions is as follows:

[0044]

[0045] Where φ, θ, and ψ are the Euler angles of the direction cosine matrices of the planar fixed frame and the inertial frame. Through the mapping from the three-node positions to quaternions, the terminal constraint of the target attitude pointing in the detector's attitude maneuver mission can be represented by the target positions of the three nodes. The quaternions can be converted into Euler angles, plane normal vector pointing, and azimuth-elevation angles.

[0046] Based on the mapping relationship between the three nodes of the detector and the overall planar attitude of the detector represented by quaternions, and combined with the flexible three-node deformation and internal force equations of equation (12), the nodal planar coupled dynamic model is constructed as follows:

[0047]

[0048] In the formula, ω a Let U be the angular velocity of the asteroid to which the probe is attached, U be the gravitational potential of the probe in the asteroid's vicinity, T be the thrust of the node thruster, and iF be the net internal force on the node.

[0049] Step 3: Based on the RRT algorithm, an improved local optimization expansion strategy is constructed. In this strategy, the terminal state corresponding to the target attitude is set as the target state point, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path. With shortening the distance to the target attitude as the optimization objective, the nodal-plane coupled dynamics model constructed in Step 2 is used as a linear constraint in the quadratic programming problem. Solving this problem ensures that the pointing constraint, bounded constraints of control force and angular velocity, and nodal-plane coupled dynamics constraints are simultaneously satisfied during the attitude maneuver. Using this local optimization expansion strategy, new state points are sampled within a single time step neighborhood of the state point to be expanded, thus incrementally expanding within the safe space of the bounded constraints of control force and angular velocity. Through the improved RRT algorithm based on this local optimization expansion strategy, the expansion process from the initial state point to the terminal state point is connected to form a path, resulting in an attitude maneuver path, three-node motion trajectory, and control thrust that satisfy the pointing constraint, bounded constraints, and dynamic constraints, ensuring smooth and backtrack-free attitude maneuvering to the target attitude under multiple constraints.

[0050] The basic RRT algorithm is implemented as follows: The RRT algorithm is a fast random tree search algorithm, the purpose of which is to quickly plan the attitude maneuver path from the initial state to the terminal state. Starting with the state vector x_init composed of the initial three node positions, velocity, and thrust, a state point x_random is randomly selected in the state space with a certain probability. From all the current state points in the attitude path tree, the state point closest to x_random is selected, called the nearest state point x_near. Then, a step distance is extended from x_near towards x_random to obtain a new state point x_new. During the extension process, it is determined whether there is a conflict with the attitude pointing constraint. If there is no conflict, the new state point x_new is accepted and added to the attitude path tree. If x_new conflicts with the attitude pointing constraint, it means that the newly extended state point does not meet the safety requirements, so the new state point is discarded, and the random extension target state point x_random is selected again. Through the continuous extension and expansion described above, when the state point in the attitude path tree is close enough to the terminal state, the extension of the attitude path tree stops. At this point, starting from the state point closest to the terminal state, the parent state point is searched upwards in sequence, and a feasible attitude maneuver path from the initial state to the terminal state can be obtained.

[0051] Attitude maneuver planning involves planning the control variables (three-node thrust), three-node velocity, and a state vector sequence representing the attitude maneuver path, consisting of the three-node positions. The state space is chosen as follows: Attitude dynamics and kinematics determine the relationship from step k to step (k+1) in the state space. The continuous states in the state space are discretized into state points, and adjacent points satisfy nodal-planar coupled dynamic constraints. These nodal-planar coupled dynamic constraints are represented using the first-order Euler method.

[0052] r(k+1)=r(k)+ΔT·v(k+1) (15)

[0053]

[0054] Integrating equation (15), we obtain the constraint equation:

[0055] DX = G (16)

[0056] Among them, from equation (14):

[0057] X = [u T (k+1),v T (k+1),r T (k+1)] T

[0058]

[0059]

[0060] Based on the RRT algorithm, a local optimization expansion strategy is constructed: the terminal state corresponding to the target attitude is set as a randomly expanded target state point x_random, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path; with shortening the distance to the target attitude as the optimization objective, the nodal-plane coupled dynamics model constructed in step 2 is used as a linear constraint in the quadratic programming problem to construct a quadratic programming problem. By solving the quadratic programming problem, the pointing constraint, the bounded constraints of control force and angular velocity, and the nodal-plane coupled dynamics constraints during the target attitude maneuver are simultaneously satisfied. With the above local optimization expansion strategy, new state points are sampled in the single time step neighborhood of the state point to be expanded, thereby incrementally expanding within the safe space of the bounded constraints of control force and angular velocity, obtaining a feasible attitude maneuvering path from the initial state to the terminal state.

