Satellite Attitude Pointing Adjustment Method Based on Multi-Body Momentum Transfer

Abstract

The present invention discloses a satellite attitude pointing adjustment method based on multi-body momentum moment transfer, which includes calculating an attitude error value according to a target attitude angle and an initial attitude angle of satellite rotation; calculating an angular acceleration of rotation based on the attitude error value; solving for the angular acceleration of rotation of the satellite body based on the attitude dynamics equation of momentum moment; updating the angular velocity of rotation of the satellite body and the angular velocity of rotation and the rotation angle of the end rod of the robotic arm; determining whether the rotation angle satisfies the joint angle range constraint condition, and if so, proceeding to the next step, otherwise terminating the algorithm; updating the real part and the imaginary part of the quaternion, then calculating three components of the attitude angle of satellite rotation, then calculating the attitude angle of satellite rotation, and then calculating the attitude error value between the attitude angle of satellite rotation and the target attitude angle; and finally determining whether the attitude error value is less than a preset threshold, and if so, performing attitude pointing adjustment according to the three components, otherwise returning to the step of calculating the angular acceleration of rotation.

Description

Technical Field

[0001] The present invention relates to satellite attitude adjustment technology, and particularly to a satellite attitude pointing adjustment method based on multi-body momentum transfer. Background Art

[0002] Satellite attitude control has always been one of the core technologies for satellites to perform on-orbit service tasks. Existing attitude control actuators include reaction wheels, chemical thrusters, control moment gyroscopes (CMGs), and magnetometers, etc. The attitude control of a reaction wheel (the schematic diagram of a reaction wheel can be referred to Figure 1 ) conforms to the law of conservation of angular momentum, that is, the derivative of the angular momentum of a particle with respect to a fixed point in space with respect to time is equal to the moment of the acting force about the same point. The attitude of the satellite is stabilized and controlled by the exchange of angular momentum between the flywheel system and the small satellite body.

[0003] When an external disturbance torque Md acts on the satellite in space, in the space coordinate system, the system will generate a certain attitude angle deviation relative to the reference axis. The on-board attitude sensor measures the change in the attitude angle and transmits the deviation to the control system. The flywheel control system changes the angular velocity Ω of the flywheel rotation according to the pre-set control instructions, and then generates a control torque Mc corresponding to the disturbance torque, which can fully absorb the influence of the disturbance torque Md on the attitude of the satellite body, so as to correct the attitude deviation of the satellite body and stabilize the attitude angle, and eliminate the influence of the disturbance torque on the satellite body.

[0004] Disadvantages of reaction wheels: The flywheel control system has the problem of speed saturation. When the flywheel accelerates or deflects in a certain direction to overcome some non-periodic disturbances, it will eventually reach the maximum allowable rotational speed. In this extreme state, the flywheel will no longer be able to absorb the excess angular momentum of the spacecraft and lose its control ability. This state is called saturation, and saturation is a shortcoming that the flywheel system itself cannot overcome. Therefore, to avoid this situation, the flywheel system needs to be equipped with another system to perform desaturation, which means that the flywheel system cannot operate independently and must cooperate with a second control means. After the speed reaches the saturation state, the commonly used unloading method requires the use of fuel.

[0005] At present, most of the chemical thruster systems applied on spacecraft (the schematic diagram of a chemical thruster system can be referred to Figure 2 ) belong to active control, including types such as cold gas propulsion, chemical propulsion, electric propulsion, and new concept propulsion. The chemical thruster system obtains thrust by burning fuel in the combustion chamber to form high pressure and then converting it into high-speed gas flow. Similar to rockets, some use solid fuel, some use a single fuel such as hydrazine, and some use a combination of multiple fuels.

[0006] The chemical thrusters on the satellite generate thrust by burning propellants. According to Newton's third law, the ejected gas changes the attitude of the satellite under the action of the reaction force. The thrusters on the satellite are usually arranged at different positions or angles. The attitude control system controls the ejection time and direction of different thrusters according to the feedback of sensors, generates different torques, and realizes the adjustment of the satellite's attitude.