[0061] The specific algorithm of the improved RRT algorithm based on the local optimization expansion strategy is as follows:

[0062] ① Generate a state space, including the initial state x_init, the terminal state x_goal, and the attitude pointing constraint region X_obs. Let the initial state point Tr(0) of the attitude path tree be x_init.

[0063] ② Set x_random = x_goal. For x_random, find the nearest x_near on the pose path tree as the neighboring state point. To find the neighboring state point, the following evaluation function is introduced to represent the distance from the state point to the terminal state corresponding to the target pose:

[0064]

[0065] Where a and b are positive definite matrices. This indicates the deviation between the current position and the target position. This indicates the deviation between the current speed and the target speed.

[0066] The nearest state point x_near is obtained from equation (17), and x_near is taken as the current extended state point X(k).

[0067] ③ Design control objectives,

[0068]

[0069] Where, r e (k+1) and v e (k+1) represent the position deviation and velocity deviation for steps k+1, respectively, and can be expressed as:

[0070]

[0071] Where, r random and v random To randomly expand the position and velocity vectors corresponding to the target state points, in the local optimization expansion strategy, i.e., r goal and v goal .

[0072] If the velocity at the terminal state is set to zero, then the final linearly constrained quadratic programming expression is:

[0073] J(k+1)=X T MX+f T X (20)

[0074] stDX=G

[0075] |u i |≤γ T i = 1, 2, ..., 9

[0076] |v i |≤γ v i = 1, 2, ..., 9

[0077] in, DX = G represents the nodal planar coupling dynamic constraint, and the inequality constraint includes directional constraints and bounded constraints.

[0078] By solving the above quadratic programming problem, the next state point X(k+1) can be obtained from the current state X(k), denoted as x_new.

[0079] ④ Based on the formula and whether x_new satisfies the evaluation function that is less than x_near, if it does, assign the value of x_new to the attitude path tree Tr(i); if it does not, return to step ③.

[0080] ⑤ Check if Tr(i) has reached the terminal state. If not, let k = k + 1 and return to step ②; if it has reached the terminal state, stop the search.

[0081] Step 4: Based on Step 3, plan the attitude maneuver path, three-node motion trajectory and control thrust that meet the constraints, and ensure that the attitude maneuver is smooth and without backflip under the pointing constraint to reach the target attitude, so as to realize the smooth and stable attitude maneuver of the flexible probe, realize the flexible attachment of the asteroid probe, and improve the stability and reliability of the attitude maneuver of the flexible attachment of the asteroid.

[0082] Beneficial effects:

[0083] 1. The target guidance attitude planning method for a three-node flexible probe attached to an asteroid disclosed in this invention simplifies the model of the flexible three-node probe into a three-node-connecting beam system based on the structure and motion characteristics of the flexible body three-node system. It characterizes the influence of flexible connection and deformation on the internal forces of the three nodes, establishes the deformation and internal force equations of the flexible three nodes, and calculates the internal forces and internal moments between the nodes by taking the relative motion displacement and deformation between the nodes as input. This facilitates the dynamic modeling of the flexible probe and, in turn, facilitates the subsequent steps to realize the target guidance attitude planning of the three-node flexible probe attached to an asteroid.

[0084] 2. The asteroid-attached three-node flexible probe target guidance attitude planning method disclosed in this invention represents the probe's attitude through the angular relationship between the three-node planar fixed frame and the inertial frame. It establishes a mapping relationship from the three-node positions to the overall planar attitude of the probe represented by quaternions, and uses the three-node positions to describe the relative positions of the nodes and the overall attitude pointing of the flexible probe. Based on the mapping relationship, combined with the deformation and internal force equations of the flexible three nodes, a nodal planar coupled dynamic model is constructed to achieve attitude description and dynamic constraint characterization of the flexible three-node probe, facilitating the planning and solution of attitude maneuver paths, three-node motion trajectories, and control thrust.

[0085] 3. The target-guided attitude planning method for a three-node flexible asteroid-attached probe disclosed in this invention improves the RRT algorithm by constructing a local optimization extension strategy. In the local optimization extension strategy, the terminal state corresponding to the target attitude is set as the extended target state point, enhancing the purposefulness of maneuvering along the attitude path. With shortening the distance to the target attitude as the optimization objective, a quadratic programming problem is constructed using a nodal plane coupled dynamics model. Solving the quadratic programming problem ensures that the pointing constraint, control force, and bounded angular velocity constraints, as well as the nodal plane coupled dynamics constraints, are simultaneously satisfied during the attitude maneuvering process. Through the improved RRT algorithm based on the local optimization extension strategy, the extension process from the initial state point to the terminal state point is connected to form a path, resulting in an attitude maneuvering path, three-node motion trajectory, and control thrust that satisfy the pointing constraint, bounded constraint, and dynamics constraints.

[0086] 4. The target guidance attitude planning method for a three-node flexible probe for asteroid attachment disclosed in this invention, on the basis of achieving the above-mentioned beneficial effects 1, 2, and 3, ensures that the attitude maneuver is smooth and without backflipping to the target attitude under the pointing constraint, and can realize the smooth and stable attitude maneuver of the flexible probe for flexible attachment of asteroid probe, thereby improving the stability and reliability of the attitude maneuver of flexible attachment of asteroid. Attached Figure Description

[0087] Figure 1 This is a flowchart of the target guidance attitude planning method for a three-node flexible probe attached to an asteroid, as disclosed in this invention.

[0088] Figure 2 It is a simplified model of a flexible body and a fixed connection between nodes;

[0089] Figure 3 It is the attitude maneuver path of the probe in the celestial coordinate system;

[0090] Figure 4 It is a three-node motion trajectory in an inertial coordinate system;

[0091] Figure 5 shows the position change of the center of mass in the translational frame during attitude maneuvering. Figure 5a The curve shows the change of the centroid coordinates over time. Figure 5b This represents the trajectory of the center of mass's position change in space.

[0092] Figure 6 It is a three-node position time curve;

[0093] Figure 7 It is a three-node velocity-time curve;

[0094] Figure 8 It is a three-node thrust-time curve;

[0095] Figure 9 It is a three-node internal force time curve;

[0096] Figure 10 It is the distance-time curve from the target's attitude position. Detailed Implementation

[0097] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0098] like Figure 1 As shown in this embodiment, the target guidance attitude planning method for a three-node flexible probe attached to an asteroid is implemented in the following specific steps:

[0099] Step 1: Based on the three-node structure and motion characteristics of the flexible body, the flexible three-node detector model is simplified into a three-node-connecting beam system. This model can characterize the influence of flexible connections and deformation on the internal forces of the three nodes, establishing the deformation and internal force equations for the flexible three nodes. Based on these equations, using the relative displacement and deformation between nodes as input, the internal forces and moments between the nodes are calculated, facilitating the dynamic modeling of the flexible detector in Step 2.

[0100] Based on the three-node structure and motion characteristics of the flexible body, the deformation and internal force equations of the flexible three-node system are established. The flexible three-node detector model is simplified to a three-node-connecting beam system, that is, the flexible three-node detector model is simplified to three rigid body nodes connected in pairs by beam elements; the three nodes form the three vertices of an equilateral triangle with a side length of L0. The relative displacement and rotation between nodes are negligible quantities in spatial scale measurements, but are input quantities that need to be considered in mechanical analysis. The lumped mass method is used to equivalently concentrate the mass of the flexible surface on the nodes. The inertial coordinate system is {OXYZ}, the origin O is the center point of the equilateral triangle configuration when the flexible detector is not deformed, and the centroid of each node is O. i ,(i=1,2,3).

[0101] Establish three fixed connections {O} on the three nodes respectively. i X i Y i Z i The wavy line represents the reference value for the undeformed configuration. In the undeformed configuration, shaft and The shaft is located at In the plane, Shaft point to ( Shaft point to ), shaft edge The plane normal points upwards from the detector. The axes form a right-handed rectangular coordinate system.

[0102] According to the invention, there are flexible three-node deformation and internal force equations.

[0103]

[0104] In the formula, the unit of force is N, the unit of torque is N·mm, the unit of displacement is mm, and the unit of rotation angle is rad.

[0105] Consider a detector with a disk-shaped flexible surface. The center of the three nodes is 0.6m away from the center of the disk. The Young's modulus of the flexible surface is E = 2MPa and the Poisson's ratio is μ = 0.4.