[0007] Disadvantages of chemical thrusters: First of all, chemical thrusters need to consume a large amount of fuel to generate thrust and torque, which may cause the problem of insufficient fuel for the satellite during long-term missions. Especially in deep space exploration or long-term operation missions, the consumption of fuel will limit the effective working time and operating ability of the satellite. Usually, spacecraft need to frequently adjust their attitudes, so the consumption of propellants is large, while the propellants carried by the spacecraft are limited, which requires regular rocket launches for replenishment, so the use cost of thrusters is high.

[0008] Secondly, the control accuracy of chemical thrusters is relatively low. Due to their relatively large thrust and difficult to accurately adjust, it is difficult to achieve very fine attitude adjustments, so it is not suitable for tasks that require high-precision control. Compared with other more precise attitude control methods, chemical thrusters have certain disadvantages in terms of accuracy and efficiency. These factors limit the application of chemical thrusters in some high-demand tasks, especially for satellite systems that require long-term stable operation and high-precision attitude adjustment. Summary of the Invention

[0009] Aiming at the above deficiencies in the prior art, the satellite attitude pointing adjustment method based on multi-body momentum moment transfer provided by the present invention solves the problem that the existing attitude control methods need to consume fuel when relying on devices such as fuel or flywheels for adjustment, resulting in a short in-orbit life of the satellite.

[0010] In order to achieve the above invention purpose, the technical solution adopted by the present invention is:

[0011] Provide a satellite attitude pointing adjustment method based on multi-body momentum moment transfer, which includes the steps of:

[0012] S1. Calculate the attitude error value according to the target attitude angle and the initial attitude angle of the satellite rotation;

[0013] S2. Based on the attitude error value, use PD feedback control to obtain the rotational angular acceleration of the end rod of the robotic arm;

[0014] S3. Substitute the rotational angular acceleration and angular velocity of the end rod of the robotic arm and the rotational angular velocity of the satellite body into the satellite's attitude dynamics equation based on momentum moment to solve for the rotational angular acceleration of the satellite body;

[0015] S4. Update the rotational angular velocity of the satellite body, as well as the rotational angular velocity and rotational angle of the end rod of the robotic arm, respectively, according to the rotational angular accelerations of the satellite body and the end rod of the robotic arm.

[0016] S5. Determine whether the rotational angle satisfies the constraint conditions of the joint angle range of motion. If so, proceed to step S6; otherwise, terminate the satellite attitude pointing adjustment method.

[0017] S6. Update the real part and imaginary part of the quaternion according to the angular velocity components of the rotational angular velocity of the satellite body on the xyz axes; calculate the three components of the attitude angle of the satellite rotation based on the updated real part and imaginary part.

[0018] S7. Calculate the attitude angle of the satellite rotation according to the three components, and calculate the attitude error value between the attitude angle of the satellite rotation and the target attitude angle.

[0019] S8. Determine whether the attitude error value is less than the preset threshold. If so, perform attitude pointing adjustment according to the three components; otherwise, return to step S2.

[0020] Further, the expression of the attitude dynamics equation of the satellite based on the angular momentum is:

[0021]

[0022] where J is the moment of inertia of the satellite body; is the rotational angular acceleration of the satellite body; ω bi is the rotational angular velocity of the satellite body; J w is the moment of inertia of the end rod of the robotic arm; ω w is the rotational angular velocity of the end rod of the robotic arm; T env is the environmental torque; is the rotational angular acceleration of the end rod of the robotic arm.

[0023] Further, the expressions for updating the rotational angular velocity of the satellite body, as well as the rotational angular velocity and rotational angle of the end rod of the robotic arm are:

[0024]

[0025]

[0026] φ w (t) = φ w (t - 1) + ω w Δt

[0027] where ω bi (t) and ω bi (t - 1) are the rotational angular velocities of the satellite body at time t and time t - 1, respectively; ω w (t) and ωw The angular velocities of the end link of the robotic arm at time t and at time t - 1 are ω(t) and ω(t - 1) respectively; φ w (t) and φ w (t - 1) are the rotation angles of the end link of the robotic arm at time t and at time t - 1 respectively; Δt is the discrete time step.