[0106] Assume the equivalent cross-section of the beam element is rectangular, with a length of... The width is bb = 1m, and the thickness is hh = 0.02m. The relevant parameters are as follows:

[0107]

[0108]

[0109]

[0110] Step 2: Represent the detector's attitude by the angular relationship between the three-node planar fixed frame and the inertial frame. Establish a mapping relationship between the three-node positions and the overall planar attitude of the detector represented by quaternions. Use the three-node positions to describe the relative positions of the nodes and the overall attitude orientation of the flexible detector. Based on this mapping relationship, and combined with the flexible three-node deformation and internal force equations from Step 1, construct a nodal planar coupled dynamic model. This nodal planar coupled dynamic model enables the attitude description and dynamic constraint characterization of the flexible three-node detector, facilitating the planning and solution of attitude maneuvering paths, three-node motion trajectories, and control thrust in Step 3.

[0111] The overall planar attitude of the detector is described using three-node positions instead of quaternions or angle quantities. The positions (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) of the three nodes in the inertial frame represent the fixed system {O} established based on the plane composed of the three nodes. b X b Y b Z b The orientation of}. Fixed connection to the origin O. b Coinciding with the origin of the inertial frame, X b axis and Y b The axis lies in the O1O2O3 plane, X b The axis is O b Pointing to O1, Z b The axis points upwards along the normal of the O1O2O3 plane, Y b Axis and X b Z b This forms a right-handed rectangular coordinate system.

[0112] The mapping relationship between the three node positions of the detector (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) and the overall planar attitude of the detector represented by quaternions is as follows:

[0113]

[0114] Where φ, θ, and ψ are the Euler angles of the direction cosine matrices of the planar fixed frame and the inertial frame. Through the mapping from the three-node positions to quaternions, the terminal constraint of the target attitude pointing in the detector's attitude maneuver mission can be represented by the target positions of the three nodes. The quaternions can be converted into Euler angles, plane normal vector pointing, and azimuth-elevation angles.

[0115] Based on the mapping relationship between the three nodes of the detector and the overall planar attitude of the detector represented by quaternions, and combined with the flexible three-node deformation and internal force equations of equation (21), the nodal planar coupled dynamic model is constructed as follows:

[0116]

[0117] In the formula, ω a Let U be the angular velocity of the asteroid to which the probe is attached, U be the gravitational potential of the probe in the asteroid's vicinity, T be the thrust of the node thruster, and iF be the net internal force on the node.

[0118] In the simulation example, an optical sensor is installed on the detector along the z-axis, and its unit direction vector is represented by r. B This indicates that it is necessary to avoid two bright celestial bodies during attitude maneuvers, and the unit direction vector in this system is represented by r. I1 ,r I2 This indicates that r is required. B With r I1 ,r I2 The minimum included angles between them are θ1 and θ2; the initial attitude (position) and velocity of the detector are r0 and v0, respectively, and the attitude (azimuth-elevation) and velocity of the target are [az]. f ,el f ],v f The node has a mass of m and a maximum speed amplitude of γ. v The maximum amplitude of the control force is γ T The specific values ​​are shown in Table 1.

[0119] Table 1 Simulation conditions

[0120]

[0121] Step 3: Based on the RRT algorithm, an improved local optimization expansion strategy is constructed. In this strategy, the terminal state corresponding to the target attitude is set as the target state point, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path. With shortening the distance to the target attitude as the optimization objective, the nodal-plane coupled dynamics model constructed in Step 2 is used as a linear constraint in the quadratic programming problem. Solving this problem ensures that the pointing constraint, bounded constraints of control force and angular velocity, and nodal-plane coupled dynamics constraints are simultaneously satisfied during the attitude maneuver. Using this local optimization expansion strategy, new state points are sampled within a single time step neighborhood of the state point to be expanded, thus incrementally expanding within the safe space of the bounded constraints of control force and angular velocity. Through the improved RRT algorithm based on this local optimization expansion strategy, the expansion process from the initial state point to the terminal state point is connected to form a path, resulting in an attitude maneuver path, three-node motion trajectory, and control thrust that satisfy the pointing constraint, bounded constraints, and dynamic constraints, ensuring smooth and backtrack-free attitude maneuvering to the target attitude under multiple constraints.

[0122] Attitude maneuver planning involves planning the control variables (three-node thrust), three-node velocity, and a state vector sequence representing the attitude maneuver path, consisting of the three-node positions. The state space is chosen as follows: Attitude dynamics and kinematics determine the relationship from step k to step (k+1) in the state space. The continuous states in the state space are discretized into state points, and adjacent points satisfy nodal-planar coupled dynamic constraints. These nodal-planar coupled dynamic constraints are represented using the first-order Euler method.