[0028] Further, step S6 further includes:

[0029] S61. Calculate the rates of change of the real part and the imaginary parts of the quaternion based on the angular velocity components of the satellite body on the x, y, and z axes:

[0030]

[0031] where q0(t - 1) is the real part of the quaternion at time t - 1; q1(t - 1), q2(t - 1), and q3(t - 1) are all the imaginary parts of the quaternion at time t - 1; and are the rates of change of the real part and the imaginary parts of the quaternion at time t respectively; ω x , ω y and ω z are the angular velocity components of ω bi on the x, y, and z axes respectively;

[0032] S62. Update the real number of the quaternion based on the rates of change of the real part and the imaginary parts of the quaternion:

[0033]

[0034] where the value of k is 0, 1, 2, and 3; when k = 0, q0(t) and q0(t - 1) are the real parts at time t and at time t - 1 respectively, is the rate of change of the real part at time t; when k = 1, 2, and 3, q k (t) and q k (t - 1) are the k-th imaginary parts at time t and at time t - 1 respectively, is the rate of change of the imaginary part at time t;

[0035] S63. Calculate the three components of the attitude angle of the satellite rotation based on the real part and the imaginary parts of the quaternion at time t:

[0036]

[0037] θ(t) = arcsin( - 2(q1(t)q3(t) - q0(t)q2(t)))

[0038]

[0039] where, θ(t) and ψ(t) are respectively the three components of the attitude angle of the satellite rotation at time t; q1(t), q2(t) and q3(t) are respectively the imaginary parts of the quaternions corresponding to k = 1, 2 and 3 at time t.

[0040] Furthermore, the method for obtaining the constraint conditions of the joint angle range of motion includes:

[0041] A1. Divide the manipulator of the satellite into a first-level manipulator and a second-level manipulator. The first-level manipulator is the manipulator between the satellite body and the end rod of the manipulator; the second-level manipulator is the end rod of the manipulator.

[0042] A2. According to the geometric model of the satellite, calculate the coordinates of the centroid position of the satellite body:

[0043]

[0044]

[0045]

[0046] where α is the rotation angle of the first-level manipulator relative to the satellite; r is the length of the first-level manipulator; L is the dimension length of the satellite body; η is the angle between the pointing vector of the first-level manipulator and the vector from the rotation axis to the centroid position; δ x , δ y is the uncertainty of the equivalent satellite body centroid position caused by the other two manipulators not in the same plane; (X0, Y0) is the centroid coordinate of the satellite body.

[0047] A3. Taking the joint rotation axis of the second-level manipulator as the center and the distance from the joint rotation axis of the second-level manipulator to the centroid of the second-level manipulator as the radius to draw a circle, and calculate the coordinates of the tangent points of the two rays passing through the centroid of the satellite body and the circle:

[0048]

[0049]

[0050]

[0051]

[0052] where d is the distance from the joint rotation axis of the second-level manipulator to the centroid of the second-level manipulator; (X1, Y1), (X2, Y2) are the coordinates of the two tangent points to the circle respectively.

[0053] A4. According to the coordinates of the two tangent points to the circle, calculate the lower limit and the upper limit of the rotation angle of the end rod of the manipulator:

[0054]

[0055] Among them, θ1 and θ2 are respectively the lower limit and the upper limit of the rotation angle of the end rod of the robotic arm;

[0056] A5. Use θ1 < φ w < θ2 as the constraint condition for the range of motion of the joint angle.

[0057] Furthermore, the expression for the rotational angular acceleration of the end rod of the robotic arm obtained by using PD feedback control is:

[0058]

[0059] Among them, is the rotational angular acceleration of the end rod of the robotic arm; K p is the proportional gain; K d is the derivative gain; e is the attitude error value; is the rate of change of the attitude error value.

[0060] Furthermore, the satellite body is a cube structure, and three space robotic arms are evenly and orthogonally distributed on the satellite body. The rotation axis of the end rod of each robotic arm corresponds one-to-one with the three rotational degrees of freedom of the satellite body, and the end axis of each robotic arm is parallel to the X, Y, and Z axes of the satellite respectively.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] Achieve zero-fuel-consumption high-precision attitude pointing adjustment: Through the robotic arm and the principle of momentum transfer, with the cooperation of information such as the rotational angular acceleration and rotational angular velocity of the robotic arm and the satellite body, the adjustment of the satellite attitude pointing can be achieved through the movement of the robotic arm, achieving high-precision attitude control without relying on fuel, and avoiding the problems of flywheel unloading and thruster fuel consumption in traditional attitude adjustment methods. The attitude adjustment is achieved through the movement of the robotic arm, greatly extending the on-orbit working life of the robotic satellite, and is particularly suitable for satellite application scenarios with long-term mission execution.

[0063] Propose a decoupled robotic arm layout design: By evenly combining space robotic arms on a cube satellite, a maximally decoupled design is formed, realizing a scheme that can achieve high-precision attitude adjustment control only relying on the end of the robotic arm. Description of the Drawings

[0064] Figure 1 It is the schematic diagram of the reaction wheel scheme.

[0065] Figure 2 It is the schematic diagram of the chemical thruster.

[0066] Figure 3It is a flowchart of a satellite attitude pointing adjustment method based on multi-body momentum moment transfer.

[0067] Figure 4 It is a layout design diagram of the satellite.

[0068] Figure 5 It is a geometric model diagram of the joint angle range under controllable attitude angles.

[0069] Figure 6 It is an attitude angle error diagram in the simulation example. Specific implementation manner

[0070] The following describes the specific implementation manner of the present invention to facilitate the understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific implementation manner. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0071] To facilitate the understanding of this solution, the following gives the definitions of some professional terms in the technical solution:

[0072] 1. The attitude of a satellite refers to the pointing of the satellite body coordinate system in the space reference system. To facilitate the description of the physical quantities of satellite motion and establish the corresponding satellite motion equations, multiple coordinate systems need to be established. Generally, the orbital coordinate system is used as the coordinate system for space reference, and the current attitude angle of the satellite is determined through the conversion relationship between the satellite body coordinate system and the orbital coordinate system.

[0073] 2. The coordinate origin O of the orbital coordinate system is set at the center of mass of the satellite. Among them, the OZ o axis points to the center of the earth, the OX o axis is perpendicular to the OZ o axis and they are both located in the orbital plane, pointing to the flight direction of the satellite. The coordinate axis direction of the OY o axis is established through the right-hand coordinate system rule.

[0074] 3. The coordinate origin O of the body coordinate system is set at the center of mass of the satellite. The three axes of the coordinate system coincide with the principal axes of inertia of the satellite. The rotation angle between the satellite body coordinate system and the orbital coordinate system is defined as the attitude angle of the satellite.

[0075] 4. A quaternion is a four-dimensional number, consisting of a real part and three imaginary parts, expressed as q = (q0, q1, q2, q3). It is used to represent rotational operations in three-dimensional space because it can avoid the gimbal lock problem and support efficient calculations. Quaternions are often used in robotics and spacecraft attitude control.

[0076] 5. The attitude angle is used to describe the rotation angle of an object relative to a fixed coordinate system in three-dimensional space, usually represented by Euler angles (Roll, Pitch, Yaw). The attitude angle can intuitively describe the rotation of an object around the x, y, and z axes and is widely used in attitude control in the fields of aviation, aerospace, and robotics.

[0077] 6. The desired attitude is the ideal attitude angle or direction in the control target of a system (such as a satellite or a robot). It is the reference angle or direction used by the control system to guide or adjust the current attitude so that the system reaches the target position. The desired attitude is usually achieved through a feedback control system.

[0078] 7. The angular momentum is a measure of the rotational motion of an object and is equal to the product of the moment of inertia of the object and its angular velocity. The angular momentum is conserved during rotation unless an external torque is applied to the object. The concept of angular momentum is used in physics and engineering to describe the inertial characteristics of rotating objects.

[0079] 8. A robotic arm is a mechanical device with multiple joints that can mimic the movement of a human arm. A robotic arm usually consists of multiple rigid rods and rotating or sliding joints and can be used for operations such as grasping, handling, and assembly. Robotic arms are widely used in industrial automation, medical, and aerospace fields.

[0080] 9. A robotic satellite: refers to a space robot system where the mass of the base is similar to the mass of the robotic arm. The robotic arm controls the attitude and position of the base by adjusting its own movement to achieve specific task objectives.