[0123] r(k+1)=r(k)+ΔT·v(k+1) (27)

[0124]

[0125] Integrating equation (27), we obtain the constraint equation:

[0126] DX = G (28)

[0127] Among them, from equation (26):

[0128] X = [u T (k+1),v T (k+1),r T (k+1)] T

[0129]

[0130]

[0131] Based on the RRT algorithm, a local optimization expansion strategy is constructed: the terminal state corresponding to the target attitude is set as a randomly expanded target state point x_random, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path; with shortening the distance to the target attitude as the optimization objective, the nodal-plane coupled dynamics model constructed in step 2 is used as a linear constraint in the quadratic programming problem to construct a quadratic programming problem. By solving the quadratic programming problem, the pointing constraint, the bounded constraints of control force and angular velocity, and the nodal-plane coupled dynamics constraints during the target attitude maneuver are simultaneously satisfied. Using the above local optimization expansion strategy, new state points are sampled within a single time step neighborhood of the state point to be expanded, thereby incrementally expanding within the safe space of the bounded constraints of control force and angular velocity, obtaining a feasible attitude maneuver path from the initial state to the terminal state.

[0132] The specific algorithm flow of the improved RRT algorithm based on the local optimization expansion strategy described above is as follows:

[0133] ② Generate a state space, including the initial state x_init, the terminal state x_goal, and the attitude pointing constraint region X_obs. Let the initial state point Tr(0) of the attitude path tree be x_init.

[0134] ② Set x_random = x_goal. For x_random, find the nearest x_near on the pose path tree as the neighboring state point. To find the neighboring state point, the following evaluation function is introduced to represent the distance from the state point to the terminal state corresponding to the target pose:

[0135]

[0136] Where a and b are positive definite matrices. This indicates the deviation between the current position and the target position. This indicates the deviation between the current speed and the target speed.

[0137] The nearest state point x_near is obtained from equation (29), and x_near is taken as the current extended state point X(k).

[0138] ③ Design control objectives,

[0139]

[0140] Where, r e (k+1) and v e (k+1) represent the position deviation and velocity deviation for steps k+1, respectively, and can be expressed as:

[0141]

[0142] Where, r random and v random To randomly expand the position and velocity vectors corresponding to the target state points, in the local optimization expansion strategy, i.e., r goal and v goal .

[0143] If the velocity at the terminal state is set to zero, then the final linearly constrained quadratic programming expression is:

[0144] J(k+1)=X T MX+f T X (32)

[0145] stDX=G

[0146] |u i |≤γ T i = 1, 2, ..., 9

[0147] |v i |≤γ vi = 1, 2, ..., 9

[0148] in, DX = G represents the nodal planar coupling dynamic constraint, and the inequality constraint includes directional constraints and bounded constraints.

[0149] By solving the above quadratic programming problem, the next state point X(k+1) can be obtained from the current state X(k), denoted as x_new.

[0150] ④ Based on the formula and whether x_new satisfies the evaluation function that is less than x_near, if it does, assign the value of x_new to the attitude path tree Tr(i); if it does not, return to step ③.

[0151] ⑤ Check if Tr(i) has reached the terminal state. If not, let k = k + 1 and return to step ②; if it has reached the terminal state, stop the search.

[0152] The simulation environment was Matlab 2020a, with a computer CPU clock speed of 3.6 GHz and 8 GB of memory. A target-oriented locally extended attitude planning method was used to simulate and solve the problem. Figure 3 The diagram shows the probe's attitude maneuver path in the celestial coordinate system, with the circular areas representing taboo constraints. It can be seen that the infrared telescope successfully avoided brightly lit objects during the maneuver, and the maneuver path was safe. Figure 4 This represents the trajectory of three nodes in an inertial coordinate system, where the node motion exhibits rotation. Figure 5a and Figure 5b This indicates the change in the position of the center of mass in the translational frame during the attitude maneuver. The center of mass basically returns to its original position after the attitude maneuver is completed, and the attitude maneuver has little impact on the overall trajectory.

[0153] Figure 6-9 The diagram shows the time histories of the probe's three-node positions, velocities, thrust, and internal forces during its attitude maneuver. It can be seen that both velocity and thrust (control force) satisfy bounded constraints.

[0154] The distance to the target's attitude position is defined using the following formula:

[0155]

[0156] In the formula: a = 100, b = 5.

[0157] Figure 10 The changes in the distance from the target during attitude maneuvers are demonstrated, and it can be determined that a back-wrap situation occurs during attitude maneuvers without quaternion description.

[0158] In summary, in the target guidance attitude planning method for the three-node flexible probe attached to an asteroid in this invention, the improved RRT algorithm based on the local optimization extension strategy proves through simulation results that the algorithm can guarantee the satisfaction of pointing constraints, bounded constraints, and dynamic constraints. Given the initial and final attitudes, it can plan and generate attitude maneuver paths, three-node motion trajectories, and control thrust, thus meeting the attitude maneuver mission requirements of the three-node probe in the asteroid flexible attachment mission.

[0159] Step 4: Verify the completion of the planning and generation of the attitude maneuver path, three-node motion trajectory and control thrust that meet the constraints, to ensure that the attitude maneuver is smooth and without backflip under the pointing constraint, to achieve smooth and stable attitude maneuver of the flexible probe, to realize the flexible attachment of the asteroid probe, and to improve the stability and reliability of the attitude maneuver of the asteroid flexible attachment.

[0160] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A target guidance attitude planning method for a three-node flexible probe attached to an asteroid, characterized in that: Includes the following steps, Step 1: Based on the three-node structure and motion characteristics of the flexible body, the flexible three-node detector model is simplified into a three-node-connecting beam system. The influence of flexible connection and deformation on the internal forces of the three nodes is characterized by the three-node-connecting beam system model, and the deformation and internal force equations of the flexible three nodes are established. Based on the deformation and internal force equations of flexible three nodes, the internal forces and internal moments between nodes are calculated by taking the relative motion displacement and deformation between nodes as inputs. Step 2: Represent the detector's attitude by the angular relationship between the three-node planar fixed system and the inertial frame, establish a mapping relationship from the three-node positions to the overall planar attitude of the detector represented by quaternions, and use the three-node positions to describe the relative positions of the nodes and the overall attitude orientation of the flexible detector; based on the mapping relationship, and combined with the flexible three-node deformation and internal force equations from Step 1, construct a nodal planar coupled dynamic model; realize the attitude description and dynamic constraint characterization of the flexible three-node detector through the nodal planar coupled dynamic model; Step 3: Based on the RRT algorithm, the RRT algorithm is improved by constructing a local optimization expansion strategy. In the local optimization expansion strategy, the terminal state corresponding to the target attitude is set as the target state point, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path. With shortening the distance to the target attitude as the optimization objective, the nodal-plane coupled dynamics model constructed in Step 2 is used as the linear constraint in the quadratic programming problem to construct a quadratic programming problem. By solving the quadratic programming problem, the pointing constraint, the bounded constraints of control force and angular velocity, and the nodal-plane coupled dynamics constraints during the attitude maneuver are simultaneously satisfied. With the above local optimization expansion strategy, new state points are sampled in the single time step neighborhood of the state point to be expanded, thereby incrementally expanding within the safe space of the bounded constraints of control force and angular velocity. By using the improved RRT algorithm based on the local optimization expansion strategy, the expansion process from the initial state point to the terminal state point is connected to form a path, thereby obtaining the attitude maneuver path, three-node motion trajectory and control thrust that satisfy the pointing constraint, bounded constraint and dynamic constraint, ensuring that the attitude maneuver is smooth and reaches the target attitude without backspinning under multiple constraints. Step 4: Based on Step 3, plan the attitude maneuver path, three-node motion trajectory and control thrust that meet the constraints, and ensure that the attitude maneuver is smooth and without backflip under the pointing constraint to reach the target attitude, so as to realize the smooth and stable attitude maneuver of the flexible probe, realize the flexible attachment of the asteroid probe, and improve the stability and reliability of the attitude maneuver of the flexible attachment of the asteroid.