[0081] 10. A joint is the connection point between adjacent rigid rods in a robotic arm, allowing relative movement between the two parts. A joint can be a rotary joint (providing rotational movement) or a sliding joint (providing linear movement). A joint is the core component for the flexible movement of a robotic arm. Through the combination of multiple joints, a robotic arm can achieve complex spatial movements.

[0082] 11. The end effector is the farthest part of the robotic arm and is used to directly interact with objects or the environment.

[0083] 12. The satellite body is the main structural part of the satellite, containing the main control system, propulsion system, communication system, and other payloads. The satellite body is the core component for attitude control and structural support and usually works in conjunction with the attitude control system to achieve space missions.

[0084] 13. Euler angles: A set of angular parameters that describe the attitude of a rigid body in three-dimensional space, represented by three angles (Roll, Pitch, and Yaw). These angles describe how an object rotates from an initial reference coordinate system to the current attitude and are commonly used in aviation, aerospace, and robotics.

[0085] such as Figure 4As shown, in this solution, the satellite body is a cube structure, and three space manipulators are evenly and orthogonally distributed on the satellite body. The rotation axis of the end rod of each manipulator corresponds one by one to the three rotational degrees of freedom of the satellite body, and the end axis of each manipulator is parallel to the X, Y, and Z axes of the satellite respectively. After the satellite adopts the above structure, it can ensure the maximum decoupling between the manipulators, enabling each manipulator to independently control the adjustment of a certain attitude angle, and making the center of mass of the satellite close to the center of mass of the satellite body through symmetry, which is convenient for subsequent analysis.

[0086] Reference Figure 3 , Figure 3 shows a flowchart of a satellite attitude pointing adjustment method based on multi-body momentum moment transfer; as Figure 3 shown, this method S includes steps S1 to S8.

[0087] In step S1, according to the target attitude angle and the initial attitude angle of the satellite rotation, calculate the attitude error value e = φ target ―φ, where φ target is the target attitude angle, and φ is the initial attitude angle of the satellite rotation;

[0088] In step S2, based on the attitude error value, use PD feedback control to obtain the rotational angular acceleration of the end rod of the manipulator:

[0089]

[0090] where, is the rotational angular acceleration of the end rod of the manipulator; K p is the proportional gain; K d is the differential gain; e is the attitude error value; is the change rate of the attitude error value.

[0091] In step S3, substitute the rotational angular acceleration and angular velocity of the end rod of the manipulator and the rotational angular velocity of the satellite body into the satellite attitude dynamics equation based on momentum moment to solve for the rotational angular acceleration of the satellite body.

[0092] In implementation, the preferred expression of the satellite attitude dynamics equation based on momentum moment in this solution is:

[0093]

[0094] where, J is the moment of inertia of the satellite body; is the rotational angular acceleration of the satellite body; ω bi is the rotational angular velocity of the satellite body; J w is the moment of inertia of the end rod of the manipulator; ω w is the rotational angular velocity of the end rod of the manipulator; T envis the environmental torque; is the angular acceleration of the rotation of the end rod of the robotic arm.

[0095] In step S4, according to the angular accelerations of the rotation of the satellite body and the end rod of the robotic arm, the angular velocity of the rotation of the satellite body and the angular velocity and rotation angle of the end rod of the robotic arm are updated respectively.

[0096] When implemented, the preferred expressions for updating the angular velocity of the rotation of the satellite body and the angular velocity and rotation angle of the end rod of the robotic arm in this solution are:

[0097]

[0098]

[0099] φ w (t) = φ w (t - 1) + ω w Δt

[0100] where, ω bi (t) and ω bi (t - 1) are the angular velocities of the rotation of the satellite body at time t and time t - 1 respectively; ω w (t) and ω w (t - 1) are the angular velocities of the rotation of the end rod of the robotic arm at time t and time t - 1 respectively; φ w (t) and φ w (t - 1) are the rotation angles of the end rod of the robotic arm at time t and time t - 1 respectively; Δt is the discrete time step.

[0101] In step S5, it is judged whether the rotation angle satisfies the constraint condition of the movement range of the joint angle. If so, step S6 is entered; otherwise, the satellite attitude pointing adjustment method is terminated.

[0102] Next, in combination with Figure 5 the geometric model of the joint angle range under the controllable attitude angle shown, the acquisition method of the constraint condition of the movement range of the joint angle in this solution is described:

[0103] A1. Divide the robotic arm of the satellite into a first-level robotic arm and a second-level robotic arm. The first-level robotic arm is the robotic arm between the satellite body and the end rod of the robotic arm; the second-level robotic arm is the end rod of the robotic arm. Assume that the robotic arm includes 5 connecting rods, then the first-level robotic arm is the first connecting rod to the fourth connecting rod; if the robotic arm includes 6 connecting rods, then the first-level robotic arm is the first connecting rod to the fifth connecting rod.

[0104] A2. According to the geometric model of the satellite, calculate the coordinates of the centroid position of the satellite body:

[0105]

[0106]

[0107]

[0108] Among them, α is the rotation angle of the first-level robotic arm relative to the satellite; r is the length of the first-level robotic arm; L is the dimension length of the satellite body; η is the included angle between the pointing vector of the first-level robotic arm and the vector from the rotation axis to the centroid position; δ x , δ y is the uncertainty of the centroid position of the equivalent satellite body by two other robotic arms not in the same plane; (X0, Y0) is the centroid coordinate of the satellite body;

[0109] A3. Taking the joint rotation axis of the second-level robotic arm as the center and the distance from the joint rotation axis of the second-level robotic arm to the centroid of the second-level robotic arm as the radius to make a circle, and calculating the coordinates of the tangent points of the two rays passing through the centroid of the satellite body and the circle:

[0110]

[0111]

[0112]

[0113]

[0114] Among them, d is the distance from the joint rotation axis of the second-level robotic arm to the centroid of the second-level robotic arm; (X1, Y1), (X2, Y2) are the coordinates of the two tangent points with the circle respectively;

[0115] A4. According to the coordinates of the two tangent points with the circle, calculating the lower limit and the upper limit of the rotation angle of the end rod of the robotic arm:

[0116]

[0117] Among them, θ1 and θ2 are the lower limit and the upper limit of the rotation angle of the end rod of the robotic arm respectively;

[0118] A5. Using θ1 < φ w < θ2 as the constraint condition for the movement range of the joint angle.

[0119] In step S6, according to the angular velocity components of the satellite body's rotation angular velocity on the xyz axes, updating the real part and the imaginary part of the quaternion; based on the updated real part and imaginary part, calculating the three components of the attitude angle of the satellite rotation; step S6 further includes:

[0120] S61. According to the angular velocity components of the satellite body's rotation angular velocity on the xyz axes, calculating the change rates of the real part and the imaginary part of the quaternion:

[0121]

[0122] Among them, q0(t−1) is the real part of the quaternion at time t−1; q1(t−1), q2(t−1), and q3(t−1) are all the imaginary parts of the quaternion at time t−1; and are the change rates of the real part and the imaginary part of the quaternion at time t, respectively; ω x , ω y and ω z are the angular velocity components of ω bi on the xyz axes, respectively;

[0123] S62. Update the real number of the quaternion according to the change rates of the real part and the imaginary part of the quaternion:

[0124]

[0125] where k takes values of 0, 1, 2, and 3; when k = 0, q0(t) and q0(t−1) are the real parts at times t and t−1, respectively, is the change rate of the real part at time t; when k = 1, 2, and 3, q k (t) and q k (t−1) are the k-th imaginary parts at times t and t−1, respectively, is the change rate of the imaginary part at time t;

[0126] S63. Calculate the three components of the attitude angle of the satellite rotation according to the real part and the imaginary part of the quaternion at time t:

[0127]

[0128] θ(t) = arcsin(−2(q1(t)q3(t) − q0(t)q2(t)))

[0129]

[0130] where, θ(t) and ψ(t) are the three components of the attitude angle of the satellite rotation at time t, respectively; q1(t), q2(t), and q3(t) are the imaginary parts of the corresponding quaternions when k = 1, 2, and 3 at time t, respectively.

[0131] In step S7, calculate the attitude angle of the satellite rotation according to the three components, and calculate the attitude error value between the attitude angle of the satellite rotation and the target attitude angle;

[0132] In step S8, determine whether the attitude error value is less than the preset threshold. If so, perform attitude pointing adjustment according to the three components; otherwise, return to step S2.