2. The target guidance attitude planning method for a three-node flexible asteroid-attached probe as described in claim 1, characterized in that: Step 1 is implemented as follows: Based on the three-node structure and motion characteristics of the flexible body, the deformation and internal force equations of the flexible three-node are established. The flexible three-node detector model is simplified into a three-node-connecting beam system, that is, the following simplification is made: the flexible three-node detector model is simplified into 3 rigid body nodes connected in pairs by beam elements; the 3 nodes form the three vertices of an equilateral triangle with a side length of L0. The relative displacements and rotations between nodes are negligible in spatial scale measurements but are input quantities that need to be considered in mechanical analysis. The lumped mass method is used to equivalently concentrate the mass of the flexible surface onto the nodes. The inertial coordinate system is {OXYZ}, with the origin O being the center point of the equilateral triangle configuration when the flexible detector is not deformed, and the centroid of each rigid body node is O. i i = 1, 2, 3; Define a beam element with length L, elastic modulus E, and shear modulus G; equivalent cross-sectional area A, moments of inertia I and I', and polar moment of inertia J; and two nodes j and k, with nodal forces and moments {F}. xj ,F yj ,F zj M xj M yj M zj ,F xk ,F yk ,F zk M xk M yk M zk }, the nodal displacements and nodal rotations are {u xj ,u yj ,u zj ,θ xj ,θ yj ,θ zj ,u xk ,u yk ,u zk ,θ xk ,θ yk ,θ zk The stiffness equation of the beam element is: In the formula: K ~ (L, E, G, A, I, I', J) Establish three fixed connections {O} on the three nodes respectively. i X i Y i Z i The wavy line represents the reference value for the undeformed configuration. In the undeformed configuration, shaft and The shaft is located at In the plane, Shaft point to Shaft point to shaft edge The plane normal points upwards from the detector. The axes form a right-handed rectangular coordinate system; {O i X i Y i Z i The direction cosine matrix relative to the inertial frame {OXYZ} is A. i When the detector deforms, the rigid body node j rotates. Rotate to {O i X i Y i Z i The direction cosine matrix of this rotation for In an inertial frame, the relative displacement of the nodes when the detector deforms. In the beam element jk between nodes j and k, the nodal displacements are: in x1 (12) =in y1 (12) =in z1 (12) =in x1 (13) =in y1 (13) =in z1 (13) =0 (4) Let u=[u x2 (12) u y2 (12) u z2 (12) θ x2 θ y2 θ z2 u x3 (13) u y3 (13) u z3 (13) θ x3 θ y3 θ z3 ] T In the formula θ xi θ yi θ zi For each rigid body node i, the rest is about... axis, axis, Rotation of the axis; coordinate system In the diagram, the resultant internal forces and resultant internal moments acting on beams 12 and 13 at node 1 are: The resultant internal forces and resultant internal moments of beams 12 and 23 acting on node 2 are: The resultant internal forces and resultant internal moments of beams 13 and 23 acting on node 3 are: Equations (9)-(11) combined form the deformation and internal force equations of a flexible three-node system. In the formula, the unit of force is N, the unit of torque is N·mm, the unit of displacement is mm, and the unit of rotation angle is rad.

3. The target guidance attitude planning method for a three-node flexible asteroid attachment probe as described in claim 2, characterized in that: Step 2 is implemented as follows: For a flexible three-node detector, the overall planar attitude of the detector is described by quaternions or other angular quantities. The overall planar attitude of the detector is described using three-node positions instead of quaternions or angle quantities. The positions (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) of the three nodes in the inertial frame represent the fixed system {O} established based on the plane composed of the three nodes. b X b Y b Z b The orientation of the}; fixed connection to the origin O b Coinciding with the origin of the inertial frame, X b axis and Y b The axis lies in the O1O2O3 plane, X b The axis is O b Pointing to O1, Z b The axis points upwards along the normal of the O1O2O3 plane, Y b Axis and X b Z b Construct a right-handed rectangular coordinate system; The mapping relationship between the three node positions of the detector (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) and the overall planar attitude of the detector represented by quaternions is as follows: Where φ, θ, and ψ are the Euler angles of the direction cosine matrices of the planar fixed frame and the inertial frame; through the mapping from the three-node positions to quaternions, the terminal constraint of the target attitude pointing of the detector attitude maneuver mission can be represented by the target positions of the three nodes; the quaternions can be converted into Euler angles, plane normal vector pointing, and azimuth-elevation angles. Based on the mapping relationship between the three nodes of the detector and the overall planar attitude of the detector represented by quaternions, and combined with the flexible three-node deformation and internal force equations of equation (12), the nodal planar coupled dynamic model is constructed as follows: In the formula, ω a Let U be the angular velocity of the asteroid to which the probe is attached, U be the gravitational potential of the probe in the asteroid's vicinity, T be the thrust of the node thruster, and iF be the net internal force on the node.