[0133] The effect of the satellite attitude pointing adjustment method of this solution will be described below in combination with simulation:

[0134] Given that the target attitude angle is [0.1, 0.08, 0.13] rad, assuming that the rotation angle α of the first-stage robotic arms of the three space robotic arms of the satellite relative to the satellite is 120° each, the initial angles of the joint rotation angles (i.e., the initial attitude angles of the satellite rotation) are 81° each, the damping coefficient of the joint extreme values is 1000 N*m / deg, and the disturbances of the environmental torques are sinusoidal disturbances with amplitudes of 0.1 N.m, 0.13 N.m, and 0.08 N.m and frequencies of 2 Hz / s each. By restricting the joint angle range and controlling it, the attitude angle error diagram is obtained as shown in Figure 6 shown Figure 6 The nested diagram in it is the enlarged diagram of the attitude angle error from 14.5 s to 15 s, used to show how large the specific error accuracy is. It can be seen from the nested diagram that the maximum accuracy error is only less than 1x10e5.

[0135] In Figure 6 the three lines represent the error changes of the three attitude angles respectively. The curves phi, theta, and psi correspond to θ(t) and ψ(t). The abscissa is the time t (s), and the ordinate is the attitude angle error value (rad), reflecting that the three attitude angle errors of the satellite gradually tend to 0 with the control, which indicates the effectiveness of the control.

[0136] Combined with Figure 6 it can be found that the attitude of the satellite quickly reaches the ideal state, and can overcome the disturbance of the environmental torque. Finally, the stable accuracy can reach 1x10^-5, achieving zero-fuel high-precision rapid alignment.

Claims

1. A satellite attitude pointing adjustment method based on multi-body momentum moment transfer, characterized in that, Including the steps: S1. Calculate the attitude error value according to the target attitude angle and the initial attitude angle of the satellite rotation; S2. Based on the attitude error value, use PD feedback control to obtain the rotational angular acceleration of the end link of the manipulator; S3. Substitute the rotational angular acceleration and angular velocity of the end link of the manipulator and the rotational angular velocity of the satellite body into the attitude dynamics equation of the satellite based on angular momentum, and solve to obtain the rotational angular acceleration of the satellite body; S4. According to the rotational angular accelerations of the satellite body and the end link of the manipulator, update the rotational angular velocity of the satellite body, the rotational angular velocity and rotational angle of the end link of the manipulator respectively; S5. Judge whether the rotational angle meets the joint angle range constraint condition. If so, enter step S6; otherwise, terminate the satellite attitude pointing adjustment method; S6. Update the real part and imaginary part of the quaternion according to the angular velocity components of the rotational angular velocity of the satellite body on the x, y, and z axes; based on the updated real part and imaginary part, calculate the three components of the attitude angle of the satellite rotation; S7. Calculate the attitude angle of the satellite rotation according to the three components, and calculate the attitude error value between the attitude angle of the satellite rotation and the target attitude angle; S8. Judge whether the attitude error value is less than the preset threshold. If so, perform attitude pointing adjustment according to the three components; otherwise, return to step S2.

2. The satellite attitude pointing adjustment method according to claim 1, wherein The expression of the attitude dynamics equation of the satellite based on angular momentum is: Among them, J is the moment of inertia of the satellite body; is the angular acceleration of the satellite body's rotation; ω bi is the angular velocity of the satellite body's rotation; J w is the moment of inertia of the end rod of the robotic arm; ω w is the angular velocity of the end rod of the robotic arm; T env is the environmental torque; is the angular acceleration of the end rod of the robotic arm.

3. The satellite attitude pointing adjustment method according to claim 2, wherein, The expressions for updating the rotational angular velocity of the satellite body, the rotational angular velocity and rotational angle of the end link of the manipulator are: φ w (t) = φ w (t - 1) + ω w Δt where, ω bi (t) and ω bi (t−1) are the rotational angular velocities of the satellite body at time t and at time t - 1, respectively; ω w (t) and ω w (t−1) are the rotational angular velocities of the end link of the robotic arm at time t and at time t - 1, respectively; φ w (t) and φ w (t−1) are the rotation angles of the end link of the robotic arm at time t and at time t - 1, respectively; Δt is the discrete time step.

4. The satellite attitude pointing adjustment method according to claim 2, wherein Step S6 further includes: S61. Calculate the change rates of the real part and imaginary part of the quaternion according to the angular velocity components of the rotational angular velocity of the satellite body on the x, y, and z axes; where, \(q_0(t - 1)\) is the real part of the quaternion at time \(t - 1\); \(q_1(t - 1)\), \(q_2(t - 1)\), and \(q_3(t - 1)\) are all the imaginary parts of the quaternion at time \(t - 1\); and are the rates of change of the real and imaginary parts of the quaternion at time \(t\), respectively; \(\omega\) x 、\(\omega\) y and \(\omega\) z are the angular velocity components of \(\omega\) bi on the \(x\), \(y\), and \(z\) axes, respectively. S62. Update the real number of the quaternion according to the change rates of the real part and imaginary part of the quaternion; Among them, the value of k is 0, 1, 2, and 3; when k = 0, q0(t) and q0(t−1) are the real parts at times t and t - 1 respectively, is the change rate of the real part at time t; when k = 1, 2, and 3, q k (t) and q k (t−1) are the k-th imaginary parts at times t and t - 1 respectively, is the change rate of the imaginary part at time t; S63. Calculate the three components of the attitude angle of the satellite rotation according to the real part and imaginary part of the quaternion at time t: θ(t)=arcsin(―2(q1(t)q3(t)―q0(t)q2(t))) wherein, θ(t) and ψ(t) are respectively the three components of the attitude angle of the satellite rotation at time t; q1(t), q2(t) and q3(t) are respectively the imaginary parts of the corresponding quaternions when k = 1, 2 and 3 at time t.

5. The satellite attitude pointing adjustment method according to claim 1, characterized in that, The method for obtaining the joint angle range constraint condition includes: A1. Divide the manipulator of the satellite into a first-level manipulator and a second-level manipulator. The first-level manipulator is the manipulator between the satellite body and the end link of the manipulator; the second-level manipulator is the end link of the manipulator; A2. According to the geometric model of the satellite, calculate the coordinates of the centroid position of the satellite body; Where, α is the rotation angle of the first-level robotic arm relative to the satellite; r is the length of the first-level robotic arm; L is the dimension length of the satellite body; η is the angle between the pointing vector of the first-level robotic arm and the vector from the rotation axis to the centroid position; δ x , δ y is the uncertainty of the centroid position of the equivalent satellite body caused by two other robotic arms not in the same plane; (X0, Y0) are the centroid coordinates of the satellite body; A3. With the joint rotation axis of the second-level manipulator as the center and the distance from the joint rotation axis of the second-level manipulator to the centroid of the second-level manipulator as the radius, draw a circle, and calculate the coordinates of the tangent points of the two rays passing through the centroid of the satellite body and the circle; where d is the distance from the joint rotation axis of the second-level manipulator to the centroid of the second-level manipulator; (X1, Y1), (X2, Y2) are the coordinates of the two tangent points to the circle respectively; A4. According to the coordinates of the two tangent points to the circle, calculate the lower limit and upper limit of the rotation angle of the end link of the manipulator: where θ1 and θ2 are the lower limit and upper limit of the rotation angle of the end link of the manipulator respectively; A5. Adopt θ1 < φ w <θ2 as the constraint condition for the range of motion of the joint angle, φ w is the rotation angle of the end link of the robotic arm.

6. The satellite attitude pointing adjustment method according to claim 1, characterized in that, The expression for obtaining the rotational angular acceleration of the end link of the manipulator by using PD feedback control is: Among them, is the angular acceleration of the rotation of the end rod of the robotic arm; K p is the proportional gain; K d is the derivative gain; e is the attitude error value; is the change rate of the attitude error value.

7. The satellite attitude pointing adjustment method according to any one of claims 1-6, characterized in that The satellite body is of a cubic structure, and three space manipulators are evenly and orthogonally distributed on the satellite body. The rotation axes of the end rods of each manipulator correspond one by one to the three rotational degrees of freedom of the satellite body, and the end axes of each manipulator are parallel to the X, Y, and Z axes of the satellite respectively.

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