4. The target guidance attitude planning method for a three-node flexible asteroid-attached probe as described in claim 3, characterized in that: Step 3 is implemented as follows: The RRT algorithm is implemented as follows: The RRT algorithm is a fast random tree search algorithm, the purpose of which is to quickly plan the attitude maneuver path from the initial state to the terminal state. Starting with the state vector x_init composed of the initial three node positions, velocities, and thrust, a state point x_random is randomly selected in the state space with a certain probability. From all the current state points in the attitude path tree, the state point closest to x_random is selected, called the nearest state point x_near. Then, a step distance is extended from x_near towards x_random to obtain a new state point x_new. During the extension process, a decision is made... If there is no conflict with the attitude pointing constraint, the new state point x_new is accepted and added to the attitude path tree. If x_new conflicts with the attitude pointing constraint, it means that the new state point does not meet the safety requirements. The new state point is then discarded, and the target state point x_random is randomly selected again. Through the above continuous extension, when the state point in the attitude path tree is close enough to the terminal state, the extension of the attitude path tree is stopped. At this time, starting from the state point closest to the terminal state, the parent state point is searched upwards in sequence to obtain a feasible attitude maneuver path from the initial state to the terminal state. Attitude maneuver planning involves planning the control variables, three-node velocities, and a state vector sequence representing the attitude maneuver path, consisting of the three-node positions. The state space is selected as follows: Attitude dynamics and kinematics determine the relationship from step k to step (k+1) in the state space. The continuous state in the state space is discretized into state points, and adjacent points satisfy nodal-plane coupling dynamic constraints. The nodal-plane coupling dynamic constraints are represented by the first-order Euler method. r(k+1)=r(k)+ΔT·v(k+1) (15) Integrating equation (15), we obtain the constraint equation: DX = G (16) Among them, from equation (14): X(k+1)=[u T (k+1),v T (k+1),r T (k+1)] T Based on the RRT algorithm, a local optimization expansion strategy is constructed: the terminal state corresponding to the target attitude is set as a randomly expanded target state point x_random, and the point closest to the target state point is selected as the state point to be expanded, enhancing the purposefulness of maneuvering along the attitude path; with the goal of shortening the distance to the target attitude, the nodal-plane coupled dynamics model constructed in step 2 is used as a linear constraint in the quadratic programming problem to construct a quadratic programming problem. By solving the quadratic programming problem, the pointing constraint, the bounded constraints of control force and angular velocity, and the nodal-plane coupled dynamics constraints in the target attitude maneuvering process are simultaneously satisfied; with the above local optimization expansion strategy, new state points are sampled in the single time step neighborhood of the state point to be expanded, thereby incrementally expanding within the safe space of the bounded constraints of control force and angular velocity, and obtaining a feasible attitude maneuvering path from the initial state to the terminal state.

5. The target guidance attitude planning method for a three-node flexible probe attached to an asteroid as described in claim 4, characterized in that: The specific algorithm of the improved RRT algorithm based on the local optimization expansion strategy is as follows: ① Generate a state space, including the initial state x_init, the terminal state x_goal, and the attitude pointing constraint region X_obs. Let the initial state point Tr(0) of the attitude path tree be x_init. ② Set x_random = x_goal. For x_random, find the nearest x_near on the pose path tree as the neighboring state point. To find the neighboring state point, the following evaluation function is introduced to represent the distance from the state point to the terminal state corresponding to the target pose: Where a and b are positive definite matrices. This indicates the deviation between the current position and the target position. This indicates the deviation between the current speed and the target speed; The nearest state point x_near is obtained from equation (17), and x_near is taken as the current extended state point X(k). ③ Design control objectives, Where, r e (k+1) and v e (k+1) represent the position deviation and velocity deviation for steps k+1, respectively, and can be expressed as: Where, r random and v random To randomly expand the position and velocity vectors corresponding to the target state points, in the local optimization expansion strategy, i.e., r goal and v goal ; If the velocity at the terminal state is set to zero, then the final linearly constrained quadratic programming expression is: J(k+1)=X T MX+f T X (20) stDX=G |in i |≤γ T ,i=1,2,...,9 |v i |≤γ v ,i=1,2,...,9 in, DX = G represents the nodal planar coupling dynamic constraint, and the inequality constraint includes directional constraints and bounded constraints; By solving the above quadratic programming problem, the next state point X(k+1) can be obtained from the current state X(k), denoted as x_new; ④ Based on the formula and whether x_new satisfies the evaluation function that is less than x_near, if it does, assign the value of x_new to the attitude path tree Tr(i); if it does not, return to step ③. ⑤ Check if Tr(i) has reached the terminal state. If not, let k = k + 1 and return to step ②; if it has reached the terminal state, stop the search.

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